Heat Transfer in Cavities: Configurative Systematic Review

Abstract

This study is a systematic review of research on heat transfer analysis in cavities and aims to provide a comprehensive understanding of flow and heat transfer performance in various kinds of cavities with or without the presence of fins, obstacles, cylinders, and baffles. The study also examines the effects of different forces, such as magnetic force, buoyancy force, and thermophoresis effect on heat transfer in cavities. This study also focuses on different types of fluids, such as air, water, nanofluids, and hybrid nanofluids in cavities. Moreover, this review deals with aspects of flow and heat transfer phenomena for only single-phase flows. It discusses various validation techniques used in numerical studies and the different types and sizes of mesh used by researchers. The study is a comprehensive review of 297 research articles, mostly published since 2000, and covers the current progress in the area of heat transfer analysis in cavities. The literature review in this study shows that cavities with obstacles such as fins and rotating cylinders have a significant impact on enhancing heat transfer. Additionally, it is found that the use of nanofluids and hybrid nanofluids has a greater effect on enhancing heat transfer. Lastly, the study suggests future research directions in the field of heat transfer in cavities. This study’s findings have significant implications for a range of areas, including electronic cooling, energy storage systems, solar thermal technologies, and nuclear reactor systems.

1. Introduction

The study highlights that enclosed cavities have a broad area of uses, such as electronic cooling, energy storage systems, solar thermal technologies, and nuclear reactor systems. The study has considered various shapes of cavities, including square, rectangular, triangular, trapezoidal, semicircular, hexagonal, U-shaped, etc. Different types of boundary conditions are applied to the walls of the cavities, which affect the flow and thermal behavior inside the cavities. The study considers temperature, heat flux, adiabatic, and isothermal as thermal boundary conditions, such as. On the other hand, the hydraulic boundary conditions considered are fixed, moving, and elastic. Some authors have also applied magnetic field strength to enhance heat transfer or alter buoyancy effects. Different types of fluids have been used in the cavity, including pure water, air, nanofluids, phase change material, porous media, and non-Newtonian fluid.

The main mechanisms of heat transfer in enclosed cavities are natural, forced, or mixed convection. The driving force for natural convection is mainly the buoyancy force (according to Boussinesq approximation), which is caused by the change in fluid density resulting from the applied temperature difference [1,2]. Research has shown that the buoyancy force can destabilize the flow inside the enclosure, but the application of a magnetic field can stabilize it [3]. In addition, the addition of nanoparticles to the liquid inside the cavity can improve its thermal conductivity, heat capacity, and density [4]. Alqaed et al. [5] studied the use of Al₂O₃/H₂O nanofluid with an applied magnetic field. They proved that the presence of nanoparticles contributed to the fluid properties and improved heat transfer. The magnetic field also imposed a specific force (Lorentz force), which opposes the flow inside the cavity and reduces the heat transfer rate. Hatami [6] demonstrated that the presence of fins inside the cavity leads to an increase in vortices (increased mixing) which in turn leads to an enhancement of the rate of heat transfer. The interplay between the magnetic and buoyancy of a hybrid nanofluid Cu-Al₂O₃ inside a cavity leads to a decrease in flow velocity and reduced heat transfer rate [7]. Similar trends in the effect of nanofluid have been observed in different-shaped enclosures such as hexagonal [8], U-shaped [9], and trapezoidal cavities [10].

The moving boundary imposes a shear force on the fluid surface, which can lead to the generation of recirculating eddies that closes the wall of the cavity. The direction of the moving boundary can affect the strength of the shear force and the characteristics of the eddies that are formed. Additionally, for low values of Prandtl numbers, the effects of the moving boundary on the flow can be more pronounced [11]. Adding nanoparticles to a fluid can have a similar effect to that of fixed boundaries in that the fluid’s thermal conductivity enhances, and the rate of heat transfer rises. That’s because nanoparticles can enhance a fluid’s thermal conductivity and improve the rate of heat transfer. Additionally, if the fluid has been subjected to a magnetic field, the presence of the nanoparticles can lead to the generation of Lorentz force that acts in the vertical direction of the magnetic field. This force can suppress circulation and reduce the heat transfer rate. This effect is observed when the nanoparticles are magnetic nanoparticles and the intensity of the magnetic field is raised [12].

The main objective of this work is to conduct a comprehensive literature review of the hydraulic and thermal behaviors inside a cavity. The focus will be on studying the effects of different shapes of the cavity, various applied boundary conditions, and different types of working fluids. The study will compare the effects of using various types of fluids such as air, water, nanofluids, non-Newtonian fluid, etc. The study will also aim to predict correlations for the Nusselt number for different ranges of Rayleigh and Reynolds numbers at different imposed boundary conditions.

The primary conclusion of this literature review is that not many studies have been conducted on phase change materials (PCMs) in cavities, and it is not the focus of our review. Additionally, few studies have considered the use of LES and DNS models to model turbulent flow in cavities. It is also suggested that optimization should be conducted to predict the optimum shape of the cavity. Finally, more studies are needed to investigate the behavior of cavities filled with different types of fluids, such as two immiscible fluids, which can include the interaction between two different regions inside the same enclosure, such as the development of a couple of thermal boundary layer with different fluids separated by different types of partition.

Aim of the Study

A configurative systematic review process is adopted for this study to review the following:

• Model geometry, flow domain, type, CFD modeling, parameters, and meshing.
• Different types of validations are used by researchers.
• Heat transfer behavior for different flow conditions, geometries, boundary conditions, and the presence of different obstacles inside cavities.

2. Methodology

The present review employs a configurative systematic review approach to report on the heat transfer analysis inside different shapes of cavities. A flow chart of the process is provided in Figure 1. The study used various databases such as ScienceDirect, SAGE, ResearchGate, Google Scholar, and Web of Science to conduct the literature search. The search was conducted using key terms such as “Heat transfer”, “Rectangular cavity”, “Square cavity”, “Trapezoidal cavity”, “Triangular cavity”, “Hexagonal cavity”, “Octagonal cavity”, “T-shaped cavity”, “U-shaped cavity”, “C-shaped cavity”, “V-shaped cavity”, “H-shaped cavity”, “Arc-shaped cavity”, “L-shaped cavity”, “M-shaped cavity”, and “Cavity or enclosure”. The article-searching process began on 1 March 2022 and ended on 30 November 2022. One restriction was imposed during the search process, which was that the articles must be written in English.

In addition to the language restriction, the review also excluded articles that were published in ArXiv and Preprints, including conference and review articles. Book chapters, editorials, duplicate articles, articles with no data on heat transfer, articles with no full text available, and other irrelevant articles were also excluded. The authors also reviewed all the references that are connected to their research. Eligible articles were selected by two authors (G.S. & A.A.) who worked independently, screened all the articles, checked the title and abstract as well as assessed the full text. If there was any disagreement regarding the selection, a third author (S.C.S.) discussed the issues that occurred between the first two authors and then resolved the problem. Two authors (G.S. & A.A.) collected some information from the appropriate studies: author’s last name, published year, CFD tools, flow domain or shape of the domain, dimension of the study, algorithms used to solve the problem, parameters and their ranges, type of flow, name of nanofluids or hybrid nanofluids, nanofluids thermo-physical properties, validation data, and results on heat transfer analysis. A total of 2732 articles were considered, 1257 articles were removed because of duplication, 905 articles were removed for other exclusion criteria, and 570 articles were considered which were related to heat transfer analysis inside cavities. After careful screening of the title and abstract, a total of 315 articles were considered for screening of the full text. Finally, 297 articles were selected for the present review study.

The word cloud map in Figure 2 shows the most frequently used words in the abstracts of the selected articles. It appears that the main topics of these articles are natural convection and mixed convection, steady flow, and heat transfer. These articles also focus on numerical experiments, using air and nanofluids as working fluids and utilizing FVM and FEM as numerical methods. The average rate of heat transfer is often presented as a function of the Nusselt number in relation to the Richardson number and Rayleigh number.

Figure 3 shows that square cavities are the most studied among the different types of cavities, accounting for 47.5% of the total number of articles. The second most studied are triangular cavities, with 14.1% of the articles. Rectangular cavities (12.5%), trapezoidal cavities (7.4%), and cubical cavities (6.1%) are also studied in a significant number of articles. The other types of cavities are studied at much lower percentages, with T-shaped (0.7%) and U-shaped (1%) cavities being the least studied. 2.5% of articles deal with other types of cavities. Square cavities have a wide range of practical applications in various fields, such as aerospace, mechanical engineering, energy, and electronics. They have many advantages, for example, in heat transfer, fluid flow, and electromagnetic waves, and therefore are widely used in many engineering systems and devices. The high percentage of research articles focused on square cavities suggests that they are an important area of study in the field.

3. Physical Domain and Mathematical Modelling

3.1. Physical Domain

Many researchers have published a large number of articles over the years to study the hydraulic and thermal performances inside enclosures with various shapes such as square, rectangular, triangular, hexagonal, octagonal, trapezoidal, T-shaped, U-shaped, L-shaped, M-shaped, V-shaped, H-shaped, I-shaped, C-shaped, arc-shaped, and other modified geometries. These studies often introduce obstacles such as fins, cylinders, blocks, rotating blades, etc., inside these physical domains to further complicate the flow patterns and potentially enhance or degrade heat transfer rates Table 1 provides more information about this research.

3.2. Governing Equations

The Navier-Stokes equations describe the motion of a fluid and are widely used in engineering and physics to model different fluid flow phenomena. The equations consist of three main components: the continuity equation, which describes the conservation of mass, the momentum equation, which describes the forces that were applied to the fluid; and the energy equation, which describes the transfer of thermal energy. These equations can be applied to a wide range of fluid types and flow conditions, including incompressible, steady and unsteady flows, Newtonian and non-Newtonian fluids, laminar and turbulent flows, and fluids with different physical properties, such as air, water, and nanofluids. The geometry of the system can also be two or three-dimensional. Solving the Navier-Stokes equations is a challenging task and requires advanced mathematical techniques. In addition to the commonly studied body forces such as gravity and electromagnetic forces, other types of body forces can also play a role in various physical systems. These can include buoyancy forces, Brownian motion of particles, thermophoresis effect, heat generation or absorption, radiation, and the porous medium effect described by the Forchheimer-Brinkman model. These forces can have significant effects on the behavior of the system and must be taken into account when studying and modeling the system. Considering all the assumptions, the three-dimensional Navier-Stokes equation can be presented in the dimensional form (Versteeg [13]):

Continuity equation:

$$\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z}=0$$

(1)

$u$-momentum equation:

$$\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}+w\frac{\partial u}{\partial z}=-\frac{1}{\rho }\frac{\partial p}{\partial x}+\frac{\mu }{\rho }\left(\frac{{\partial }^{2}u}{\partial x^2}+\frac{{\partial }^{2}u}{\partial y^2}+\frac{{\partial }^{2}u}{\partial z^2}\right)+\mathrm{other} \mathrm{terms}$$

(2)

$v$-momentum equation:

$$\frac{\partial v}{\partial t}+u\frac{\partial v}{\partial x}+v\frac{\partial v}{\partial y}+w\frac{\partial v}{\partial z}=-\frac{1}{\rho }\frac{\partial p}{\partial y}+\frac{\mu }{\rho }\left(\frac{{\partial }^{2}v}{\partial x^2}+\frac{{\partial }^{2}v}{\partial y^2}+\frac{{\partial }^{2}v}{\partial z^2}\right)+g\beta \left(T-T_c\right) \sin \alpha +\mathrm{other} \mathrm{terms}$$

(3)

$w$-momentum equation:

$$\begin{array}{cc}\frac{\partial w}{\partial t}+u\frac{\partial w}{\partial x}+& v\frac{\partial w}{\partial y}+w\frac{\partial w}{\partial z}\hfill \\ & =-\frac{1}{\rho }\frac{\partial p}{\partial z}+\frac{\mu }{\rho }\left(\frac{{\partial }^{2}w}{\partial x^2}+\frac{{\partial }^{2}w}{\partial y^2}+\frac{{\partial }^{2}w}{\partial z^2}\right)+g\beta \left(T-T_c\right) \cos \alpha +\mathrm{other} \mathrm{terms}\end{array}$$

(4)

Energy equation:

$$\frac{\partial T}{\partial t}+u\frac{\partial T}{\partial x}+v\frac{\partial T}{\partial y}+w\frac{\partial T}{\partial z}=\frac{\kappa }{\rho C_p}\left(\frac{{\partial }^{2}T}{\partial x^2}+\frac{{\partial }^{2}T}{\partial y^2}+\frac{{\partial }^{2}T}{\partial z^2}\right)+\frac{Q}{\rho C_p}\left(T-T_c\right)+\mathrm{other} \mathrm{terms}$$

(5)

Here, $u, v, w$ are the velocities, $p$ is the pressure, and t is the time. $x, y, z$ are the Cartesian coordinate systems, $T$ is the temperature, $\rho$ is density, $\mu$ is dynamic viscosity, $g$ is gravitational acceleration, $\alpha$ is the angle, and $\beta$ is the thermal expansion coefficient respectively.

Complex geometries are often encountered in physical systems, and numerical methods are often used to solve the system of equations that govern these systems. Some common numerical techniques used include the finite difference method, finite volume method, finite element method, lattice Boltzmann method, wavelet-based methods such as Coiflet wavelet-homotopy method, fourth-order compact formulation, dual reciprocity boundary element method, spectral element method, large eddy simulation, direct numerical simulation, radial basis function-based partition of unity method, and Improved element-free Galerkin–reduced integration penalty method. These methods can be used to solve a wide range of problems and have been applied in various fields, such as fluid dynamics, heat transfer, and solid mechanics. The problem of heat transfer analysis inside cavities can also be solved using commercial and open-source computational fluid dynamics (CFD) codes or software. Some examples of commonly used commercial CFD codes include COMSOL Multiphysics, ANSYS Fluent, and ADINA Multiphysics. There are also open-source options, such as FlexPDE and OpenFOAM that can be used to solve such problems. These codes and software can be used to perform a wide range of simulations, including heat transfer, fluid flow, and solid mechanics. They are widely used in various fields such as aerospace, automotive, and mechanical engineering and often include a range of features and capabilities such as pre-processing, solving, and post-processing.

3.3. Meshing

In order to solve the system of equations that govern a physical system, the physical domain must be discretized into a smaller number of elements or cells. This process is known as meshing. The Navier-Stokes equations are then solved on these elements or cells to determine the complex flow and thermal field nature. The accuracy of the results largely relies on the number of cells used in the mesh, and smaller cells are preferred to obtain higher accuracy. However, there is a trade-off between the accuracy and computational resources required. It is necessary to find a balance between the computational time and cost and the desired accuracy of the solution.

Researchers have used a variety of meshing techniques to discretize the physical domain and solve the Navier-Stokes equations. These include uniform or non-uniform meshing with rectangular or orthogonal grids, tetrahedral meshing, and non-uniform meshing with triangular grids or clustered grids. The choice of meshing technique depends on the complexity of the geometry, the level of accuracy required, and the computational resources available. It is observed that many researchers have used structured meshes as opposed to unstructured meshes. This is because structured meshes are typically less computationally expensive and require less time for simulation. Additionally, most of the researchers carry out grid-independent tests (GIT) to ensure that the solution does not depend on the grid size. GIT is a vital part of numerical simulations, and it is important that researchers present a clear and detailed discussion of GIT. However, it is also seen that some researchers did not present a clear and detailed discussion on GIT.

A lack of comparison between the performance of uniform meshes and dense non-uniform or fine meshes on flow and temperature fields is often missing in the literature. This can make it difficult for readers to understand the effects of mesh resolution on the solution and the accuracy of the simulation. Comparing the results of simulations using different meshes is an important part of any numerical study, and it is known as a mesh independence study. This is particularly important for complex flow features and can help readers to understand or revisit the study. By comparing the performance of uniform meshes and dense non-uniform or fine meshes, one can determine the optimal mesh resolution for a specific problem and also identify the errors and uncertainties associated with the simulation. Therefore, a clear presentation of the mesh independence study is important for future readers to understand the study and to replicate the simulations.

Table 1. (a): Research performed from 1989 to 2013. (b) The research was performed from 2014 to 2019. (c): Research performed from 2020 to 2023.

(a)
Ref.	CFD Methods and Algorithms	Flow Domain	Dimension, Type of Flow	Parameters and Ranges	Meshing
Wee et al. [2]	Experimental, FDM, DADI	Rectangular cavity	2D, unsteady, laminar	2 $\times$ 105 ≤ GrT ≤ 2 $\times$ 106, 10 ≤ GrC ≤ 2 $\times$ 105, 2 $\times$ 104 ≤ Ra ≤ 1.47 $\times$ 106	-
Moallemi & Jjang [11]	FVM, SIMPLIER	Lid-driven square cavity	2D, steady, laminar, non-Newtonian	102 ≤ Re ≤ 2200, 0.01 ≤ Pr ≤ 50, 0.01 ≤ Ri ≤ 10	Non-uniform grid, 42 $\times$ 42
Sasaguchi et al. [14]	Grid generation	Rectangular cavity with cylinders	2D, unsteady, laminar	N/A	Uniform mesh, 31 $\times$ 101, 31 $\times$ 121
Al-Amiri et al. [15]	FEM	Lid-driven cavity with wavy wall	2D, steady, laminar, mixed convection	Pr = 0.71, 1, Gr = 104, 0.1 ≤ Ri ≤ 10, 0 ≤ Am ≤ 0.075, 0 ≤ $\lambda$ ≤ 3, Re = 500	-
Saha et al. [16]	FEM	Inclined rectangular enclosure	2D, natural convection, steady, laminar	Pr = 0.71, 103 ≤ Gr ≤ 106, 0.5 ≤ A ≤ 1.0, 0 ≤ $\varphi$ ≤ 30	Non-uniform, six nodded 6394 elements
Saha et al. [17]	FVM	Triangular cavity	2D, natural convection	Pr = 0.71, Gr = 1.33 $\times$ 106, 0.5 ≤ A ≤ 1.0	360 $\times$ 90, 720 $\times$ 160, 270 $\times$ 90 for A = 0.2, 0.5, 1.0
Tiwari & Das [18]	FVM, SIMPLE, QUICK, TDMA	Double lid-driven square cavity	2D, unsteady	Pr = 6.2, 0.1 ≤ Ri ≤ 10, 103 ≤ Ra ≤ 106, 0 ≤ $\chi$ ≤ 0.2, Cu-water nanofluid	Uniform grid, 61 $\times$ 61
Saha et al. [19]	FEM	Inclined sinusoidal enclosure	2D, steady, natural convection, laminar	Pr = 0.71, 103 ≤ Gr ≤ 106, 0 ≤ $\varphi$ ≤ 45	Non-uniform grid, 5240 elements
Varol et al. [20]	FDM	Triangular cavity	2D, natural convection	0.25 ≤ A ≤ 1.0, 102 ≤ Ra ≤ 103	Uniform grid, 61 $\times$ 61
Chen & Cheng [21]	FVM, SOR	Lid-driven triangular cavity	2D, mixed convection, unsteady, laminar	Pr = 0.71, Re = 100, Gr = 5 $\times$ 105	41 $\times$ 41
Noor et al. [22]	FDM, QUICK, RK-4, SOLA	Double lid-driven square cavity	2D, unsteady, laminar	Pr = 0.71, 10 ≤ Re ≤ 103, 1 ≤ $\varpi$ ≤ 5	Clustered grid, 125 $\times$ 125
Ouertatani et al. [23]	FVM, QUICK. CDS, RBSOR	Double lid-driven cubic cavity	3D, mixed convection, unsteady, laminar	Pr = 0.71, 102 ≤ Re ≤ 103, 10−3 $\le$ Ri ≤ 10	64 $\times$ 64 $\times$ 64
Basak et al. [24]	FEM	Triangular porous cavities	2D, natural convection, steady	10−5 ≤ Da ≤ 10−1, 0.015 ≤ Pr ≤ 103, 103 ≤ Ra ≤ 5105	20 $\times$ 20–28 $\times$ 28 bi-quadratic elements
Lei & O’Neill [25]	FVM, SIMPLE, CDS, SUR	Square cavity with different corners	2D, unsteady, natural convection	Pr = 6.62, 0 ≤ Ra ≤ 108	16,000 cells
Saha [26]	FEM	Sinusoidal corrugated enclosure	2D, steady	Pr = 0.71, 103 ≤ Gr ≤ 106, 0 ≤ Ha ≤ 102	Non-uniform grid, 4928 elements
Saha et al. [27]	FEM	Octagonal enclosure	2D, natural convection, steady, laminar	Pr = 0.71, 7, 20, 50, 103 ≤ Ra ≤ 106	Non-uniform, 10,466 elements
Saha et al. [28]	FVM, QUICK, SIMPLE	Triangular enclosure	2D, natural convection, unsteady	Pr = 0.72, 104 ≤ Ra ≤ 7.2 $\times$ 106, A = 0.2, 0.5, 1.0	270 $\times$ 90, 320 $\times$ 80, 360 $\times$ 90 for A = 1, 0.5 & 0.2
Saha et al. [29]	FVM, QUICK, SIMPLE	Triangular enclosure	2D, natural convection, unsteady	Pr = 0.72, 7.2 $\times$ 103 ≤ Ra ≤ 1.5 $\times$ 106, A = 0.2, 0.5, 1.0	270 $\times$ 90, 320 $\times$ 80, 360 $\times$ 90 for A = 1, 0.5 & 0.2
Saha et al. [30]	FVM, QUICK, SIMPLE	Triangular enclosure	2D, natural convection, unsteady	Pr = 0.72, 5 ≤ Ra ≤ 1.5 $\times$ 107, A = 0.2, 0.5, 1.0	360 $\times$ 120, 320 $\times$ 90, 360 $\times$ 90 for A = 1, 0.5 & 0.2
Sivasankaran et al. [31]	FVM, UDS, CDS, SOR	Lid-driven square cavity	2D, unsteady, laminar, mixed convection	Pr = 0.71, 0 ≤ Am ≤ 1, 0 ≤ $\varphi$ ≤ $\pi$, 0.1 ≤ Ri ≤ 102, 102 ≤ Re ≤ 103	Uniform grid, 81 $\times$ 81
Sivakumar et al. [32]	FVM, SIMPLE, QUICK. CDS	Lid-driven square cavity	2D, mixed convection, unsteady, laminar	Pr = 0.71, 102 ≤ Re ≤ 103, 102 ≤ Gr ≤ 106, 10−2 ≤ Ri ≤ 102	Uniform grid, 81 $\times$ 81
Al-Amiri & Khanafer [33]	ADINA, FSI, FEM, ALE	Lid-driven square cavity	2D, steady, laminar	Pr = 0.71, 102 ≤ Re, Gr ≤ 103	Non-uniform mesh, 120 $\times$ 120
Cheng [34]	Compact formulation, SOR, ADI	Lid-driven square cavity	2D, mixed convection	10 ≤ Re ≤ 2200, 100 ≤ Gr ≤ 4.86 $\times$ 106, 10−2 ≤ Pr ≤ 50, 10−2 ≤ Ri ≤ 102	256 $\times$ 256
Nasrin & Parvin [35]	FEM, TFM	Lid-driven square cavity with wavy wall	2D, laminar, steady, mixed convection	30 ≤ Re ≤ 300, 0 ≤ Ha ≤ 50, Pr = 0.71, Ra = 104	Non-uniform, 37,123 nodes, 5604 elements
Saha [36]	FVM, QUICK	Triangular cavity	2D, unsteady, natural convection	0.2 ≤ A ≤ 1.0, 5 ≤ Pr ≤ 100, Ra = 107	-
Saha [37]	FVM, SIMPLE, QUICK	Triangular cavity	2D, unsteady, natural convection	0.2 ≤ A ≤ 1.0, 5 ≤ Pr ≤ 100, 5 $\times$ 106 ≤ Ra ≤ 108	-
Yu et al. [38]	Fluent, FVM, QUICK, SIMPLE	Square cavity	2D, unsteady, natural convection	104 ≤ Ra ≤ 106, 0 ≤ $\chi$ ≤ 0.04, CuO–H2O nanofluid	100 $\times$ 100
Al-Farhany & Turan [39]	FVM, SIMPLER	Inclined rectangular porous cavity	2D, unsteady, natural convection	0 ≤ ϕ ≤ 85, 0.1 ≤ Le ≤ 10, −5 ≤ N ≤ 5, Pr = 4.5, Ra = 5 × 106	-
Arani et al. [40]	FVM, SIMPLIER, TDMA, CDS, UDS	Lid-driven square cavity	2D, mixed convection, laminar, steady	10−3 ≤ Ri ≤ 10, 0 ≤ $\chi$ ≤ 0.1, Gr = 102, Re = 102 Cu–H2O nanofluid	Uniform grid. 80 $\times$ 80
Basak et al. [41]	FEM	Porous triangular cavities	2D, natural convection, steady	Pr = 0.025, 1000, 10−5 ≤ Da ≤ 10−3, Ra = 5 $\times$ 105	28 $\times$ 28 bi-quadratic elements
Chamkha & Abu-Nada [42]	FVM, CDS, UDS, SOR, SUR	Double lid-driven square cavity	2D, mixed convection, steady, laminar	0.001 ≤ Ri ≤ 10, 0 ≤ $\chi$ ≤ 0.1, H2O-Al2O3 nanofluid	Uniform grid, 81 $\times$ 81
Nasrin & Parvin [43]	FEM	Trapezoidal cavity	2D, free convection, steady, laminar	Ra = 105, $\chi$ = 0.05, 0.65 ≤ A ≤ 2, 1.47 ≤ Pr ≤ 8.81, Cu–H2O nanofluid	40,295 nodes, 10,936 elements
Raji et al. [44]	FVM, SIMPLIER	Square cavity with blocks	2D, natural convection, laminar, steady	103 ≤ Ra ≤ 108, Pr = 0.71	254 $\times$ 254
Saha & Gu [45]	FVM	Triangular enclosure	2D, natural convection, unsteady	Pr = 0.7, Ra = 105, A = 0.5	Triangular grid, 8143 nodes
Saha & Gu [46]	FVM	Triangular enclosure	2D, natural convection, unsteady	Pr = 0.72, 5.0 $\times$ 104 ≤ Ra ≤ 106, A = 0.5	-
Teamah & El-Maghlany [47]	FVM, CDS, GS, TDMA	Square cavity	2D, steady, laminar	103 ≤ Ra ≤ 107, 0 ≤ Ha ≤ 60, 0 ≤ $\chi$ ≤ 0.06, −10 ≤ q ≤ 10, Pr = 6.2, H2O based Al2O, Cu, TiO2 nanofluids	60 $\times$ 60
Ahmed et al. [48]	Collocated FVM, UDS, CDS, TDMA	Inclined lid-driven square cavity	2D, mixed convection, laminar, steady	10−2 ≤ Ri ≤ 102, 0 ≤ $Am$ ≤ 1.0, 0 ≤ Ha ≤ 100, 0 ≤ $\phi$ ≤ 90	Uniform grid. 81 $\times$ 81
Bhardwaj & Dalal [49]	FDM, QUICK, SOR, CDS	Porous triangular cavity	2D, natural convection, laminar	103 ≤ Ra ≤ 106, 10−4 ≤ Da ≤ 10−2, Am = 0.05	Orthogonal mesh, 41 $\times$ 41
Cho et al. [50]	FVM, SIMPLEC, TDMA	Lid-driven cavity with wavy surfaces	2D, mixed convection, laminar, steady	0 ≤ $\chi$ ≤ 0.1, 10−2 ≤ Ri ≤ 103, 101 ≤ Gr ≤ 104, 0 ≤ $Am$ ≤ 0.2, Pr = 6.2, H2O based Cu, Al2O3, TiO2 nanofluids	101 $\times$ 201
Elsherbiny & Ragab [51]	-	Inclined rectangular cavities	2D, laminar, natural convection	102 ≤ Ra ≤ 106, 0.5 ≤ A ≤ 5, 0 ≤ $\phi$ ≤ 180	Uniform mesh, 42 $\times$ 42
Huelsz & Rechtman [52]	LBM	Inclined square cavity	2D, natural convection, laminar, unsteady	Pr = 0.71, −180 ≤ $\phi$ ≤ 180, 103 ≤ Ra ≤ 106	103 $\times$ 103
Khanafer & Aithal [53]	ADINA, FEM, NR	Lid-driven square cavity with cylinder	2D, steady, laminar, mixed convection	Pr = 0.7, 104 ≤ Gr ≤ 106, 0.01 ≤ Ri ≤ 10, Re = 102	Non-uniform grid, 19,520 nodes
Ramakrishna et al. [54]	FEM	Trapezoidal cavities	2D, free convection, laminar	30 ≤ $\phi$ ≤ 90, Pr = 0.015, 7.2, 103 ≤ Ra ≤ 105	28 $\times$ 28 bi-quadratic elements
Sivasankaran et al. [55]	FVM, UDS, CDS	Inclined lid-driven square cavity	2D, unsteady, laminar, mixed convection	Pr = 0.71, 0.01 ≤ Ri ≤ 102, 0 ≤ $\phi$ ≤ 90	81 $\times$ 81
(b)
Ref.	CFD Methods and Algorithms	Flow Domain	Dimension, Type of Flow	Parameters and Ranges	Meshing
Sathitamoorthy & Chamkha [56]	FEM	Square cavity with thin partition	2D, natural convection, steady	Pr = 0.7, 100, 103 ≤ Rah ≤ 105	20 $\times$ 20 elements, 41 $\times$ 41 grid points
Abu-Nada & Chamkha [57]	FVM, SOR, SUR, UDS	Lid-driven square cavity with wavy wall	2D, mixed convection, laminar, steady	Pr = 6.57, 0.01 ≤ Ri ≤ 102, 0 ≤ $\chi$ ≤ 0.09, H2O-CuO nanofluid	Uniform grid, 81 $\times$ 81
Ait-Taleb et al. [58]	FDM, SIMPLE, TDMA	Rectangular cavities with tiles	2D, steady, laminar	8.7 $\times$ 103 ≤ Rah ≤ 1.8 $\times$ 105, 4.1 $\times$ 105 ≤ RaH ≤ 1.23 $\times$ 107, Pr = 0.71	Non-uniform mesh, 80 $\times$ 40
Cheng & Liu [59]	Ansys Fluent, FVM, SOR, ADI	Lid-driven square and rectangular cavities	2D, unsteady	Pr = 0.71, 10−2 ≤ Ri ≤ 102, 0.2 ≤ A ≤ 5, 0 ≤ $\phi$ ≤ 90, Re = 102	Uniform grid, 640 $\times$ 128, 128 $\times$ 128, 128 $\times$ 640
Cho [60]	FVM, SIMPLE, TDMA	Square cavity with wavy wall	2D, natural convection, laminar, steady	103 ≤ Ra ≤ 106, 0 ≤ $\chi$ ≤ 0.04, Pr = 6.2, H2O-Al2O3 nanofluid	101 $\times$ 201
Kalteh et al. [61]	FDM, CDS, SUR	Lid-driven square cavity with block	2D, steady, mixed convection	Gr = 102, 0.000625 ≤ Ri ≤ 4, 0 ≤ $\chi$ ≤ 0.05, H2O based Al2O3, TiO2, Ag, CuO nanofluids	Regular grid, 80 $\times$ 80
Khanafer [62]	ADINA, FEM, FSI, ALE	Lid-driven square cavity	2D, steady, laminar, mixed convection	Pr = 0.7, 102 ≤ Gr ≤ 104, 10−4 ≤ Ri ≤ 1.0, 102 ≤ Re ≤ 103	Non-uniform, 120 $\times$ 120
Muthtamilselvan & Doh [63]	FVM, SIMPLE, QUICK, TDMA	Lid-driven square cavity	2D, steady, mixed convection	0 ≤ Rai ≤ 105, Pr = 6.2, 10−2 ≤ Ri ≤ 10, 0 ≤ $\chi$ ≤ 0.06, Cu-H2O nanofluid	Uniform grid, 41 $\times$ 41
Ramakrishna et al. [64]	FEM	Porous trapezoidal cavity	2D, natural convection, laminar, steady	10−5 ≤ Da ≤ 10−3, 30 ≤ $\phi$ ≤ 90, Pr = 0.015, 103	28 $\times$ 28 bi-quadratic elements
Ray & Chatterjee [65]	Fluent, FVM	Lid-driven square cavity	2D, steady, mixed convection	0.1 ≤ Ri ≤ 10, 0 ≤ Ha ≤ 50, 0 ≤ J ≤ 5, Re = 102, Pr = 0.71	Non-uniform, 56,126 mixed elements
Saha & Gu [66]	Fluent, FVM	Triangular cavity	2D, unsteady, natural convection	Pr = 0.72, 105 ≤ Ra ≤ 108, A = 0.2, 0.5, 1.0	Non-uniform grid, 400 $\times$ 100
Xu & Saha [67]	FVM, SIMPLE, QUICK	Square cavity with fin	2D, unsteady, natural convection	Pr = 0.71, 105 ≤ Ra ≤ 109	Non-uniform grid, 198 $\times$ 198
Cui et al. [68]	Fluent, FVM, SIMPLE, QUICK	Triangular cavity	3D, natural convection, unsteady	A = 0.5, Pr = 6.98, Ra = 2.08 $\times$ 106	Non-uniform grid, 100 $\times$ 66$\times$ 45
Elsherbiny & Ismail [69]	FDM, TDMA, CDS	Inclined rectangular cavities	2D, laminar, steady	Pr = 0.71, 0 ≤ $\phi$ ≤ 180, 103 ≤ Ra ≤ 106, A = 1, 5, 10	Uniform grid, 42 $\times$ 42
Elsherbiny & Ragab [51]	-	Inclined rectangular cavities	2D, laminar, natural convection	Pr = 0.71, 0 ≤ $\phi$ ≤ 180, 102 ≤ Ra ≤ 106	Uniform mesh, 42 $\times$ 42
Groşan et al. [70]	FDM, CDS	Porous square cavity	2D, steady, natural convection	Ra = 10, 100, Le = 1, 10, H2O, aluminum foam, carbon nanotubes	227 $\times$ 227
Moumni et al. [71]	FVM, AB, QUICK, CDS, Euler, RBSOR	Double lid-driven square cavity	2D, unsteady, laminar	1 ≤ Re ≤ 102, Pr = 6.2, 10−2 ≤ Ri ≤ 20, 0 ≤ $\chi$ ≤ 0.2, H2O based Cu, Ag, Al2O3, TiO2 nanofluids	Uniform grid, 120 $\times$ 120
Saha & Gu [72]	Fluent, FVM, QUICK	Triangular enclosure	2D, natural convection, steady, unsteady	105 ≤ Ra ≤ 106, Pr = 0.72, A = 0.2, 0.5, 1.0	Non-uniform grid
Sheremet & Pop [73]	FDM, CDS, SOR	Lid-driven square cavity	2D, unsteady, laminar, mixed convection	Re = 102, Pr = 6.26, 10 ≤ Gr ≤ 105, 10 ≤ Le ≤ 104, N, Nb, Nt = 0.1 to 0.4	Uniform grid, 400 $\times$ 400
Sojoudi et al. [74]	Fluent, FVM	Triangular cavity	2D, natural convection, unsteady	103 ≤ Ra ≤ 106, 0.2 ≤ A ≤ 1, Pr = 0.72	15,700 triangular elements
Armaghani et al. [75]	FVM, SIMPLE	L-shaped cavity with baffle	2D, steady, natural convection	Pr = 0.71, 104 ≤ Ra ≤ 106, 0.1 ≤ A ≤ 0.7, 0 ≤ Bf ≤ 0.3, 0 ≤ $\chi$ ≤ 0.04, Al2O3-H2O nanofluid	Uniform grid, 100 $\times$ 100
Jmai et al. [76]	FVM, QUICK, SOR, multigrid	Double lid-driven square cavity	2D, unsteady, laminar, mixed convection	10−2 ≤ Ri ≤ 102, 0 ≤ $\chi$ ≤ 0.1, Cu–H2O nanofluid	Non-uniform grid, 64 $\times$ 64
Kareem et al. [77]	Fluent, URANS, LES, FVM, SIMPLE	Cubic lid-driven cavity	3D, unsteady, mixed convection, turbulent	Re = 5000, 10,000, 15,000 and 30,000	Structured, non-uniform, 1,699,200 grids
Kareem et al. [78]	FVM, UDS, SIMPLE	Lid-driven trapezoidal cavity	2D, mixed convection	0 ≤ $\chi$ ≤ 0.04, 0.1 ≤ Ri ≤ 10, 102 ≤ Re ≤ 1200, 0 ≤ $\phi$ ≤ 60, 0.5 ≤ A ≤ 2, H2O based Al2O3, CuO, SiO2, TiO2 nanofluids	Unstructured, non-uniform 5470 grids
Mamourian et al. [79]	FVM, SIMPLE	Lid-driven square cavity	2D, steady, laminar, Mixed convection	10−2 ≤ Ri ≤ 102, 0 ≤ $\chi$ ≤ 0.1, Gr = 102, Am = 0.25, Cu–H2O nanofluid	Structured non-uniform, 101 $\times$ 201
Mejri et al. [80]	LBM	Triangular cavity	2D, natural convection, laminar	103 ≤ Ra ≤ 106, 0 ≤ $\phi$ ≤ 315, Ma = 0.1	-
Rahmati et al. [81]	LBM	Double lid-driven cavity	2D, mixed convection, laminar, steady	Gr = 100, Pr = 6.57, 10−2 ≤ Ri ≤ 102, 0 ≤ $\chi$ ≤ 0.06, Cu-H2O nanofluid	100 $\times$ 100
Rashad et al. [12]	FVM, ADI, SIMPLE, UDS, CDS	Lid-driven square cavity	2D, mixed convection, laminar	0 ≤ Ha ≤ 100, 10−3 ≤ Ri ≤ 10, 0 ≤ $\chi$ ≤ 0.01, Cu-H2O nanofluid	Uniform grid, 81 $\times$ 81
Selimefendigil & Öztop [82]	FEM, ALE	Lid-driven inclined square cavity	2D, steady	10−2 ≤ Ri ≤ 102, 0 ≤ $\chi$ ≤ 0.05, 103 ≤ Rai ≤ 106, 0 ≤ Ha ≤ 50, 0 ≤ $\phi$ ≤ 90, 5$\times$ 102 ≤ E ≤ 106, CuO-H2O nanofluid	Non-uniform mesh, 10,916 nodes
Selimefendigil & Öztop [83]	FEM, FSI, ALE	Triangular cavity	2D, natural convection, steady	104 ≤ Ra ≤ 106, 104 ≤ Rai ≤ 107, 0 ≤ Ha ≤ 40, 0 ≤ $\phi$ ≤ 90, Pr = 7.1, 5 $\times$ 102 ≤ E ≤ 105	-
Selimefendigil et al. [84]	FEM, NR	Lid-driven square cavity	2D, Mixed convection	10−2 ≤ Ri ≤ 102, 0 ≤ Ha ≤ 50, 0 ≤ $\phi$ ≤ 90, 0 ≤ $\chi$ ≤ 0.05, CuO-H2O nanofluid	Non-uniform,. 17,408 elements
Sojoudi et al. [85]	FVM, QUICK, SIMPLE	Triangular cavity	2D, unsteady, natural convection	103 ≤ Ra ≤ 106, 0.2 ≤ A ≤ 1.0, Pr = 0.72	15,600 triangular elements
Sojoudi et al. [86]	FVM, QUICK, SIMPLE	Triangular cavity	2D, unsteady, natural convection	103 ≤ Ra ≤ 106, 0.2 ≤ A ≤ 1.0, Pr = 0.71	360 $\times$ 75, 360 $\times$ 90, 360 $\times$ 120 for A = 0.2, 0.5, 1
Aparna & Seetharamu [87]	FEM	Porous trapezoidal cavity	2D, natural convection	100 ≤ Ra ≤ 2000	41 $\times$ 41
Alsabery et al. [88]	COMSOL, FEM	Trapezoidal cavity	2D, unsteady, non-Newtonian, laminar	104 ≤ Ra ≤ 106, 0 ≤ $\chi$ ≤ 0.2, 0.1 ≤ Pr ≤ 103, 0 ≤ $\phi$ ≤ 21.8, H2O based TiO2, Cu, Al2O3, Ag nanofluids	Non-uniform, 4690 elements
Al-Weheibi et al. [89]	COMSOL, FEM	Trapezoidal enclosure	2D, natural convection, unsteady, laminar	103 ≤ Ra ≤ 106, 0 ≤ $\chi$ ≤ 0.1, 0.25 ≤ A ≤ 1.0	6-noded 403,388 elements, 204,436 grids
Balla et al. [90]	FEM	Inclined porous square cavity	2D, free convection, laminar	0.01 ≤ $\chi$ ≤ 0.3, 101 ≤ Ra ≤ 103, 0 ≤ M ≤ 10, 0 ≤ $\phi$ ≤ 90, H2O based TiO2, Cu, Al2O3, SiO2 nanofluids	6-noded triangular grid, 5000 elements, 2601 nodes
Cui et al. [91]	FVM	Prismatic enclosure	3D, unsteady, natural convection	100 ≤ Ra ≤ 106, Pr = 0.71	Non-uniform grid, 100 $\times$ 66 $\times$ 45
Das et al. [92]	FEM	Square & triangular cavities	2D, steady, laminar	Pr = 0.7, 103 ≤ Ra ≤ 105	34 $\times$ 34 biquadratic elements
Gangawane [93]	Fluent, FVM, SIMPLE, QUICK	Lid-driven cavity with triangular block	2D, steady, laminar, mixed convection	1 ≤ Re ≤ 103, 0 ≤ Gr ≤ 105, Pr = 1, 50, 102, b = 10%, 20%, 30%	Unstructured, non-uniform, 26,318 nodes, 9126 elements
Ghalambaz et al. [94]	FEM, FSI, ALE	Square cavity with oscillating elastic fin	2D, natural convection, laminar, unsteady	Pr = 0.7, 104 ≤ Ra ≤ 107, 10−3 ≤ Am ≤ 0.1, 1 ≤ Tr ≤ 103, 108 ≤ E ≤ 1013	27,131 domain elements, 1022 boundary elements
Gibanov et al. [95]	FDM	Lid-driven square cavity with block	2D, steady, laminar, mixed convection	10−2 ≤ Ri ≤ 10, 0 ≤ $\chi$ ≤ 0.05, Re = 102, Pr = 6.82, Al2O3-H2O nanofluid	Uniform grid, 200 $\times$ 200
Gibanov et al. [96]	FDM	Lid-driven inclined square cavity	2D, unsteady, mixed convection	Ri =1, Re = 102, Pr = 6.26, Da = 10−7, 10−3, 0 ≤ Ha ≤ 102, 0 ≤ $\chi$ ≤ 0.05, 0 ≤ $\phi$ ≤ $\mathsf{\pi }$, ferrofluid	Uniform grid, 200 $\times$ 200
Hammami et al. [97]	FVM, QUICK, RBSOR	Double lid-driven cubic cavity with cylinder	3D, unsteady	102 ≤ Re ≤ 1500, Pr	Staggered grid non-uniform, 80 $\times$ 80 $\times$ 80
Hatami [6]	FEM, FlexPDE	Rectangular cavity with heated fins	2D, steady	0.03 ≤ $\chi$ ≤ 0.09, H2O based TiO2, Al2O3 nanofluids	-
Hatami et al. [98]	FEM, RSM, FlexPDE	Lid-driven T-shaped porous cavity	2D, steady, mixed convection	Ri = 0.1, Re = 50, Da = 0.001, H2O based TiO2, Cu, Al2O3 nanofluids	-
Hussain et al. [99]	FEM, GE, CN	Double lid-driven square cavity	2D, steady, mixed convection	1 ≤ Re102, 0 ≤ $\phi$ ≤ 45, 0.01 ≤ Ri ≤ 10, 0 ≤ $\chi$ ≤ 0.04, Al2O3-H2O nanofluid	Uniform grid, 65,536 elements
Javed et al. [100]	FEM	Trapezoidal porous cavities	2D, free convection, steady	Pr = 6.2, 10−5 ≤ Da ≤ 10−3, 105 ≤ Ra ≤ 107, 0 ≤ Ha ≤ 60, 0 ≤ $\chi$ ≤ 0.03, Cu-H2O nanofluid	6 noded 704 elements, 1000 grids
Kareem & Gao [101]	Fluent, LES, URANS, SIMPLEC, QUICK	Lid-driven cubic cavity with cylinder	3D, unsteady, mixed convection, turbulent	Pr, Re = 5000, 10,000, 15,000, 30,000, 0 ≤ $\Omega$ ≤ 10	Structured, non-uniform cells, 929,160 elements
Khanafer & Aithal [102]	ADINA, FEM	Lid-driven square cavity with cylinder	2D, steady, laminar, mixed convection	0.01 ≤ Ri ≤ 10, Re = 100, −10 ≤ $\omega$ ≤ 10	150 $\times$ 150
Khatamifar et al. [103]	DNS, SIMPLE, QUICK	Rectangular cavity with partition	2D, natural convection, unsteady	105 ≤ Ra ≤ 109, Pr = 0.71, 0.05 ≤ Tp ≤ 0.2	Non-uniform mesh, 300 $\times$ 250
Mojumder et al. [104]	FEM	Lid-driven L-shaped cavity	2D, mixed convection, laminar, steady	1 ≤ Re ≤ 100, 103 ≤ Gr ≤ 105, 10−5 ≤ Da ≤ 10−3, Pr = 6.2	Triangular mesh, 4452 elements
Selimefendigil et al. [105]	FEM, ALE, FSI	Lid-driven square cavity	2D, steady	0.01 ≤ Ri ≤ 5, 0 ≤ Ha ≤ 50, 102 ≤ Re ≤ 103, CuO-H2O nanofluid	Triangular elements, 17,224 grids
Selimefendigil et al. [106]	FEM, ALE, NR	Lid-driven Trapezoidal cavity with cylinder	3D, steady, laminar, mixed convection	0.5 ≤ Ri ≤ 50, 0 ≤ $\phi$ ≤ 20, 0 ≤ $\chi$ ≤ 0.04, 103 ≤ E ≤ 105, CuO-H2O nanofluid	Tetrahedral elements
Selimefendigil & Öztop [107]	FEM, FSI, ALE	Lid-driven triangular cavity	2D, mixed convection, steady	0.05 ≤ Ri ≤ 50, 0 ≤ $\chi$ ≤ 0.04, Pr = 6.8, 104 ≤ RaI ≤ 108, 500 ≤ E ≤ 105, H2O–CuO nanofluid	Non-uniform grid, 26,306 elements
Sheremet et al. [108]	FDM	Triangular cavities	2D, natural convection	Pr = 0.7, 104 ≤ Ra ≤ 2 $\times$ 105, 102 ≤ Le ≤ 104, 0 ≤ N ≤ 5, Nb = Nt = 0.1	Uniform grid, 300 $\times$ 150
Yu et al. [3]	FDM, UCS, TVD, RK	Rectangular cavity	2D, unsteady, laminar	Pr = 0.025, A = 2, 0 ≤ Ha ≤ 50, 0 ≤ Le ≤ 20	Uniform grid, 41 $\times$ 81
Aghakhani et al. [109]	FDLBM	C-shaped cavity	2D, laminar, non-Newtonian	103 ≤ Ra ≤ 105, 0 ≤ Ha ≤ 40, 0.2 ≤ A ≤ 0.6	160 $\times$ 160
Astanina et al. [110]	FDM	Lid-driven square porous cavity	2D, steady, mixed convection	0.01 ≤ Ri ≤ 10, 0 ≤ $\chi$ ≤ 0.04, 10−7 ≤ Da ≤ 10−3, Da2 = 10−5, Re = 102, Pr = 6.82, H2O–Al2O3 nanofluid	Uniform grid, 200 $\times$ 200
Alsabery et al. [111]	FEM, FEA, NR	Double lid-driven square cavity with block	2D, steady, laminar, mixed convection	1 ≤ Re ≤ 500, 10−2 ≤ Ri ≤ 102, 0 ≤ $\chi$ ≤ 0.04, Pr = 4.623, Le = 3.5 $\times$ 105, Sc = 3.55 $\times$ 104, H2O–Al2O3 nanofluid	Uniform triangular grid, 12,232 grids
Balootaki et al. [112]	LBM-BGK	Lid-driven rectangular cavity with block	2D, mixed convection	10−2 ≤ Ri ≤ 50, Re = 100, Pr = 0.7	450 $\times$ 150
Bhowmick et al. [113]	FEM, SIMPLE, QUICK	V-shaped cavity	2D, natural convection	2.26 $\times$ 105 ≤ Ra ≤ 2.26 $\times$ 109, 0.1 ≤ A ≤ 1.0, Pr = 6.63	Non-uniform, 800 $\times$ 150
Cho [114]	FVM, TDMA, SIMPLE	Lid-driven cavity with wavy surface	2D, steady, laminar, mixed convection	10−2 ≤ Ri ≤ 102, 0 ≤ $\chi$ ≤ 0.04, 1 ≤ Re ≤ 200, Pr = 6.2, 0 ≤ Am ≤ 0.6, H2O–Cu nanofluid	101 $\times$ 1001
Gangawane et al. [115]	Fluent, FVM, SIMPLE, QUICK	Lid-driven square cavity with block	2D, steady, laminar, mixed convection	Ri= 0.01, 1, 10, Pr= 1, 1 ≤ Re ≤ 103	Unstructured, 17,874 nodes, 17,598 elements
Gibanov et al. [116]	FDM	Lid-driven square cavity	2D, mixed convection, laminar, unsteady	10−2 ≤ Ri ≤ 10, 0 ≤ $\chi$ ≤ 0.05, 1.0 ≤ K ≤ 20.0, Re = 100, Pr = 6.82, H2O–Al2O3 nanofluid	Uniform grid, 100 $\times$ 100
Hussain et al. [117]	FEM, CN, GE	Double lid-driven square cavity	2D, laminar, unsteady, mixed convection	0 ≤ $\chi$ ≤ 0.04, 10−2 ≤ Ri ≤ 10, 0 ≤ Ha ≤ 102, 0 ≤ $\phi$ ≤ 90, H2O–Al2O3 nanofluid	Non-uniform triangular grid, 65,536 elements
Javed & Siddiqui [118]	FEM	Square cavity with square blockage	2D, free convection, steady, laminar	105 ≤ Ra ≤ 107, Pr = 0.062, 0 ≤ $\chi$ ≤ 0.06, 0 ≤ Ha ≤ 60, H2O–Cobalt ferrofluid	Non-uniform, 6-noded 1776 elements
Karbasifar et al. [119]	SIMPLEC	Lid-driven cubic cavity with cylinder	3D, laminar, steady, mixed convection	10−2 ≤ Ri ≤ 102, $\chi$ = 0, 0.1%, 0.2%, $\phi$ = 0, 15, 45, H2O–Al2O3 nanofluid	-
Kareem & Gao [120]	Fluent, URANS, SIMPLEC, QUICK	Lid-driven Cubical cavity with cylinder	3D, mixed convection, unsteady, turbulent	5000 ≤ Re ≤ 104, −5 ≤ Ω ≤ 5, SiO2-H2O nanofluid	929,160 grids
Mikhailenko et al. [121]	FDM, CDS, Thomas, SOR	Rotating square cavity with obstacle	2D, laminar, unsteady	Pr = 0.7, Ra = 105, 0 ≤ $\phi$ ≤ 180, 0 ≤ Ta ≤ 106, 0.1 ≤ Os ≤ 1.0, 0.0 ≤ ε ≤ 0.9	101 $\times$ 101
Oglakkaya & Bozkaya [122]	DRBEM	Lid-driven square cavity	2D, mixed convection, unsteady, laminar	Pr = 0.71, Re = 102, Am = 0.05, Ha = 0, 25, 50, 0 ≤ $\phi$ ≤ 90, J = 0, 1, 3, 5, 103 ≤ Ra ≤ 105	400 grids
Razera et al. [123]	Fluent, FVM, SIMPLEC	Lid-driven square cavity	2D, steady, laminar, mixed convection	101 ≤ Re ≤ 103, 103 ≤ Ra ≤ 106, Pr = 0.71	Non-uniform, 33,248 volumes
Selimefendigil & Öztop [124]	FEM, COBYLA	Lid-driven trapezoidal cavity	2D, mixed convection	0.01 ≤ Ri ≤ 25, 0 ≤ Ha ≤ 40, 0 ≤ $\phi$ ≤ 90, 0 ≤ $\chi$ ≤ 0.03, H2O–Al2O3 nanofluid	6282, 4685 and 3691 elements for different $\phi$
Sheikholeslami [125]	LBM	Lid-driven square cavity with hot sphere	3D, forced convection	10−3 ≤ Da ≤ 102, 30 ≤ Re ≤ 180, 0 ≤ Ha ≤ 40, H2O–Al2O3 nanofluid	81 $\times$ 81 $\times$ 81
Sheremet et al. [126]	FDM	Porous square vented cavity	2D, mixed convection, unsteady	104 ≤ Ra ≤ 106, Nb = Nt = 10−6, 10−5 ≤ Da ≤ 10−2, 50 ≤ Re ≤ 300, Pr = 6.82, Le = 103, N = 1, H2O–Al2O3 nanofluid	Uniform grid, 201 $\times$ 201
Taghizadeh & Asaditaheri [127]	OpenFOAM, FVM. SIMPLE	Lid-driven square cavity with cylinder	2D, laminar, mixed convection	0.01 ≤ Ri ≤ 10, 10−5 ≤ Da ≤ 10−2, 0 ≤ $\phi$ ≤ 90, Re = 100, Pr = 0.7	Non-uniform, 11,200
Zhai et al. [128]	FVM, SIMPLE, QUICK	Triangular Roof	2D, unsteady, natural convection	104 ≤ Ra ≤ 107, 0.1 ≤ A ≤ 1.0, Pr = 0.71	Non-uniform mesh, 600 $\times$ 600
Zhou et al. [129]	LBM, OpenMP	Double lid-driven cubic cavity	3D, mixed convection, laminar, unsteady	0.1 ≤ Ri ≤ 102, 0 ≤ $\chi$ ≤ 0.04, H2O–Al2O3 nanofluid	101 $\times$ 101 $\times$ 101
Alnaqi et al. [130]	FDM	Square cavity with a fin	2D, laminar, steady	0 ≤ Ha ≤ 60, 103 ≤ Ra ≤ 106, 0 ≤ Rd ≤ 3, 0 ≤ $\chi$ ≤ 0.06, H2O–Al2O3 nanofluid	Uniform grid. 120 $\times$ 120
Al-Rashed et al. [131]	FVM, SIMPLEC	Inclined lid-driven cubical cavity	3D, steady, mixed convection, laminar	Re, Gr, Pr, 1 ≤ Ri ≤ 102, 0 ≤ $\phi$ ≤ 45, H2O–Al2O3 nanofluid	-
Barnoon et al. [132]	FVM, SIMPLE	Lid-driven square cavity with cylinders	2D, steady, laminar, mixed convection	0 ≤ Ha ≤ 30, 1 ≤ Ri ≤ 102, 0 ≤ $\phi$ ≤ 90, 0.01 ≤ $\chi$ ≤ 0.03, H2O–Al2O3 nanofluid	Non-uniform grid, 19,297 elements
Bhowmick et al. [133]	Fluent, FVM, SIMPLE	V-shaped triangular cavity	2D, natural convection, unsteady	1 ≤ Ra ≤ 108, A = 0.5, Pr = 0.71	800 $\times$ 150
Cho [134]	FVM, SIMPLE, TDMA	Lid-driven cavity with wavy wall	2D, laminar, mixed convection	1 ≤ Re ≤ 300, 0 ≤ Ha ≤ 50, 10−2 ≤ Re ≤ 102, 0 ≤ Am ≤ 0.7, 0 ≤ $\chi$ ≤ 0.04, 0 ≤ $\phi$ ≤ 360, Cu-H2O nanofluid	Non-uniform grid, 101 $\times$ 1001
Cui et al. [135]	FVM	Prismatic enclosure	3D, unsteady, natural convection	100 ≤ Ra ≤ 107, Pr = 0.71, 0.1 ≤ A ≤ 1.5	Non-uniform mesh, 138 $\times$ 42 $\times$ 51
Hadavand et al. [136]	FVM, SIMPLEC	Lid-driven sim-circular cavity	2D, mixed convection, laminar, steady	1 ≤ Ri ≤ 10, $\phi$ = −90 to 90, 0 ≤ $\chi$ ≤ 0.06, Ag-H2O nanofluid	Unorganized triangular grid, 44,896 grids
Hamid et al. [137]	FEM	Trapezoidal cavity	2D, steady, non-Newtonian, natural convection, laminar	104 ≤ Ra ≤ 105.5, Pr = 20	-
Jiang & Zhou [4]	FVM, QUICK, CDS, PISO	Rectangular cavity	2D, steady, laminar	0 ≤ $\chi$ ≤ 0.25, dp = 13, 36, 50 nm, distilled H2O-Al2O3, PGW-ZnO nanofluids	Non-uniform orthogonal grid, 200 $\times$ 50
Karatas & Derbentli [138]	Experimental research	Rectangular cavity	3D, unsteady	4.5 $\times$ 103 ≤ Rai ≤ 1.13 $\times$ 108, A = 1, 2.09, 3, 4, 5, 6	-
Lamarti et al. [139]	LBM	Lid-driven square cavity	2D, mixed convection, laminar	Pr = 0.71, 102 ≤ Re ≤ 103, 102 ≤ Gr ≤ 106, 1 ≤ $\omega$ ≤ 5	100 $\times$ 100
Louaraychi et al. [140]	FVM, SIMPLER, TDMA	Double lid-driven rectangular cavity	2D, unsteady, mixed convection	1 ≤ Ra ≤ 107, 0.1 ≤ Pe ≤ 500, A = 24	Uniform grid, 381 $\times$ 121
Mohebbi et al. [141]	LBM	Γ-shaped enclosure with obstacle	2D, natural convection, steady, laminar	103 ≤ Ra ≤ 106, 0 ≤ $\chi$ ≤ 0.05, 0.2 ≤ A ≤ 0.6, Al2O3-H2O nanofluid	100 $\times$ 100
Selimefendigil & Öztop [142]	FEM, ALE, NR	Lid-driven L-shaped cavity	2D, steady, mixed convection	0.03 ≤ Ri ≤ 30, 0 ≤ $\chi$ ≤ 180, 104 ≤ RaI ≤ 106, 0 ≤ Ha ≤ 50, CuO-H2O nanofluid	Non-uniform, 19,112 elements
(c)
Ref.	CFD Methods and Algorithms	Flow Domain	Dimension, Type of Flow	Parameters and Ranges	Meshing
Abu-Hamdeh et al. [143]	FVM, SIMPLE, CDS, UDS, TDMA	Lid-driven porous square open cavity	2D, mixed convection, steady	102 ≤ Re ≤ 103, 10−3 ≤ Da ≤ 0.1, 103 ≤ Gr ≤ 105	Staggered grid, 48 $\times$ 48
Afrand et al. [144]	SIMPLE	Triangular cavity	2D, free convection, laminar, steady	104 ≤ Ra ≤ 106, 0 ≤ Ha ≤ 40, 0 ≤ $\phi$ ≤ 90, 0 ≤ $\chi$ ≤ 0.06, Al2O3-H2O nanofluid	Staggered grid
Alsabery et al. [145]	FEM	Lid-driven square cavity	2D, mixed convection, steady, laminar	1 ≤ Re ≤ 500, 0.01 ≤ Ri ≤ 100, 0 ≤ Ha ≤ 50, 0 ≤ $\varphi$ ≤ 0.04, Al2O3-H2O nanofluid	Triangular grid, 6402 elements
Alsabery et al. [146]	FEM	Lid-driven cubic cavity with cylinder	3D, mixed convection, steady	Re = 10, 100, Pr = 4.623, 10−2 ≤ Ri ≤ 102, 0 ≤ $\chi$ ≤ 0.04, Le = 3.5 $\times$ 105, Sc = 3.55 $\times$ 104, Al2O3-H2O nanofluid	Non-uniform triangular grid, 175,778 elements
Bilal et al. [147]	FEM	Triangular cavity with cylinder	2D, laminar, steady, free convection	103 ≤ Ra ≤ 106, 0.2 ≤ Pr ≤ 7	Hybrid grid
Cho [148]	FVM, SIMPLE, TDMA	Square cavity with wavy walls	2D, natural convection, steady, laminar	Pr = 6.2, 102 ≤ Ra ≤ 106, 10−6 ≤ Da ≤ 10−2, 0 ≤ $\chi$ ≤ 0.04, Cu-H2O nanofluid	101 $\times$ 1001
Ganesh et al. [149]	FEM	Square Cavity with different obstacles	2D, steady, laminar	103 ≤ Ra ≤ 106, 0 ≤ $\chi$ ≤ 0.08, 103 ≤ RaE ≤ 106, 103 ≤ RaI ≤ 105 Al2O3-H2O/Ethylene Glycol nanofluid	Circular: 6979 elements, Square: 21,916 elements, Triangular: 19,431 elements
Haq et al. [150]	FEM	Lid-driven hexagonal cavity with obstacle	2D, steady	200 ≤ Re ≤ 500, Pr = 6.2, 10−6 ≤ Ri ≤ 1, 0 ≤ Ha ≤ 20, SWCNT-H2O nanofluid	Non-uniform triangular elements
Khan et al. [151]	FEM	Porous trapezoidal cavity	2D	Pr = 6.2, 102 ≤ Ha ≤ 104, 104 ≤ Ra ≤ 105, 0 ≤ $\chi$ ≤ 0.2%, Fe3O4-H2O ferrofluid	-
Li et al. [152]	FDLBM	Triangular enclosure	2D, laminar, non-Newtonian, steady	103 ≤ Ra ≤ 105, 0 ≤ Ha ≤ 60, 0 ≤ $\phi$ ≤ 90	160 $\times$ 160 or 19,600 nodes
Liu & Huang [153]	DNS, QUICK, SIMPLE, CDS	Rectangular cavities with or without fins	2D, unsteady, turbulent	1.15 $\times$ 108 ≤ Ra ≤ 3.68 $\times$ 109	Non-uniform grid, 400 $\times$ 360 cells
Rammane et al. [154]	TS, MLS, NR, HO-MFA	Lid-driven square cavity	2D, steady	102 ≤ Re ≤ 2 $\times$ 104	Mesh free
Saha et al. [155]	FVM, SIMPLE, QUICK	Triangular enclosure	2D, unsteady, natural convection	Pr = 0.72, 105 ≤ Ra ≤ 109, 0.2 ≤ A ≤ 1.0	380 $\times$ 80, 380 $\times$ 100, 380 $\times$ 160 for A = 0.2, 0.5, 1
Selimefendigil & Öztop [156]	FVM, QUICK, SIMPLE	U-shaped corrugated cavity	2D, forced convection, laminar, steady	102 ≤ Re ≤ 103, 0 ≤ Ha ≤ 50, 10−4 ≤ Da ≤ 5 $\times$ 10−2, CNT-H2O nanofluid	Non-uniform grid, 38,874 grids
Soomro et al. [157]	FEM	Lid-driven Triangular cavity with obstacle	2D, mixed convection, laminar, steady	200 ≤ Re ≤ 600, 0.01 ≤ Ri ≤ 1, 0 ≤ Ha ≤ 20, Pr = 6.2	Around 5000 nodes
Thiers et al. [158]	SEM, NeK5000, GMRES	Rectangular cavity	2D, unsteady	A = 4, Pr = 0.71, Ra = 9 $\times$ 107	183 $\times$ 169
Aljabair et al. [159]	FDM, CDS, UDS, SOR	Sinusoidal lid-driven cavity	2D, mixed convection, laminar	1 ≤ Re ≤ 1000, 0 ≤ Ra ≤ 107, 0 ≤ $\chi$ ≤ 0.07, Cu-H2O nanofluid	41 $\times$ 41
Alsabery et al. [160]	FEM	Wavy lid-driven square cavity	2D, laminar, steady, mixed convection	0.01 ≤ Ri ≤ 10, Re = 100, 0 ≤ $\varphi$ ≤ 0.04, H2O/Cu-Al2O3 hybrid nanofluid	-
Çolak et al. [161]	OpenFOAM, FVM, SIMPLE	Lid-driven cavity with porous block	2D, mixed convection, steady	10−1 ≤ Ri ≤ 10, Gr = 105, 10−7 ≤ Da ≤ 10−1, Pr = 6.2	Uniform grid, 201 $\times$ 201
Eshaghi et al. [162]	FEM	H-shaped cavity with a baffle inside	2D, natural convection, laminar	104 ≤ Ra ≤ 106, 2 ≤ Le ≤ 8, 1 ≤ N ≤ 3, −60 ≤ $\phi$. ≤ 60, Cu-Al2O3-H2O hybrid nanofluid	-
Fayz-Al-Asad et al. [163]	FEM	Triangular cavity	2D, natural convection, steady	Pr = 0.71, 104 ≤ Ra ≤ 106	6718 elements, 13,112 nodes
Hasnaoui et al. [164]	LBM, MRT, BGK	Rectangular cavity	2D, biry mixture	Sr = −0.5, 0, 0.5, 0 ≤ Ra ≤ 80, Pr = 0.71, A = 2, Le = 2	120 $\times$ 240
Hussain et al. [165]	FEM	Double lid-driven cavity with fins	2D, laminar, steady	0 ≤ Ha ≤ 100, 0 ≤ $\phi$ ≤ 90, 0.01 ≤ Ri ≤ 1, Pr = 6.2, Re = 100, $\chi$ = 0.02, Cu-H2O nanofluid	33,177 grids
Hoston et al. [166]	IEFG–RIPM	Lid-driven square cavity	2D, steady	Re = 10,000, 15,000, 20,000, 25,000, 30,000 and 35,000	150 $\times$ 150 (Refined at cavity walls)
Ibrahim & Hirpho [167]	COMSOL, FEM	Trapezoidal cavity	2D, mixed convection, laminar	Ha = 0, 50, Ri = 0.1, 1, 10, Re = 100, Am = 0.25, 0.5, 1	91 $\times$ 91
Ikram et al. [168]	FEM, ALE	Hexagonal cavity with rotating modulator	2D, forced convection, unsteady, laminar	Pr = 0.71, 102 ≤ Re ≤ 103, 103 ≤ Bi ≤ 104, 103 ≤ Ra ≤ 107	Non-uniform, 48,548 elements
Joe & Perumal [169]	OpenFOAM, FVM	Rectangular cavity containing cylinders	2D, unsteady	Pr = 0.72, Re = 1600	Unstructured triangular cells
Mondal & Mahapatra [170]	FDM, BiCGStab	Trapezoidal cavity	2D, mixed convection, steady, laminar	Pr = 6.2, N = 5, 0.5 ≤ A ≤ 2, 10−2 ≤ Ri ≤ 102, 102 ≤ Re ≤ 103, 45 ≤ $\phi$ ≤ 90, 0 ≤ $\chi$ ≤ 0.5, 20 ≤ Ha ≤ 40, 1 ≤ Le ≤ 2, Al2O3-H2O nanofluid	81 $\times$ 81
Mebarek-Oudina et al. [171]	FEM	Trapezoidal porous cavity with zigzag wall	2D, laminar, steady	0 ≤ Ha ≤ 100, 0 ≤ $\phi$ ≤ 90, 103 ≤ Ra ≤ 105, 0 ≤ $\chi$ ≤ 0.08, Cu-Al2O3/H2O hybrid nanofluid	Triangular grid, 20,296 elements
Saha et al. [172]	FVM	Rectangular cavity with baffles	2D, laminar, steady	50 ≤ Re ≤ 250 Ri = 0, 2, 4	45 $\times$ 51
Saha et al. [173]	FVM, SIMPLE, QUICK	Triangular cavity	2D, natural convection	Pr = 0.72, 103 ≤ Ra ≤ 106, A = 0.2, 0.5, 1.0	360 $\times$ 75, 360 $\times$ 90, 360 $\times$ 120 for A = 0.2, 0.5, 1
Shah et al. [174]	FEM, NR	Lid-driven trapezoidal cavity with obstacle	2D, mixed convection, steady, laminar	10−2 ≤ Ri ≤ 10, 0.1 ≤ Le ≤ 10, 300 ≤ Re ≤ 500, −10 ≤ N ≤ 10, Pr = 0.71	Non-uniform, approx. 3200 elements
Shahid et al. [175]	MRT-LBM	Triangular lid driven cavity	2D, mixed convection, unsteady	Pr = 0.71, 1, 7, 10−2 ≤ Ri ≤ 102, 104 ≤ Gr ≤ 107	-
Shahid et al. [176]	MRT-LBM	Lid-driven rectangular cavity with obtacles	2D, mixed convection, laminar	Pr = 0.71, 1, 7, 10−2 ≤ Ri ≤ 102, 103 ≤ Gr ≤ 106, A = 0.2, 0.5, 2, 5	Not clearly mentioned for different A
Shekaramiz et al. [177]	OpenFOAM, FVM, SIMPLE	Wavy triangular cavity	2D, free convection, steady	5 $\times$ 103 ≤ Ra ≤ 2 $\times$ 105, Pr = 4.6, 0 ≤ Ha ≤ 50, 0 ≤ $\phi$ ≤ 90, $\chi$ = 2%, H2O-Fe3O4 nanofluid	16,000 and 12,000 nodes
Tizakast et al. [178]	FVM, SIMPLER	Lid-driven rectangular cavity	2D, laminar, unsteady, non-Newtonian	RaT ≤ 5 $\times$ 106, Pe ≤ 103, 10−3 ≤ Le ≤ 103, 10−3 ≤ N ≤ 103, 0.6 ≤ n ≤ 1.4	Uniform grid, A = 24:381 $\times$ 121
Velkennedy et al. [179]	FDM, ADI, CDS	Rectangular vented cavity	2D, laminar, unsteady	103 ≤ Ra ≤ 106, Pr = 0.71	181 $\times$ 121
Xiong et al. [180]	FEM	Lid-driven triangular cavity	2D, mixed convection	Pr = 6.2, 0 ≤ Ha ≤ 40, 0 ≤ Re ≤ 103, 0.01 ≤ Ri ≤ 2	Uniform triangular mesh
Abbas et al. [181]	FEM	Square cavity with obstacles	2D, steady, laminar	0 ≤ $\chi$ ≤ 0.04, 10 ≤ Ha ≤ 40, 103 ≤ Ra ≤ 107, Cu-H2O nanofluid	59,173 elements
Ahmed et al. [182]	Coiflet wavelet-homotopy method	Lid-driven square porous cavity	2D, unsteady	Pr = 6.2, 10 ≤ Ri ≤ 102, 10−4 ≤ Da ≤ 10−1, 3 ≤ Le ≤ 106, Al2O3-Cu/H2O hybrid nanofluid	-
Alam et al. [8]	FEM	Semi-circular cavity	2D, unsteady, semi-circular cavity, free convection	Pr = 23.0, 6.84, 1 ≤ dp ≤ 10, 0 ≤ $\chi$ ≤ 0.05, 0 ≤ Ha ≤ 100, 104 ≤ RaT ≤ 106, ZnO, Fe3O4, Co, Al2O3, Ag nanoparticles, H2O & kerosene as base fluids	15,817 elements
Ali et al. [183]	Comsol, FEM	Lid-driven square cavity	2D, mixed convection, steady	Re = 1, 10, 102, Ha = 0, 10, 25, $\chi$ = 0, 1%, 5%, Pr = 6.2, Gr = 102, Al2O3-H2O nanofluid	Non-uniform, 30,550 nodes, 60,036 elements
Alqaed et al. [5]	FVM, SIMPLE	Rectangular cavity with triangular blades	2D, steady, laminar	103 ≤ Ra ≤ 105, 0 ≤ Ha ≤ 30, $\chi$ = 0.3, Al2O3-H2O nanofluid	150 $\times$ 450
Acharya & Chamkha [184]	FEM	Hexagonal cavity with parallel fins	2D, laminar, steady	103 ≤ Ra ≤ 105, 0 ≤ Ha ≤ 100, 0 ≤ $\chi$ ≤ 0.04, Pr = 6.2, Al2O3-H2O nanofluid	Non-uniform, 34,502 elements
Batool et al. [185]	FVM, SIMPLE	Lid-driven square cavity	2D, steady, laminar	100 ≤ Re ≤ 400, micropolar nanofluids	Staggered grid
Charqui et al. [186]	FVM, SIMPLE, TDMA	Tall partitioned cavity	2D, natural convection, laminar	Pr = 0.71, 7, A = 40	Uniform mesh, 80 $\times$ 200
Cui et al. [187]	FVM, SIMPLE	Triangular cavity	3D, natural convection, unsteady	Pr = 0.7, 102 ≤ Ra ≤ 107, 0.1 ≤ A ≤ 1.5	Non-uniform mesh, 141 $\times$ 41 $\times$ 51
Dahani et al. [188]	LBM, MRT, BGK operator	Double lid-driven square cavity	2D, unsteady	0 ≤ $\phi$ ≤ 180, Re = 102, 10−2 ≤ Ri ≤ 102, 102 ≤ Gr ≤ 106, Pr = 0.71	Uniform grid, 160 $\times$ 160
Esfe et al. [9]	Fluent, FVM, SIMPLE	U-shaped porous enclosure	2D, steady	103 ≤ Ra ≤ 105, 0 ≤ $\chi$ ≤ 0.03, Al2O3-H2O nanofluid	Approx 1600 cells
Geridonmez & Oztop [10]	Rbf-Pum	Right Isosceles triangular cavity	2D, natural convection, steady, laminar	0 ≤ Ha ≤ 100, 0.25 ≤ A ≤ 1, Pr = 6.07, Ra = 105, 0 ≤ $\chi$ ≤ 0.02, Al2O3-Cu/H2O nanofluid	1,842,025 & 1,741,596 nodes
Hirpho & Ibrahim [189]	FEM	Trapezoidal enclosure	2D, mixed convection, non-Newtonian, steady, laminar	10−1 ≤ Ri ≤ 102, Re = 100, Pr = 20, 0 ≤ $\chi$ ≤ 0.02, Al2O3-Cu/H2O hybrid nanofluid	201 $\times$ 201
Khalil et al. [190]	Fluent, FVM, RSM	Porous trapezoidal cavity with wavy wall	2D, steady	0 ≤ Ha ≤ 40, 0 ≤ Am ≤ 20, 5 $\times$ 102 ≤ Ra ≤ 2.4 $\times$ 104	320 $\times$ 320
Liu [191]	CDS, SIMPLE, QUICK	Rectangular cavity with fins	2D, free convection, unsteady	0 ≤ $\phi$ ≤ 40, Ra = 1.84 $\times$ 109	360 $\times$ 400
Noor et al. [192]	FEM	Lid-driven trapezoidal cavity with obstacle	2D, forced convection, steady	102 ≤ Re ≤ 700, 10−3 ≤ Ri ≤ 10, 0 ≤ Ha ≤ 102	Trangular grid, 4622 nodes. 8929 elements
Nouraei et al. [193]	FVM, SIMPLE	Semi-circular vented cavity	2D, mixed convection, laminar, steady	10 ≤ Re ≤ 100, 0 ≤ $\chi$ ≤ 0.06, Cu-H2O nanofluid	52,000 grids
Polasanapalli & Anupindi [194]	LBM	Concentric circular annular cavity	2D, mixed convection, unsteady	104 ≤ Ra ≤ 106, 0 ≤ Re ≤ 104, Pr = 0.71, 0 ≤ $\phi$ ≤ 360, 10−3 ≤ Ri ≤ 103	120 $\times$ 120, 180 $\times$ 180
Prince et al. [195]	COMSOL, FEM	Trapezoidal cavity with different surface	2D, natural convection	Pr = 0.716, 103 ≤ Ra ≤ 106, Materials: Pinewood, plexiglas, dry concrete, glass fiber	Rectangle: 6112, Triangle: 10,191, Sinusoidal: 5993 elements
Rahaman et al. [196]	Fluent, FVM, CDS, SIMPLE	Trapezoidal cavity	2D, unsteady, natural convection	Pr = 0.71, 100 ≤ Ra ≤ 108, A = 0.5	Non-uniform, 300 $\times$ 100
Roy et al. [197]	FEM	Square enclosure with blocks	2D, unsteady, natural convection	Pr = 6.2, 0 ≤ Rd ≤ 3, 0 ≤$\chi$ ≤ 0.09, 104 ≤ Ra ≤ 106, 0 ≤ Ha ≤ 60, Cu- Al2O3/H2O hybrid nanofluid	Triangular 65,740 elements
Shah et al. [198]	FEM, NR	Lid-driven corrugated porous cavity	2D, mixed convection, laminar, steady	102 ≤ Re ≤ 400, 0 ≤ $\chi$ ≤ 0.05, 10−5 ≤ Da ≤ 10−1, Pr = 6.2, 10−2 ≤ Ri ≤ 100, CuO-H2O nanofluid	Approx 8000 elements
Tizakast et al. [199]	FVM, SIMPLE	Lid-driven Rectangular cavity	2D, unsteady non-Newtonian, laminar	2 ≤ A ≤ 30, 102 ≤ RaT ≤ 107, 10−3 ≤ Le ≤ 103, 0.1 ≤ Pe ≤ 104	-
Xia et al. [200]	UPWIND	T-shaped lid-driven cavity	2D, mixed convection	0 ≤ $\chi$ ≤ 0.03, 0.1 ≤ Re ≤ 10, 0.2 ≤ A ≤ 0.4, Al2O3-H2O nanofluid	Uniform mesh, 250,000 cells
Zarei et al. [201]	FVM, SIMPLE	Square cavity with wavy walls	2D, steady	Ra = 104, 0 ≤ Am ≤ 0.15, 0 ≤ $\chi$ ≤ 0.04, Cu-H2O nanofluid	135,008 triangular cells
Zhang et al. [202]	FVM, SIMPLE	Semi-elliptic lid-driven cavity	2D, mixed convection, steady, laminar	0 ≤ $\chi$ ≤ 0.06, Gr = 5 $\times$ 104, 15 $\times$ 104, 25 $\times$ 104, 4 $\times$ 105, 10−1 ≤ Ri ≤ 10, Pr = 6.2, Ag-H2O nanofluid	43,905 triangular grids
Akhter et al. [7]	FEM	square cavity with cylinder	2D, steady	104 ≤ Ra ≤ 5 $\times$ 106, Pr = 6.2, 0 ≤ $\chi$ ≤ 0.05, 0 ≤ Ha ≤ 102, Cu-Al2O3/H2O hybrid nanofluid	24,961 nodes, 49,188 elements
He et al. [203]	Experimental, FVM, SIMPLE	Cubic cavity	3D	0 ≤ B ≤ 133, 0 ≤ $\chi$ ≤ 0.03, 6.9 $\times$ 105 ≤ Ram ≤ 11.6 $\times$ 105, Fe3O4-Paraffin nanofluid	50 $\times$ 50 $\times$ 50
Ikram et al. [204]	FEM, ALE	Hexagonal cavity with rotating modulator	2D, forced convection, unsteady, laminar	Pr = 0.71, 102 ≤ Re ≤ 103, 104 ≤ Ra ≤ 106, Bi = 104	49,874, 50,672 and 52,601 elements
Ouri et al. [205]	Comsol, FEM, ANFIS	L-shaped cavity with rotating cylinder	2D, unsteady	200 ≤ Re ≤ 103, 102 ≤ Rew ≤ 103, 0 ≤ Ha ≤ 40, 0 ≤ $\chi$ ≤ 0.02, Ag-MgO/H2O hybrid nanofluid	Non-uniform triangular 65,216 elements
Sayed et al. [206]	FVM, LES, URANS	Cubical cavity	3D, unsteady	Ra = 109, Pr = 0.71, Prt = 0.9	166,375 cells

Table 1. (a): Research performed from 1989 to 2013. (b) The research was performed from 2014 to 2019. (c): Research performed from 2020 to 2023.

(a)
Ref.	CFD Methods and Algorithms	Flow Domain	Dimension, Type of Flow	Parameters and Ranges	Meshing
Wee et al. [2]	Experimental, FDM, DADI	Rectangular cavity	2D, unsteady, laminar	2 $\times$ 105 ≤ GrT ≤ 2 $\times$ 106, 10 ≤ GrC ≤ 2 $\times$ 105, 2 $\times$ 104 ≤ Ra ≤ 1.47 $\times$ 106	-
Moallemi & Jjang [11]	FVM, SIMPLIER	Lid-driven square cavity	2D, steady, laminar, non-Newtonian	102 ≤ Re ≤ 2200, 0.01 ≤ Pr ≤ 50, 0.01 ≤ Ri ≤ 10	Non-uniform grid, 42 $\times$ 42
Sasaguchi et al. [14]	Grid generation	Rectangular cavity with cylinders	2D, unsteady, laminar	N/A	Uniform mesh, 31 $\times$ 101, 31 $\times$ 121
Al-Amiri et al. [15]	FEM	Lid-driven cavity with wavy wall	2D, steady, laminar, mixed convection	Pr = 0.71, 1, Gr = 104, 0.1 ≤ Ri ≤ 10, 0 ≤ Am ≤ 0.075, 0 ≤ $\lambda$ ≤ 3, Re = 500	-
Saha et al. [16]	FEM	Inclined rectangular enclosure	2D, natural convection, steady, laminar	Pr = 0.71, 103 ≤ Gr ≤ 106, 0.5 ≤ A ≤ 1.0, 0 ≤ $\varphi$ ≤ 30	Non-uniform, six nodded 6394 elements
Saha et al. [17]	FVM	Triangular cavity	2D, natural convection	Pr = 0.71, Gr = 1.33 $\times$ 106, 0.5 ≤ A ≤ 1.0	360 $\times$ 90, 720 $\times$ 160, 270 $\times$ 90 for A = 0.2, 0.5, 1.0
Tiwari & Das [18]	FVM, SIMPLE, QUICK, TDMA	Double lid-driven square cavity	2D, unsteady	Pr = 6.2, 0.1 ≤ Ri ≤ 10, 103 ≤ Ra ≤ 106, 0 ≤ $\chi$ ≤ 0.2, Cu-water nanofluid	Uniform grid, 61 $\times$ 61
Saha et al. [19]	FEM	Inclined sinusoidal enclosure	2D, steady, natural convection, laminar	Pr = 0.71, 103 ≤ Gr ≤ 106, 0 ≤ $\varphi$ ≤ 45	Non-uniform grid, 5240 elements
Varol et al. [20]	FDM	Triangular cavity	2D, natural convection	0.25 ≤ A ≤ 1.0, 102 ≤ Ra ≤ 103	Uniform grid, 61 $\times$ 61
Chen & Cheng [21]	FVM, SOR	Lid-driven triangular cavity	2D, mixed convection, unsteady, laminar	Pr = 0.71, Re = 100, Gr = 5 $\times$ 105	41 $\times$ 41
Noor et al. [22]	FDM, QUICK, RK-4, SOLA	Double lid-driven square cavity	2D, unsteady, laminar	Pr = 0.71, 10 ≤ Re ≤ 103, 1 ≤ $\varpi$ ≤ 5	Clustered grid, 125 $\times$ 125
Ouertatani et al. [23]	FVM, QUICK. CDS, RBSOR	Double lid-driven cubic cavity	3D, mixed convection, unsteady, laminar	Pr = 0.71, 102 ≤ Re ≤ 103, 10−3 $\le$ Ri ≤ 10	64 $\times$ 64 $\times$ 64
Basak et al. [24]	FEM	Triangular porous cavities	2D, natural convection, steady	10−5 ≤ Da ≤ 10−1, 0.015 ≤ Pr ≤ 103, 103 ≤ Ra ≤ 5105	20 $\times$ 20–28 $\times$ 28 bi-quadratic elements
Lei & O’Neill [25]	FVM, SIMPLE, CDS, SUR	Square cavity with different corners	2D, unsteady, natural convection	Pr = 6.62, 0 ≤ Ra ≤ 108	16,000 cells
Saha [26]	FEM	Sinusoidal corrugated enclosure	2D, steady	Pr = 0.71, 103 ≤ Gr ≤ 106, 0 ≤ Ha ≤ 102	Non-uniform grid, 4928 elements
Saha et al. [27]	FEM	Octagonal enclosure	2D, natural convection, steady, laminar	Pr = 0.71, 7, 20, 50, 103 ≤ Ra ≤ 106	Non-uniform, 10,466 elements
Saha et al. [28]	FVM, QUICK, SIMPLE	Triangular enclosure	2D, natural convection, unsteady	Pr = 0.72, 104 ≤ Ra ≤ 7.2 $\times$ 106, A = 0.2, 0.5, 1.0	270 $\times$ 90, 320 $\times$ 80, 360 $\times$ 90 for A = 1, 0.5 & 0.2
Saha et al. [29]	FVM, QUICK, SIMPLE	Triangular enclosure	2D, natural convection, unsteady	Pr = 0.72, 7.2 $\times$ 103 ≤ Ra ≤ 1.5 $\times$ 106, A = 0.2, 0.5, 1.0	270 $\times$ 90, 320 $\times$ 80, 360 $\times$ 90 for A = 1, 0.5 & 0.2
Saha et al. [30]	FVM, QUICK, SIMPLE	Triangular enclosure	2D, natural convection, unsteady	Pr = 0.72, 5 ≤ Ra ≤ 1.5 $\times$ 107, A = 0.2, 0.5, 1.0	360 $\times$ 120, 320 $\times$ 90, 360 $\times$ 90 for A = 1, 0.5 & 0.2
Sivasankaran et al. [31]	FVM, UDS, CDS, SOR	Lid-driven square cavity	2D, unsteady, laminar, mixed convection	Pr = 0.71, 0 ≤ Am ≤ 1, 0 ≤ $\varphi$ ≤ $\pi$, 0.1 ≤ Ri ≤ 102, 102 ≤ Re ≤ 103	Uniform grid, 81 $\times$ 81
Sivakumar et al. [32]	FVM, SIMPLE, QUICK. CDS	Lid-driven square cavity	2D, mixed convection, unsteady, laminar	Pr = 0.71, 102 ≤ Re ≤ 103, 102 ≤ Gr ≤ 106, 10−2 ≤ Ri ≤ 102	Uniform grid, 81 $\times$ 81
Al-Amiri & Khanafer [33]	ADINA, FSI, FEM, ALE	Lid-driven square cavity	2D, steady, laminar	Pr = 0.71, 102 ≤ Re, Gr ≤ 103	Non-uniform mesh, 120 $\times$ 120
Cheng [34]	Compact formulation, SOR, ADI	Lid-driven square cavity	2D, mixed convection	10 ≤ Re ≤ 2200, 100 ≤ Gr ≤ 4.86 $\times$ 106, 10−2 ≤ Pr ≤ 50, 10−2 ≤ Ri ≤ 102	256 $\times$ 256
Nasrin & Parvin [35]	FEM, TFM	Lid-driven square cavity with wavy wall	2D, laminar, steady, mixed convection	30 ≤ Re ≤ 300, 0 ≤ Ha ≤ 50, Pr = 0.71, Ra = 104	Non-uniform, 37,123 nodes, 5604 elements
Saha [36]	FVM, QUICK	Triangular cavity	2D, unsteady, natural convection	0.2 ≤ A ≤ 1.0, 5 ≤ Pr ≤ 100, Ra = 107	-
Saha [37]	FVM, SIMPLE, QUICK	Triangular cavity	2D, unsteady, natural convection	0.2 ≤ A ≤ 1.0, 5 ≤ Pr ≤ 100, 5 $\times$ 106 ≤ Ra ≤ 108	-
Yu et al. [38]	Fluent, FVM, QUICK, SIMPLE	Square cavity	2D, unsteady, natural convection	104 ≤ Ra ≤ 106, 0 ≤ $\chi$ ≤ 0.04, CuO–H2O nanofluid	100 $\times$ 100
Al-Farhany & Turan [39]	FVM, SIMPLER	Inclined rectangular porous cavity	2D, unsteady, natural convection	0 ≤ ϕ ≤ 85, 0.1 ≤ Le ≤ 10, −5 ≤ N ≤ 5, Pr = 4.5, Ra = 5 × 106	-
Arani et al. [40]	FVM, SIMPLIER, TDMA, CDS, UDS	Lid-driven square cavity	2D, mixed convection, laminar, steady	10−3 ≤ Ri ≤ 10, 0 ≤ $\chi$ ≤ 0.1, Gr = 102, Re = 102 Cu–H2O nanofluid	Uniform grid. 80 $\times$ 80
Basak et al. [41]	FEM	Porous triangular cavities	2D, natural convection, steady	Pr = 0.025, 1000, 10−5 ≤ Da ≤ 10−3, Ra = 5 $\times$ 105	28 $\times$ 28 bi-quadratic elements
Chamkha & Abu-Nada [42]	FVM, CDS, UDS, SOR, SUR	Double lid-driven square cavity	2D, mixed convection, steady, laminar	0.001 ≤ Ri ≤ 10, 0 ≤ $\chi$ ≤ 0.1, H2O-Al2O3 nanofluid	Uniform grid, 81 $\times$ 81
Nasrin & Parvin [43]	FEM	Trapezoidal cavity	2D, free convection, steady, laminar	Ra = 105, $\chi$ = 0.05, 0.65 ≤ A ≤ 2, 1.47 ≤ Pr ≤ 8.81, Cu–H2O nanofluid	40,295 nodes, 10,936 elements
Raji et al. [44]	FVM, SIMPLIER	Square cavity with blocks	2D, natural convection, laminar, steady	103 ≤ Ra ≤ 108, Pr = 0.71	254 $\times$ 254
Saha & Gu [45]	FVM	Triangular enclosure	2D, natural convection, unsteady	Pr = 0.7, Ra = 105, A = 0.5	Triangular grid, 8143 nodes
Saha & Gu [46]	FVM	Triangular enclosure	2D, natural convection, unsteady	Pr = 0.72, 5.0 $\times$ 104 ≤ Ra ≤ 106, A = 0.5	-
Teamah & El-Maghlany [47]	FVM, CDS, GS, TDMA	Square cavity	2D, steady, laminar	103 ≤ Ra ≤ 107, 0 ≤ Ha ≤ 60, 0 ≤ $\chi$ ≤ 0.06, −10 ≤ q ≤ 10, Pr = 6.2, H2O based Al2O, Cu, TiO2 nanofluids	60 $\times$ 60
Ahmed et al. [48]	Collocated FVM, UDS, CDS, TDMA	Inclined lid-driven square cavity	2D, mixed convection, laminar, steady	10−2 ≤ Ri ≤ 102, 0 ≤ $Am$ ≤ 1.0, 0 ≤ Ha ≤ 100, 0 ≤ $\phi$ ≤ 90	Uniform grid. 81 $\times$ 81
Bhardwaj & Dalal [49]	FDM, QUICK, SOR, CDS	Porous triangular cavity	2D, natural convection, laminar	103 ≤ Ra ≤ 106, 10−4 ≤ Da ≤ 10−2, Am = 0.05	Orthogonal mesh, 41 $\times$ 41
Cho et al. [50]	FVM, SIMPLEC, TDMA	Lid-driven cavity with wavy surfaces	2D, mixed convection, laminar, steady	0 ≤ $\chi$ ≤ 0.1, 10−2 ≤ Ri ≤ 103, 101 ≤ Gr ≤ 104, 0 ≤ $Am$ ≤ 0.2, Pr = 6.2, H2O based Cu, Al2O3, TiO2 nanofluids	101 $\times$ 201
Elsherbiny & Ragab [51]	-	Inclined rectangular cavities	2D, laminar, natural convection	102 ≤ Ra ≤ 106, 0.5 ≤ A ≤ 5, 0 ≤ $\phi$ ≤ 180	Uniform mesh, 42 $\times$ 42
Huelsz & Rechtman [52]	LBM	Inclined square cavity	2D, natural convection, laminar, unsteady	Pr = 0.71, −180 ≤ $\phi$ ≤ 180, 103 ≤ Ra ≤ 106	103 $\times$ 103
Khanafer & Aithal [53]	ADINA, FEM, NR	Lid-driven square cavity with cylinder	2D, steady, laminar, mixed convection	Pr = 0.7, 104 ≤ Gr ≤ 106, 0.01 ≤ Ri ≤ 10, Re = 102	Non-uniform grid, 19,520 nodes
Ramakrishna et al. [54]	FEM	Trapezoidal cavities	2D, free convection, laminar	30 ≤ $\phi$ ≤ 90, Pr = 0.015, 7.2, 103 ≤ Ra ≤ 105	28 $\times$ 28 bi-quadratic elements
Sivasankaran et al. [55]	FVM, UDS, CDS	Inclined lid-driven square cavity	2D, unsteady, laminar, mixed convection	Pr = 0.71, 0.01 ≤ Ri ≤ 102, 0 ≤ $\phi$ ≤ 90	81 $\times$ 81
(b)
Ref.	CFD Methods and Algorithms	Flow Domain	Dimension, Type of Flow	Parameters and Ranges	Meshing
Sathitamoorthy & Chamkha [56]	FEM	Square cavity with thin partition	2D, natural convection, steady	Pr = 0.7, 100, 103 ≤ Rah ≤ 105	20 $\times$ 20 elements, 41 $\times$ 41 grid points
Abu-Nada & Chamkha [57]	FVM, SOR, SUR, UDS	Lid-driven square cavity with wavy wall	2D, mixed convection, laminar, steady	Pr = 6.57, 0.01 ≤ Ri ≤ 102, 0 ≤ $\chi$ ≤ 0.09, H2O-CuO nanofluid	Uniform grid, 81 $\times$ 81
Ait-Taleb et al. [58]	FDM, SIMPLE, TDMA	Rectangular cavities with tiles	2D, steady, laminar	8.7 $\times$ 103 ≤ Rah ≤ 1.8 $\times$ 105, 4.1 $\times$ 105 ≤ RaH ≤ 1.23 $\times$ 107, Pr = 0.71	Non-uniform mesh, 80 $\times$ 40
Cheng & Liu [59]	Ansys Fluent, FVM, SOR, ADI	Lid-driven square and rectangular cavities	2D, unsteady	Pr = 0.71, 10−2 ≤ Ri ≤ 102, 0.2 ≤ A ≤ 5, 0 ≤ $\phi$ ≤ 90, Re = 102	Uniform grid, 640 $\times$ 128, 128 $\times$ 128, 128 $\times$ 640
Cho [60]	FVM, SIMPLE, TDMA	Square cavity with wavy wall	2D, natural convection, laminar, steady	103 ≤ Ra ≤ 106, 0 ≤ $\chi$ ≤ 0.04, Pr = 6.2, H2O-Al2O3 nanofluid	101 $\times$ 201
Kalteh et al. [61]	FDM, CDS, SUR	Lid-driven square cavity with block	2D, steady, mixed convection	Gr = 102, 0.000625 ≤ Ri ≤ 4, 0 ≤ $\chi$ ≤ 0.05, H2O based Al2O3, TiO2, Ag, CuO nanofluids	Regular grid, 80 $\times$ 80
Khanafer [62]	ADINA, FEM, FSI, ALE	Lid-driven square cavity	2D, steady, laminar, mixed convection	Pr = 0.7, 102 ≤ Gr ≤ 104, 10−4 ≤ Ri ≤ 1.0, 102 ≤ Re ≤ 103	Non-uniform, 120 $\times$ 120
Muthtamilselvan & Doh [63]	FVM, SIMPLE, QUICK, TDMA	Lid-driven square cavity	2D, steady, mixed convection	0 ≤ Rai ≤ 105, Pr = 6.2, 10−2 ≤ Ri ≤ 10, 0 ≤ $\chi$ ≤ 0.06, Cu-H2O nanofluid	Uniform grid, 41 $\times$ 41
Ramakrishna et al. [64]	FEM	Porous trapezoidal cavity	2D, natural convection, laminar, steady	10−5 ≤ Da ≤ 10−3, 30 ≤ $\phi$ ≤ 90, Pr = 0.015, 103	28 $\times$ 28 bi-quadratic elements
Ray & Chatterjee [65]	Fluent, FVM	Lid-driven square cavity	2D, steady, mixed convection	0.1 ≤ Ri ≤ 10, 0 ≤ Ha ≤ 50, 0 ≤ J ≤ 5, Re = 102, Pr = 0.71	Non-uniform, 56,126 mixed elements
Saha & Gu [66]	Fluent, FVM	Triangular cavity	2D, unsteady, natural convection	Pr = 0.72, 105 ≤ Ra ≤ 108, A = 0.2, 0.5, 1.0	Non-uniform grid, 400 $\times$ 100
Xu & Saha [67]	FVM, SIMPLE, QUICK	Square cavity with fin	2D, unsteady, natural convection	Pr = 0.71, 105 ≤ Ra ≤ 109	Non-uniform grid, 198 $\times$ 198
Cui et al. [68]	Fluent, FVM, SIMPLE, QUICK	Triangular cavity	3D, natural convection, unsteady	A = 0.5, Pr = 6.98, Ra = 2.08 $\times$ 106	Non-uniform grid, 100 $\times$ 66$\times$ 45
Elsherbiny & Ismail [69]	FDM, TDMA, CDS	Inclined rectangular cavities	2D, laminar, steady	Pr = 0.71, 0 ≤ $\phi$ ≤ 180, 103 ≤ Ra ≤ 106, A = 1, 5, 10	Uniform grid, 42 $\times$ 42
Elsherbiny & Ragab [51]	-	Inclined rectangular cavities	2D, laminar, natural convection	Pr = 0.71, 0 ≤ $\phi$ ≤ 180, 102 ≤ Ra ≤ 106	Uniform mesh, 42 $\times$ 42
Groşan et al. [70]	FDM, CDS	Porous square cavity	2D, steady, natural convection	Ra = 10, 100, Le = 1, 10, H2O, aluminum foam, carbon nanotubes	227 $\times$ 227
Moumni et al. [71]	FVM, AB, QUICK, CDS, Euler, RBSOR	Double lid-driven square cavity	2D, unsteady, laminar	1 ≤ Re ≤ 102, Pr = 6.2, 10−2 ≤ Ri ≤ 20, 0 ≤ $\chi$ ≤ 0.2, H2O based Cu, Ag, Al2O3, TiO2 nanofluids	Uniform grid, 120 $\times$ 120
Saha & Gu [72]	Fluent, FVM, QUICK	Triangular enclosure	2D, natural convection, steady, unsteady	105 ≤ Ra ≤ 106, Pr = 0.72, A = 0.2, 0.5, 1.0	Non-uniform grid
Sheremet & Pop [73]	FDM, CDS, SOR	Lid-driven square cavity	2D, unsteady, laminar, mixed convection	Re = 102, Pr = 6.26, 10 ≤ Gr ≤ 105, 10 ≤ Le ≤ 104, N, Nb, Nt = 0.1 to 0.4	Uniform grid, 400 $\times$ 400
Sojoudi et al. [74]	Fluent, FVM	Triangular cavity	2D, natural convection, unsteady	103 ≤ Ra ≤ 106, 0.2 ≤ A ≤ 1, Pr = 0.72	15,700 triangular elements
Armaghani et al. [75]	FVM, SIMPLE	L-shaped cavity with baffle	2D, steady, natural convection	Pr = 0.71, 104 ≤ Ra ≤ 106, 0.1 ≤ A ≤ 0.7, 0 ≤ Bf ≤ 0.3, 0 ≤ $\chi$ ≤ 0.04, Al2O3-H2O nanofluid	Uniform grid, 100 $\times$ 100
Jmai et al. [76]	FVM, QUICK, SOR, multigrid	Double lid-driven square cavity	2D, unsteady, laminar, mixed convection	10−2 ≤ Ri ≤ 102, 0 ≤ $\chi$ ≤ 0.1, Cu–H2O nanofluid	Non-uniform grid, 64 $\times$ 64
Kareem et al. [77]	Fluent, URANS, LES, FVM, SIMPLE	Cubic lid-driven cavity	3D, unsteady, mixed convection, turbulent	Re = 5000, 10,000, 15,000 and 30,000	Structured, non-uniform, 1,699,200 grids
Kareem et al. [78]	FVM, UDS, SIMPLE	Lid-driven trapezoidal cavity	2D, mixed convection	0 ≤ $\chi$ ≤ 0.04, 0.1 ≤ Ri ≤ 10, 102 ≤ Re ≤ 1200, 0 ≤ $\phi$ ≤ 60, 0.5 ≤ A ≤ 2, H2O based Al2O3, CuO, SiO2, TiO2 nanofluids	Unstructured, non-uniform 5470 grids
Mamourian et al. [79]	FVM, SIMPLE	Lid-driven square cavity	2D, steady, laminar, Mixed convection	10−2 ≤ Ri ≤ 102, 0 ≤ $\chi$ ≤ 0.1, Gr = 102, Am = 0.25, Cu–H2O nanofluid	Structured non-uniform, 101 $\times$ 201
Mejri et al. [80]	LBM	Triangular cavity	2D, natural convection, laminar	103 ≤ Ra ≤ 106, 0 ≤ $\phi$ ≤ 315, Ma = 0.1	-
Rahmati et al. [81]	LBM	Double lid-driven cavity	2D, mixed convection, laminar, steady	Gr = 100, Pr = 6.57, 10−2 ≤ Ri ≤ 102, 0 ≤ $\chi$ ≤ 0.06, Cu-H2O nanofluid	100 $\times$ 100
Rashad et al. [12]	FVM, ADI, SIMPLE, UDS, CDS	Lid-driven square cavity	2D, mixed convection, laminar	0 ≤ Ha ≤ 100, 10−3 ≤ Ri ≤ 10, 0 ≤ $\chi$ ≤ 0.01, Cu-H2O nanofluid	Uniform grid, 81 $\times$ 81
Selimefendigil & Öztop [82]	FEM, ALE	Lid-driven inclined square cavity	2D, steady	10−2 ≤ Ri ≤ 102, 0 ≤ $\chi$ ≤ 0.05, 103 ≤ Rai ≤ 106, 0 ≤ Ha ≤ 50, 0 ≤ $\phi$ ≤ 90, 5$\times$ 102 ≤ E ≤ 106, CuO-H2O nanofluid	Non-uniform mesh, 10,916 nodes
Selimefendigil & Öztop [83]	FEM, FSI, ALE	Triangular cavity	2D, natural convection, steady	104 ≤ Ra ≤ 106, 104 ≤ Rai ≤ 107, 0 ≤ Ha ≤ 40, 0 ≤ $\phi$ ≤ 90, Pr = 7.1, 5 $\times$ 102 ≤ E ≤ 105	-
Selimefendigil et al. [84]	FEM, NR	Lid-driven square cavity	2D, Mixed convection	10−2 ≤ Ri ≤ 102, 0 ≤ Ha ≤ 50, 0 ≤ $\phi$ ≤ 90, 0 ≤ $\chi$ ≤ 0.05, CuO-H2O nanofluid	Non-uniform,. 17,408 elements
Sojoudi et al. [85]	FVM, QUICK, SIMPLE	Triangular cavity	2D, unsteady, natural convection	103 ≤ Ra ≤ 106, 0.2 ≤ A ≤ 1.0, Pr = 0.72	15,600 triangular elements
Sojoudi et al. [86]	FVM, QUICK, SIMPLE	Triangular cavity	2D, unsteady, natural convection	103 ≤ Ra ≤ 106, 0.2 ≤ A ≤ 1.0, Pr = 0.71	360 $\times$ 75, 360 $\times$ 90, 360 $\times$ 120 for A = 0.2, 0.5, 1
Aparna & Seetharamu [87]	FEM	Porous trapezoidal cavity	2D, natural convection	100 ≤ Ra ≤ 2000	41 $\times$ 41
Alsabery et al. [88]	COMSOL, FEM	Trapezoidal cavity	2D, unsteady, non-Newtonian, laminar	104 ≤ Ra ≤ 106, 0 ≤ $\chi$ ≤ 0.2, 0.1 ≤ Pr ≤ 103, 0 ≤ $\phi$ ≤ 21.8, H2O based TiO2, Cu, Al2O3, Ag nanofluids	Non-uniform, 4690 elements
Al-Weheibi et al. [89]	COMSOL, FEM	Trapezoidal enclosure	2D, natural convection, unsteady, laminar	103 ≤ Ra ≤ 106, 0 ≤ $\chi$ ≤ 0.1, 0.25 ≤ A ≤ 1.0	6-noded 403,388 elements, 204,436 grids
Balla et al. [90]	FEM	Inclined porous square cavity	2D, free convection, laminar	0.01 ≤ $\chi$ ≤ 0.3, 101 ≤ Ra ≤ 103, 0 ≤ M ≤ 10, 0 ≤ $\phi$ ≤ 90, H2O based TiO2, Cu, Al2O3, SiO2 nanofluids	6-noded triangular grid, 5000 elements, 2601 nodes
Cui et al. [91]	FVM	Prismatic enclosure	3D, unsteady, natural convection	100 ≤ Ra ≤ 106, Pr = 0.71	Non-uniform grid, 100 $\times$ 66 $\times$ 45
Das et al. [92]	FEM	Square & triangular cavities	2D, steady, laminar	Pr = 0.7, 103 ≤ Ra ≤ 105	34 $\times$ 34 biquadratic elements
Gangawane [93]	Fluent, FVM, SIMPLE, QUICK	Lid-driven cavity with triangular block	2D, steady, laminar, mixed convection	1 ≤ Re ≤ 103, 0 ≤ Gr ≤ 105, Pr = 1, 50, 102, b = 10%, 20%, 30%	Unstructured, non-uniform, 26,318 nodes, 9126 elements
Ghalambaz et al. [94]	FEM, FSI, ALE	Square cavity with oscillating elastic fin	2D, natural convection, laminar, unsteady	Pr = 0.7, 104 ≤ Ra ≤ 107, 10−3 ≤ Am ≤ 0.1, 1 ≤ Tr ≤ 103, 108 ≤ E ≤ 1013	27,131 domain elements, 1022 boundary elements
Gibanov et al. [95]	FDM	Lid-driven square cavity with block	2D, steady, laminar, mixed convection	10−2 ≤ Ri ≤ 10, 0 ≤ $\chi$ ≤ 0.05, Re = 102, Pr = 6.82, Al2O3-H2O nanofluid	Uniform grid, 200 $\times$ 200
Gibanov et al. [96]	FDM	Lid-driven inclined square cavity	2D, unsteady, mixed convection	Ri =1, Re = 102, Pr = 6.26, Da = 10−7, 10−3, 0 ≤ Ha ≤ 102, 0 ≤ $\chi$ ≤ 0.05, 0 ≤ $\phi$ ≤ $\mathsf{\pi }$, ferrofluid	Uniform grid, 200 $\times$ 200
Hammami et al. [97]	FVM, QUICK, RBSOR	Double lid-driven cubic cavity with cylinder	3D, unsteady	102 ≤ Re ≤ 1500, Pr	Staggered grid non-uniform, 80 $\times$ 80 $\times$ 80
Hatami [6]	FEM, FlexPDE	Rectangular cavity with heated fins	2D, steady	0.03 ≤ $\chi$ ≤ 0.09, H2O based TiO2, Al2O3 nanofluids	-
Hatami et al. [98]	FEM, RSM, FlexPDE	Lid-driven T-shaped porous cavity	2D, steady, mixed convection	Ri = 0.1, Re = 50, Da = 0.001, H2O based TiO2, Cu, Al2O3 nanofluids	-
Hussain et al. [99]	FEM, GE, CN	Double lid-driven square cavity	2D, steady, mixed convection	1 ≤ Re102, 0 ≤ $\phi$ ≤ 45, 0.01 ≤ Ri ≤ 10, 0 ≤ $\chi$ ≤ 0.04, Al2O3-H2O nanofluid	Uniform grid, 65,536 elements
Javed et al. [100]	FEM	Trapezoidal porous cavities	2D, free convection, steady	Pr = 6.2, 10−5 ≤ Da ≤ 10−3, 105 ≤ Ra ≤ 107, 0 ≤ Ha ≤ 60, 0 ≤ $\chi$ ≤ 0.03, Cu-H2O nanofluid	6 noded 704 elements, 1000 grids
Kareem & Gao [101]	Fluent, LES, URANS, SIMPLEC, QUICK	Lid-driven cubic cavity with cylinder	3D, unsteady, mixed convection, turbulent	Pr, Re = 5000, 10,000, 15,000, 30,000, 0 ≤ $\Omega$ ≤ 10	Structured, non-uniform cells, 929,160 elements
Khanafer & Aithal [102]	ADINA, FEM	Lid-driven square cavity with cylinder	2D, steady, laminar, mixed convection	0.01 ≤ Ri ≤ 10, Re = 100, −10 ≤ $\omega$ ≤ 10	150 $\times$ 150
Khatamifar et al. [103]	DNS, SIMPLE, QUICK	Rectangular cavity with partition	2D, natural convection, unsteady	105 ≤ Ra ≤ 109, Pr = 0.71, 0.05 ≤ Tp ≤ 0.2	Non-uniform mesh, 300 $\times$ 250
Mojumder et al. [104]	FEM	Lid-driven L-shaped cavity	2D, mixed convection, laminar, steady	1 ≤ Re ≤ 100, 103 ≤ Gr ≤ 105, 10−5 ≤ Da ≤ 10−3, Pr = 6.2	Triangular mesh, 4452 elements
Selimefendigil et al. [105]	FEM, ALE, FSI	Lid-driven square cavity	2D, steady	0.01 ≤ Ri ≤ 5, 0 ≤ Ha ≤ 50, 102 ≤ Re ≤ 103, CuO-H2O nanofluid	Triangular elements, 17,224 grids
Selimefendigil et al. [106]	FEM, ALE, NR	Lid-driven Trapezoidal cavity with cylinder	3D, steady, laminar, mixed convection	0.5 ≤ Ri ≤ 50, 0 ≤ $\phi$ ≤ 20, 0 ≤ $\chi$ ≤ 0.04, 103 ≤ E ≤ 105, CuO-H2O nanofluid	Tetrahedral elements
Selimefendigil & Öztop [107]	FEM, FSI, ALE	Lid-driven triangular cavity	2D, mixed convection, steady	0.05 ≤ Ri ≤ 50, 0 ≤ $\chi$ ≤ 0.04, Pr = 6.8, 104 ≤ RaI ≤ 108, 500 ≤ E ≤ 105, H2O–CuO nanofluid	Non-uniform grid, 26,306 elements
Sheremet et al. [108]	FDM	Triangular cavities	2D, natural convection	Pr = 0.7, 104 ≤ Ra ≤ 2 $\times$ 105, 102 ≤ Le ≤ 104, 0 ≤ N ≤ 5, Nb = Nt = 0.1	Uniform grid, 300 $\times$ 150
Yu et al. [3]	FDM, UCS, TVD, RK	Rectangular cavity	2D, unsteady, laminar	Pr = 0.025, A = 2, 0 ≤ Ha ≤ 50, 0 ≤ Le ≤ 20	Uniform grid, 41 $\times$ 81
Aghakhani et al. [109]	FDLBM	C-shaped cavity	2D, laminar, non-Newtonian	103 ≤ Ra ≤ 105, 0 ≤ Ha ≤ 40, 0.2 ≤ A ≤ 0.6	160 $\times$ 160
Astanina et al. [110]	FDM	Lid-driven square porous cavity	2D, steady, mixed convection	0.01 ≤ Ri ≤ 10, 0 ≤ $\chi$ ≤ 0.04, 10−7 ≤ Da ≤ 10−3, Da2 = 10−5, Re = 102, Pr = 6.82, H2O–Al2O3 nanofluid	Uniform grid, 200 $\times$ 200
Alsabery et al. [111]	FEM, FEA, NR	Double lid-driven square cavity with block	2D, steady, laminar, mixed convection	1 ≤ Re ≤ 500, 10−2 ≤ Ri ≤ 102, 0 ≤ $\chi$ ≤ 0.04, Pr = 4.623, Le = 3.5 $\times$ 105, Sc = 3.55 $\times$ 104, H2O–Al2O3 nanofluid	Uniform triangular grid, 12,232 grids
Balootaki et al. [112]	LBM-BGK	Lid-driven rectangular cavity with block	2D, mixed convection	10−2 ≤ Ri ≤ 50, Re = 100, Pr = 0.7	450 $\times$ 150
Bhowmick et al. [113]	FEM, SIMPLE, QUICK	V-shaped cavity	2D, natural convection	2.26 $\times$ 105 ≤ Ra ≤ 2.26 $\times$ 109, 0.1 ≤ A ≤ 1.0, Pr = 6.63	Non-uniform, 800 $\times$ 150
Cho [114]	FVM, TDMA, SIMPLE	Lid-driven cavity with wavy surface	2D, steady, laminar, mixed convection	10−2 ≤ Ri ≤ 102, 0 ≤ $\chi$ ≤ 0.04, 1 ≤ Re ≤ 200, Pr = 6.2, 0 ≤ Am ≤ 0.6, H2O–Cu nanofluid	101 $\times$ 1001
Gangawane et al. [115]	Fluent, FVM, SIMPLE, QUICK	Lid-driven square cavity with block	2D, steady, laminar, mixed convection	Ri= 0.01, 1, 10, Pr= 1, 1 ≤ Re ≤ 103	Unstructured, 17,874 nodes, 17,598 elements
Gibanov et al. [116]	FDM	Lid-driven square cavity	2D, mixed convection, laminar, unsteady	10−2 ≤ Ri ≤ 10, 0 ≤ $\chi$ ≤ 0.05, 1.0 ≤ K ≤ 20.0, Re = 100, Pr = 6.82, H2O–Al2O3 nanofluid	Uniform grid, 100 $\times$ 100
Hussain et al. [117]	FEM, CN, GE	Double lid-driven square cavity	2D, laminar, unsteady, mixed convection	0 ≤ $\chi$ ≤ 0.04, 10−2 ≤ Ri ≤ 10, 0 ≤ Ha ≤ 102, 0 ≤ $\phi$ ≤ 90, H2O–Al2O3 nanofluid	Non-uniform triangular grid, 65,536 elements
Javed & Siddiqui [118]	FEM	Square cavity with square blockage	2D, free convection, steady, laminar	105 ≤ Ra ≤ 107, Pr = 0.062, 0 ≤ $\chi$ ≤ 0.06, 0 ≤ Ha ≤ 60, H2O–Cobalt ferrofluid	Non-uniform, 6-noded 1776 elements
Karbasifar et al. [119]	SIMPLEC	Lid-driven cubic cavity with cylinder	3D, laminar, steady, mixed convection	10−2 ≤ Ri ≤ 102, $\chi$ = 0, 0.1%, 0.2%, $\phi$ = 0, 15, 45, H2O–Al2O3 nanofluid	-
Kareem & Gao [120]	Fluent, URANS, SIMPLEC, QUICK	Lid-driven Cubical cavity with cylinder	3D, mixed convection, unsteady, turbulent	5000 ≤ Re ≤ 104, −5 ≤ Ω ≤ 5, SiO2-H2O nanofluid	929,160 grids
Mikhailenko et al. [121]	FDM, CDS, Thomas, SOR	Rotating square cavity with obstacle	2D, laminar, unsteady	Pr = 0.7, Ra = 105, 0 ≤ $\phi$ ≤ 180, 0 ≤ Ta ≤ 106, 0.1 ≤ Os ≤ 1.0, 0.0 ≤ ε ≤ 0.9	101 $\times$ 101
Oglakkaya & Bozkaya [122]	DRBEM	Lid-driven square cavity	2D, mixed convection, unsteady, laminar	Pr = 0.71, Re = 102, Am = 0.05, Ha = 0, 25, 50, 0 ≤ $\phi$ ≤ 90, J = 0, 1, 3, 5, 103 ≤ Ra ≤ 105	400 grids
Razera et al. [123]	Fluent, FVM, SIMPLEC	Lid-driven square cavity	2D, steady, laminar, mixed convection	101 ≤ Re ≤ 103, 103 ≤ Ra ≤ 106, Pr = 0.71	Non-uniform, 33,248 volumes
Selimefendigil & Öztop [124]	FEM, COBYLA	Lid-driven trapezoidal cavity	2D, mixed convection	0.01 ≤ Ri ≤ 25, 0 ≤ Ha ≤ 40, 0 ≤ $\phi$ ≤ 90, 0 ≤ $\chi$ ≤ 0.03, H2O–Al2O3 nanofluid	6282, 4685 and 3691 elements for different $\phi$
Sheikholeslami [125]	LBM	Lid-driven square cavity with hot sphere	3D, forced convection	10−3 ≤ Da ≤ 102, 30 ≤ Re ≤ 180, 0 ≤ Ha ≤ 40, H2O–Al2O3 nanofluid	81 $\times$ 81 $\times$ 81
Sheremet et al. [126]	FDM	Porous square vented cavity	2D, mixed convection, unsteady	104 ≤ Ra ≤ 106, Nb = Nt = 10−6, 10−5 ≤ Da ≤ 10−2, 50 ≤ Re ≤ 300, Pr = 6.82, Le = 103, N = 1, H2O–Al2O3 nanofluid	Uniform grid, 201 $\times$ 201
Taghizadeh & Asaditaheri [127]	OpenFOAM, FVM. SIMPLE	Lid-driven square cavity with cylinder	2D, laminar, mixed convection	0.01 ≤ Ri ≤ 10, 10−5 ≤ Da ≤ 10−2, 0 ≤ $\phi$ ≤ 90, Re = 100, Pr = 0.7	Non-uniform, 11,200
Zhai et al. [128]	FVM, SIMPLE, QUICK	Triangular Roof	2D, unsteady, natural convection	104 ≤ Ra ≤ 107, 0.1 ≤ A ≤ 1.0, Pr = 0.71	Non-uniform mesh, 600 $\times$ 600
Zhou et al. [129]	LBM, OpenMP	Double lid-driven cubic cavity	3D, mixed convection, laminar, unsteady	0.1 ≤ Ri ≤ 102, 0 ≤ $\chi$ ≤ 0.04, H2O–Al2O3 nanofluid	101 $\times$ 101 $\times$ 101
Alnaqi et al. [130]	FDM	Square cavity with a fin	2D, laminar, steady	0 ≤ Ha ≤ 60, 103 ≤ Ra ≤ 106, 0 ≤ Rd ≤ 3, 0 ≤ $\chi$ ≤ 0.06, H2O–Al2O3 nanofluid	Uniform grid. 120 $\times$ 120
Al-Rashed et al. [131]	FVM, SIMPLEC	Inclined lid-driven cubical cavity	3D, steady, mixed convection, laminar	Re, Gr, Pr, 1 ≤ Ri ≤ 102, 0 ≤ $\phi$ ≤ 45, H2O–Al2O3 nanofluid	-
Barnoon et al. [132]	FVM, SIMPLE	Lid-driven square cavity with cylinders	2D, steady, laminar, mixed convection	0 ≤ Ha ≤ 30, 1 ≤ Ri ≤ 102, 0 ≤ $\phi$ ≤ 90, 0.01 ≤ $\chi$ ≤ 0.03, H2O–Al2O3 nanofluid	Non-uniform grid, 19,297 elements
Bhowmick et al. [133]	Fluent, FVM, SIMPLE	V-shaped triangular cavity	2D, natural convection, unsteady	1 ≤ Ra ≤ 108, A = 0.5, Pr = 0.71	800 $\times$ 150
Cho [134]	FVM, SIMPLE, TDMA	Lid-driven cavity with wavy wall	2D, laminar, mixed convection	1 ≤ Re ≤ 300, 0 ≤ Ha ≤ 50, 10−2 ≤ Re ≤ 102, 0 ≤ Am ≤ 0.7, 0 ≤ $\chi$ ≤ 0.04, 0 ≤ $\phi$ ≤ 360, Cu-H2O nanofluid	Non-uniform grid, 101 $\times$ 1001
Cui et al. [135]	FVM	Prismatic enclosure	3D, unsteady, natural convection	100 ≤ Ra ≤ 107, Pr = 0.71, 0.1 ≤ A ≤ 1.5	Non-uniform mesh, 138 $\times$ 42 $\times$ 51
Hadavand et al. [136]	FVM, SIMPLEC	Lid-driven sim-circular cavity	2D, mixed convection, laminar, steady	1 ≤ Ri ≤ 10, $\phi$ = −90 to 90, 0 ≤ $\chi$ ≤ 0.06, Ag-H2O nanofluid	Unorganized triangular grid, 44,896 grids
Hamid et al. [137]	FEM	Trapezoidal cavity	2D, steady, non-Newtonian, natural convection, laminar	104 ≤ Ra ≤ 105.5, Pr = 20	-
Jiang & Zhou [4]	FVM, QUICK, CDS, PISO	Rectangular cavity	2D, steady, laminar	0 ≤ $\chi$ ≤ 0.25, dp = 13, 36, 50 nm, distilled H2O-Al2O3, PGW-ZnO nanofluids	Non-uniform orthogonal grid, 200 $\times$ 50
Karatas & Derbentli [138]	Experimental research	Rectangular cavity	3D, unsteady	4.5 $\times$ 103 ≤ Rai ≤ 1.13 $\times$ 108, A = 1, 2.09, 3, 4, 5, 6	-
Lamarti et al. [139]	LBM	Lid-driven square cavity	2D, mixed convection, laminar	Pr = 0.71, 102 ≤ Re ≤ 103, 102 ≤ Gr ≤ 106, 1 ≤ $\omega$ ≤ 5	100 $\times$ 100
Louaraychi et al. [140]	FVM, SIMPLER, TDMA	Double lid-driven rectangular cavity	2D, unsteady, mixed convection	1 ≤ Ra ≤ 107, 0.1 ≤ Pe ≤ 500, A = 24	Uniform grid, 381 $\times$ 121
Mohebbi et al. [141]	LBM	Γ-shaped enclosure with obstacle	2D, natural convection, steady, laminar	103 ≤ Ra ≤ 106, 0 ≤ $\chi$ ≤ 0.05, 0.2 ≤ A ≤ 0.6, Al2O3-H2O nanofluid	100 $\times$ 100
Selimefendigil & Öztop [142]	FEM, ALE, NR	Lid-driven L-shaped cavity	2D, steady, mixed convection	0.03 ≤ Ri ≤ 30, 0 ≤ $\chi$ ≤ 180, 104 ≤ RaI ≤ 106, 0 ≤ Ha ≤ 50, CuO-H2O nanofluid	Non-uniform, 19,112 elements
(c)
Ref.	CFD Methods and Algorithms	Flow Domain	Dimension, Type of Flow	Parameters and Ranges	Meshing
Abu-Hamdeh et al. [143]	FVM, SIMPLE, CDS, UDS, TDMA	Lid-driven porous square open cavity	2D, mixed convection, steady	102 ≤ Re ≤ 103, 10−3 ≤ Da ≤ 0.1, 103 ≤ Gr ≤ 105	Staggered grid, 48 $\times$ 48
Afrand et al. [144]	SIMPLE	Triangular cavity	2D, free convection, laminar, steady	104 ≤ Ra ≤ 106, 0 ≤ Ha ≤ 40, 0 ≤ $\phi$ ≤ 90, 0 ≤ $\chi$ ≤ 0.06, Al2O3-H2O nanofluid	Staggered grid
Alsabery et al. [145]	FEM	Lid-driven square cavity	2D, mixed convection, steady, laminar	1 ≤ Re ≤ 500, 0.01 ≤ Ri ≤ 100, 0 ≤ Ha ≤ 50, 0 ≤ $\varphi$ ≤ 0.04, Al2O3-H2O nanofluid	Triangular grid, 6402 elements
Alsabery et al. [146]	FEM	Lid-driven cubic cavity with cylinder	3D, mixed convection, steady	Re = 10, 100, Pr = 4.623, 10−2 ≤ Ri ≤ 102, 0 ≤ $\chi$ ≤ 0.04, Le = 3.5 $\times$ 105, Sc = 3.55 $\times$ 104, Al2O3-H2O nanofluid	Non-uniform triangular grid, 175,778 elements
Bilal et al. [147]	FEM	Triangular cavity with cylinder	2D, laminar, steady, free convection	103 ≤ Ra ≤ 106, 0.2 ≤ Pr ≤ 7	Hybrid grid
Cho [148]	FVM, SIMPLE, TDMA	Square cavity with wavy walls	2D, natural convection, steady, laminar	Pr = 6.2, 102 ≤ Ra ≤ 106, 10−6 ≤ Da ≤ 10−2, 0 ≤ $\chi$ ≤ 0.04, Cu-H2O nanofluid	101 $\times$ 1001
Ganesh et al. [149]	FEM	Square Cavity with different obstacles	2D, steady, laminar	103 ≤ Ra ≤ 106, 0 ≤ $\chi$ ≤ 0.08, 103 ≤ RaE ≤ 106, 103 ≤ RaI ≤ 105 Al2O3-H2O/Ethylene Glycol nanofluid	Circular: 6979 elements, Square: 21,916 elements, Triangular: 19,431 elements
Haq et al. [150]	FEM	Lid-driven hexagonal cavity with obstacle	2D, steady	200 ≤ Re ≤ 500, Pr = 6.2, 10−6 ≤ Ri ≤ 1, 0 ≤ Ha ≤ 20, SWCNT-H2O nanofluid	Non-uniform triangular elements
Khan et al. [151]	FEM	Porous trapezoidal cavity	2D	Pr = 6.2, 102 ≤ Ha ≤ 104, 104 ≤ Ra ≤ 105, 0 ≤ $\chi$ ≤ 0.2%, Fe3O4-H2O ferrofluid	-
Li et al. [152]	FDLBM	Triangular enclosure	2D, laminar, non-Newtonian, steady	103 ≤ Ra ≤ 105, 0 ≤ Ha ≤ 60, 0 ≤ $\phi$ ≤ 90	160 $\times$ 160 or 19,600 nodes
Liu & Huang [153]	DNS, QUICK, SIMPLE, CDS	Rectangular cavities with or without fins	2D, unsteady, turbulent	1.15 $\times$ 108 ≤ Ra ≤ 3.68 $\times$ 109	Non-uniform grid, 400 $\times$ 360 cells
Rammane et al. [154]	TS, MLS, NR, HO-MFA	Lid-driven square cavity	2D, steady	102 ≤ Re ≤ 2 $\times$ 104	Mesh free
Saha et al. [155]	FVM, SIMPLE, QUICK	Triangular enclosure	2D, unsteady, natural convection	Pr = 0.72, 105 ≤ Ra ≤ 109, 0.2 ≤ A ≤ 1.0	380 $\times$ 80, 380 $\times$ 100, 380 $\times$ 160 for A = 0.2, 0.5, 1
Selimefendigil & Öztop [156]	FVM, QUICK, SIMPLE	U-shaped corrugated cavity	2D, forced convection, laminar, steady	102 ≤ Re ≤ 103, 0 ≤ Ha ≤ 50, 10−4 ≤ Da ≤ 5 $\times$ 10−2, CNT-H2O nanofluid	Non-uniform grid, 38,874 grids
Soomro et al. [157]	FEM	Lid-driven Triangular cavity with obstacle	2D, mixed convection, laminar, steady	200 ≤ Re ≤ 600, 0.01 ≤ Ri ≤ 1, 0 ≤ Ha ≤ 20, Pr = 6.2	Around 5000 nodes
Thiers et al. [158]	SEM, NeK5000, GMRES	Rectangular cavity	2D, unsteady	A = 4, Pr = 0.71, Ra = 9 $\times$ 107	183 $\times$ 169
Aljabair et al. [159]	FDM, CDS, UDS, SOR	Sinusoidal lid-driven cavity	2D, mixed convection, laminar	1 ≤ Re ≤ 1000, 0 ≤ Ra ≤ 107, 0 ≤ $\chi$ ≤ 0.07, Cu-H2O nanofluid	41 $\times$ 41
Alsabery et al. [160]	FEM	Wavy lid-driven square cavity	2D, laminar, steady, mixed convection	0.01 ≤ Ri ≤ 10, Re = 100, 0 ≤ $\varphi$ ≤ 0.04, H2O/Cu-Al2O3 hybrid nanofluid	-
Çolak et al. [161]	OpenFOAM, FVM, SIMPLE	Lid-driven cavity with porous block	2D, mixed convection, steady	10−1 ≤ Ri ≤ 10, Gr = 105, 10−7 ≤ Da ≤ 10−1, Pr = 6.2	Uniform grid, 201 $\times$ 201
Eshaghi et al. [162]	FEM	H-shaped cavity with a baffle inside	2D, natural convection, laminar	104 ≤ Ra ≤ 106, 2 ≤ Le ≤ 8, 1 ≤ N ≤ 3, −60 ≤ $\phi$. ≤ 60, Cu-Al2O3-H2O hybrid nanofluid	-
Fayz-Al-Asad et al. [163]	FEM	Triangular cavity	2D, natural convection, steady	Pr = 0.71, 104 ≤ Ra ≤ 106	6718 elements, 13,112 nodes
Hasnaoui et al. [164]	LBM, MRT, BGK	Rectangular cavity	2D, biry mixture	Sr = −0.5, 0, 0.5, 0 ≤ Ra ≤ 80, Pr = 0.71, A = 2, Le = 2	120 $\times$ 240
Hussain et al. [165]	FEM	Double lid-driven cavity with fins	2D, laminar, steady	0 ≤ Ha ≤ 100, 0 ≤ $\phi$ ≤ 90, 0.01 ≤ Ri ≤ 1, Pr = 6.2, Re = 100, $\chi$ = 0.02, Cu-H2O nanofluid	33,177 grids
Hoston et al. [166]	IEFG–RIPM	Lid-driven square cavity	2D, steady	Re = 10,000, 15,000, 20,000, 25,000, 30,000 and 35,000	150 $\times$ 150 (Refined at cavity walls)
Ibrahim & Hirpho [167]	COMSOL, FEM	Trapezoidal cavity	2D, mixed convection, laminar	Ha = 0, 50, Ri = 0.1, 1, 10, Re = 100, Am = 0.25, 0.5, 1	91 $\times$ 91
Ikram et al. [168]	FEM, ALE	Hexagonal cavity with rotating modulator	2D, forced convection, unsteady, laminar	Pr = 0.71, 102 ≤ Re ≤ 103, 103 ≤ Bi ≤ 104, 103 ≤ Ra ≤ 107	Non-uniform, 48,548 elements
Joe & Perumal [169]	OpenFOAM, FVM	Rectangular cavity containing cylinders	2D, unsteady	Pr = 0.72, Re = 1600	Unstructured triangular cells
Mondal & Mahapatra [170]	FDM, BiCGStab	Trapezoidal cavity	2D, mixed convection, steady, laminar	Pr = 6.2, N = 5, 0.5 ≤ A ≤ 2, 10−2 ≤ Ri ≤ 102, 102 ≤ Re ≤ 103, 45 ≤ $\phi$ ≤ 90, 0 ≤ $\chi$ ≤ 0.5, 20 ≤ Ha ≤ 40, 1 ≤ Le ≤ 2, Al2O3-H2O nanofluid	81 $\times$ 81
Mebarek-Oudina et al. [171]	FEM	Trapezoidal porous cavity with zigzag wall	2D, laminar, steady	0 ≤ Ha ≤ 100, 0 ≤ $\phi$ ≤ 90, 103 ≤ Ra ≤ 105, 0 ≤ $\chi$ ≤ 0.08, Cu-Al2O3/H2O hybrid nanofluid	Triangular grid, 20,296 elements
Saha et al. [172]	FVM	Rectangular cavity with baffles	2D, laminar, steady	50 ≤ Re ≤ 250 Ri = 0, 2, 4	45 $\times$ 51
Saha et al. [173]	FVM, SIMPLE, QUICK	Triangular cavity	2D, natural convection	Pr = 0.72, 103 ≤ Ra ≤ 106, A = 0.2, 0.5, 1.0	360 $\times$ 75, 360 $\times$ 90, 360 $\times$ 120 for A = 0.2, 0.5, 1
Shah et al. [174]	FEM, NR	Lid-driven trapezoidal cavity with obstacle	2D, mixed convection, steady, laminar	10−2 ≤ Ri ≤ 10, 0.1 ≤ Le ≤ 10, 300 ≤ Re ≤ 500, −10 ≤ N ≤ 10, Pr = 0.71	Non-uniform, approx. 3200 elements
Shahid et al. [175]	MRT-LBM	Triangular lid driven cavity	2D, mixed convection, unsteady	Pr = 0.71, 1, 7, 10−2 ≤ Ri ≤ 102, 104 ≤ Gr ≤ 107	-
Shahid et al. [176]	MRT-LBM	Lid-driven rectangular cavity with obtacles	2D, mixed convection, laminar	Pr = 0.71, 1, 7, 10−2 ≤ Ri ≤ 102, 103 ≤ Gr ≤ 106, A = 0.2, 0.5, 2, 5	Not clearly mentioned for different A
Shekaramiz et al. [177]	OpenFOAM, FVM, SIMPLE	Wavy triangular cavity	2D, free convection, steady	5 $\times$ 103 ≤ Ra ≤ 2 $\times$ 105, Pr = 4.6, 0 ≤ Ha ≤ 50, 0 ≤ $\phi$ ≤ 90, $\chi$ = 2%, H2O-Fe3O4 nanofluid	16,000 and 12,000 nodes
Tizakast et al. [178]	FVM, SIMPLER	Lid-driven rectangular cavity	2D, laminar, unsteady, non-Newtonian	RaT ≤ 5 $\times$ 106, Pe ≤ 103, 10−3 ≤ Le ≤ 103, 10−3 ≤ N ≤ 103, 0.6 ≤ n ≤ 1.4	Uniform grid, A = 24:381 $\times$ 121
Velkennedy et al. [179]	FDM, ADI, CDS	Rectangular vented cavity	2D, laminar, unsteady	103 ≤ Ra ≤ 106, Pr = 0.71	181 $\times$ 121
Xiong et al. [180]	FEM	Lid-driven triangular cavity	2D, mixed convection	Pr = 6.2, 0 ≤ Ha ≤ 40, 0 ≤ Re ≤ 103, 0.01 ≤ Ri ≤ 2	Uniform triangular mesh
Abbas et al. [181]	FEM	Square cavity with obstacles	2D, steady, laminar	0 ≤ $\chi$ ≤ 0.04, 10 ≤ Ha ≤ 40, 103 ≤ Ra ≤ 107, Cu-H2O nanofluid	59,173 elements
Ahmed et al. [182]	Coiflet wavelet-homotopy method	Lid-driven square porous cavity	2D, unsteady	Pr = 6.2, 10 ≤ Ri ≤ 102, 10−4 ≤ Da ≤ 10−1, 3 ≤ Le ≤ 106, Al2O3-Cu/H2O hybrid nanofluid	-
Alam et al. [8]	FEM	Semi-circular cavity	2D, unsteady, semi-circular cavity, free convection	Pr = 23.0, 6.84, 1 ≤ dp ≤ 10, 0 ≤ $\chi$ ≤ 0.05, 0 ≤ Ha ≤ 100, 104 ≤ RaT ≤ 106, ZnO, Fe3O4, Co, Al2O3, Ag nanoparticles, H2O & kerosene as base fluids	15,817 elements
Ali et al. [183]	Comsol, FEM	Lid-driven square cavity	2D, mixed convection, steady	Re = 1, 10, 102, Ha = 0, 10, 25, $\chi$ = 0, 1%, 5%, Pr = 6.2, Gr = 102, Al2O3-H2O nanofluid	Non-uniform, 30,550 nodes, 60,036 elements
Alqaed et al. [5]	FVM, SIMPLE	Rectangular cavity with triangular blades	2D, steady, laminar	103 ≤ Ra ≤ 105, 0 ≤ Ha ≤ 30, $\chi$ = 0.3, Al2O3-H2O nanofluid	150 $\times$ 450
Acharya & Chamkha [184]	FEM	Hexagonal cavity with parallel fins	2D, laminar, steady	103 ≤ Ra ≤ 105, 0 ≤ Ha ≤ 100, 0 ≤ $\chi$ ≤ 0.04, Pr = 6.2, Al2O3-H2O nanofluid	Non-uniform, 34,502 elements
Batool et al. [185]	FVM, SIMPLE	Lid-driven square cavity	2D, steady, laminar	100 ≤ Re ≤ 400, micropolar nanofluids	Staggered grid
Charqui et al. [186]	FVM, SIMPLE, TDMA	Tall partitioned cavity	2D, natural convection, laminar	Pr = 0.71, 7, A = 40	Uniform mesh, 80 $\times$ 200
Cui et al. [187]	FVM, SIMPLE	Triangular cavity	3D, natural convection, unsteady	Pr = 0.7, 102 ≤ Ra ≤ 107, 0.1 ≤ A ≤ 1.5	Non-uniform mesh, 141 $\times$ 41 $\times$ 51
Dahani et al. [188]	LBM, MRT, BGK operator	Double lid-driven square cavity	2D, unsteady	0 ≤ $\phi$ ≤ 180, Re = 102, 10−2 ≤ Ri ≤ 102, 102 ≤ Gr ≤ 106, Pr = 0.71	Uniform grid, 160 $\times$ 160
Esfe et al. [9]	Fluent, FVM, SIMPLE	U-shaped porous enclosure	2D, steady	103 ≤ Ra ≤ 105, 0 ≤ $\chi$ ≤ 0.03, Al2O3-H2O nanofluid	Approx 1600 cells
Geridonmez & Oztop [10]	Rbf-Pum	Right Isosceles triangular cavity	2D, natural convection, steady, laminar	0 ≤ Ha ≤ 100, 0.25 ≤ A ≤ 1, Pr = 6.07, Ra = 105, 0 ≤ $\chi$ ≤ 0.02, Al2O3-Cu/H2O nanofluid	1,842,025 & 1,741,596 nodes
Hirpho & Ibrahim [189]	FEM	Trapezoidal enclosure	2D, mixed convection, non-Newtonian, steady, laminar	10−1 ≤ Ri ≤ 102, Re = 100, Pr = 20, 0 ≤ $\chi$ ≤ 0.02, Al2O3-Cu/H2O hybrid nanofluid	201 $\times$ 201
Khalil et al. [190]	Fluent, FVM, RSM	Porous trapezoidal cavity with wavy wall	2D, steady	0 ≤ Ha ≤ 40, 0 ≤ Am ≤ 20, 5 $\times$ 102 ≤ Ra ≤ 2.4 $\times$ 104	320 $\times$ 320
Liu [191]	CDS, SIMPLE, QUICK	Rectangular cavity with fins	2D, free convection, unsteady	0 ≤ $\phi$ ≤ 40, Ra = 1.84 $\times$ 109	360 $\times$ 400
Noor et al. [192]	FEM	Lid-driven trapezoidal cavity with obstacle	2D, forced convection, steady	102 ≤ Re ≤ 700, 10−3 ≤ Ri ≤ 10, 0 ≤ Ha ≤ 102	Trangular grid, 4622 nodes. 8929 elements
Nouraei et al. [193]	FVM, SIMPLE	Semi-circular vented cavity	2D, mixed convection, laminar, steady	10 ≤ Re ≤ 100, 0 ≤ $\chi$ ≤ 0.06, Cu-H2O nanofluid	52,000 grids
Polasanapalli & Anupindi [194]	LBM	Concentric circular annular cavity	2D, mixed convection, unsteady	104 ≤ Ra ≤ 106, 0 ≤ Re ≤ 104, Pr = 0.71, 0 ≤ $\phi$ ≤ 360, 10−3 ≤ Ri ≤ 103	120 $\times$ 120, 180 $\times$ 180
Prince et al. [195]	COMSOL, FEM	Trapezoidal cavity with different surface	2D, natural convection	Pr = 0.716, 103 ≤ Ra ≤ 106, Materials: Pinewood, plexiglas, dry concrete, glass fiber	Rectangle: 6112, Triangle: 10,191, Sinusoidal: 5993 elements
Rahaman et al. [196]	Fluent, FVM, CDS, SIMPLE	Trapezoidal cavity	2D, unsteady, natural convection	Pr = 0.71, 100 ≤ Ra ≤ 108, A = 0.5	Non-uniform, 300 $\times$ 100
Roy et al. [197]	FEM	Square enclosure with blocks	2D, unsteady, natural convection	Pr = 6.2, 0 ≤ Rd ≤ 3, 0 ≤$\chi$ ≤ 0.09, 104 ≤ Ra ≤ 106, 0 ≤ Ha ≤ 60, Cu- Al2O3/H2O hybrid nanofluid	Triangular 65,740 elements
Shah et al. [198]	FEM, NR	Lid-driven corrugated porous cavity	2D, mixed convection, laminar, steady	102 ≤ Re ≤ 400, 0 ≤ $\chi$ ≤ 0.05, 10−5 ≤ Da ≤ 10−1, Pr = 6.2, 10−2 ≤ Ri ≤ 100, CuO-H2O nanofluid	Approx 8000 elements
Tizakast et al. [199]	FVM, SIMPLE	Lid-driven Rectangular cavity	2D, unsteady non-Newtonian, laminar	2 ≤ A ≤ 30, 102 ≤ RaT ≤ 107, 10−3 ≤ Le ≤ 103, 0.1 ≤ Pe ≤ 104	-
Xia et al. [200]	UPWIND	T-shaped lid-driven cavity	2D, mixed convection	0 ≤ $\chi$ ≤ 0.03, 0.1 ≤ Re ≤ 10, 0.2 ≤ A ≤ 0.4, Al2O3-H2O nanofluid	Uniform mesh, 250,000 cells
Zarei et al. [201]	FVM, SIMPLE	Square cavity with wavy walls	2D, steady	Ra = 104, 0 ≤ Am ≤ 0.15, 0 ≤ $\chi$ ≤ 0.04, Cu-H2O nanofluid	135,008 triangular cells
Zhang et al. [202]	FVM, SIMPLE	Semi-elliptic lid-driven cavity	2D, mixed convection, steady, laminar	0 ≤ $\chi$ ≤ 0.06, Gr = 5 $\times$ 104, 15 $\times$ 104, 25 $\times$ 104, 4 $\times$ 105, 10−1 ≤ Ri ≤ 10, Pr = 6.2, Ag-H2O nanofluid	43,905 triangular grids
Akhter et al. [7]	FEM	square cavity with cylinder	2D, steady	104 ≤ Ra ≤ 5 $\times$ 106, Pr = 6.2, 0 ≤ $\chi$ ≤ 0.05, 0 ≤ Ha ≤ 102, Cu-Al2O3/H2O hybrid nanofluid	24,961 nodes, 49,188 elements
He et al. [203]	Experimental, FVM, SIMPLE	Cubic cavity	3D	0 ≤ B ≤ 133, 0 ≤ $\chi$ ≤ 0.03, 6.9 $\times$ 105 ≤ Ram ≤ 11.6 $\times$ 105, Fe3O4-Paraffin nanofluid	50 $\times$ 50 $\times$ 50
Ikram et al. [204]	FEM, ALE	Hexagonal cavity with rotating modulator	2D, forced convection, unsteady, laminar	Pr = 0.71, 102 ≤ Re ≤ 103, 104 ≤ Ra ≤ 106, Bi = 104	49,874, 50,672 and 52,601 elements
Ouri et al. [205]	Comsol, FEM, ANFIS	L-shaped cavity with rotating cylinder	2D, unsteady	200 ≤ Re ≤ 103, 102 ≤ Rew ≤ 103, 0 ≤ Ha ≤ 40, 0 ≤ $\chi$ ≤ 0.02, Ag-MgO/H2O hybrid nanofluid	Non-uniform triangular 65,216 elements
Sayed et al. [206]	FVM, LES, URANS	Cubical cavity	3D, unsteady	Ra = 109, Pr = 0.71, Prt = 0.9	166,375 cells

4. Validations

In computational fluid dynamics (CFD), validation is an important aspect of research. It is the process of comparing the numerical results with experimental, benchmark, or numerical results to assess the accuracy of the simulation. Validation is important for several reasons: it helps to ensure that the numerical model is implemented correctly and that the solution is not affected by any errors or bugs in the code; it also allows researchers to compare their results with other studies, and it gives an idea about the accuracy of the numerical model compared with real-world data. One common way to validate CFD simulations is to compare the numerical results with experimental data. This can be conducted by comparing the velocity, temperature, and pressure fields obtained from the simulation with measurements taken in a laboratory experiment. The percentage difference between the numerical and experimental results is used as a measure of the accuracy of the simulation. A percentage difference of less than 5% is generally considered to be a good match between the numerical and experimental results. The above-mentioned studies used different types of validations, and details of some of these are presented below. Providing detailed information about the validation process in a study is important for ensuring the accuracy of the numerical results and for providing a useful resource for future research. Moreover, according to the authors’ knowledge, no such details are available in previous studies. By presenting the details of their validation studies, the authors are providing a valuable resource for future researchers. This information can be used to compare the results of new studies with previous work and to assess the accuracy of new simulations. Additionally, the figures (Figure 4, Figure 5, Figure 6, Figure 7, Figure 8, Figure 9 and Figure 10) likely provide a visual representation of the validation results, making it easier for readers to understand and interpret the data.

For a square lid-driven cavity with mixed convection flow, the variation of the average Nusselt number with different Gr for a fixed Pr of 0.71 was studied through numerical simulations or experiments. In the case of mixed convection, as the Gr increases, the Nu_avg is expected to decrease. This is due to the lid-driven motion of the cavity. Details of the results are presented in Figure 4.

Based on the validation data presented in Figure 4a–c, the following correlations (Equations (6)–(8)) are proposed. It is worth noting that all these correlations exhibit a maximum percentage error of less than 10%, which indicates a strong relationship between the provided data and the proposed equations.

$$\overline{Nu}=0.97+\frac{0.0141\ast Re\ast Pr}{1+{\left(\frac{Gr}{756.05}\right)}^{1.12}}, {10}^2\le \mathrm{Gr}\le {10}^4, \mathrm{Re}=100, \mathrm{Pr}=0.71$$

(6)

$$\overline{Nu}=1.13+\frac{0.0099\ast Re\ast Pr}{1+{\left(\frac{Gr}{2577.39}\right)}^{2.7}}, {10}^2\le \mathrm{Gr}\le {10}^4, \mathrm{Re}=400, \mathrm{Pr}=0.71$$

(7)

$$\overline{Nu}=1.595+\frac{0.068873\ast Re\ast Pr}{1+{\left(\frac{Gr}{4971.05}\right)}^{4.85}}, {10}^2\le \mathrm{Gr}\le {10}^4, \mathrm{Re}=1000, \mathrm{Pr}=0.71$$

(8)

In a square cavity with natural convection flow, the variation of Nu_avg with different Ra for a fixed Pr of 0.71 is studied throughout the literature. We know as Ra increases, the strength of natural convection increases, and the Nu_avg increases. However, the relationship between Nu_avg and Ra can be complex, as the flow pattern and heat transfer mechanisms in the cavity can vary with changing Ra. In general, for a square cavity with natural convection flow and Pr = 0.71, the variation of the Nu_avg with Ra can be explained by different values of Ra. For low Ra < 10⁴, the heat transfer is dominated by conductive heat transfer, and Nu_avg is relatively constant and low. However, for intermediate Ra (10⁴ < Ra < 10⁸), the heat transfer is dominated by a combination of conduction and convection, and Nu_avg increases rapidly with Ra due to the onset of natural convection. Such findings are explained in Figure 5.

Based on the results displayed in Figure 5a,b, a novel correlation is introduced for the computation of Nuavg, which is presented below. The correlation (Equation (9)) exhibits a high level of consistency with the aforementioned findings, with an error range of 1.4% to less than 10%. In a few instances, the maximum error is found to be approximately 13%, but this is attributed to the researcher’s recording of low Nu_avg values.

$$\overline{Nu}=0.44+\frac{35.68\ast Pr}{1+{\left(\frac{Re}{5558557.57}\right)}^{-0.41}}, {10}^3\le \mathrm{Ra}\le {10}^6,\mathrm{Pr}=0.71$$

(9)

As shown in Figure 6, for a fixed Pr = 0.71 and low Gr = 100 in mixed convection flow in a square lid-driven cavity, Nu_avg always increases with increasing Re. This is because at low Gr, the buoyancy forces are weak, and the flow is dominated by the lid-driven motion. As Re increases, the flow becomes more vigorous, resulting in increased mixing and enhanced heat transfer.

Based on the findings depicted in Figure 6, a novel correlation for computing Nu_avg is introduced and presented below. The proposed correlation (Equation (10)) exhibits a strong association with the provided data, with a minimum and maximum error of 0.01% and 7.30%, respectively. However, for some of the given data, a higher percentage of error is observed, which is not attributable to the correlation, but rather is due to poorly recorded research data obtained by the researcher.

$$\overline{Nu}=0.9969+\frac{18.3538\ast Pr}{1+{\left(\frac{Re}{1390.5345}\right)}^{-0.93}}, 1\le \mathrm{Ra}\le {10}^3,\mathrm{Pr}=0.71$$

(10)

We know that an increase in the aspect ratio leads to an increase in the heat transfer rate. This is because an increase in the aspect ratio leads to an increase in the surface area available for heat transfer. As a result, there is more area for the fluid to exchange heat with the solid surfaces, leading to a higher heat transfer rate. Additionally, an increase in the aspect ratio can also promote greater fluid mixing and circulation, which further enhances the heat transfer rate. We also know that Nu_avg increases with increasing Ra for a porous square cavity case. At low Ra, the flow is dominated by conduction, and the heat transfer is primarily governed by thermal conduction. As Ra increases, the buoyancy forces become more significant, resulting in increased flow circulation and mixing. This enhanced mixing leads to an increase in the heat transfer rate and Nu_avg. Such findings are presented in Figure 7 and Figure 8, that is observed by a different researcher.

Based on the results depicted in Figure 7, a new correlation for determining Nuavg is proposed and put forward. The correlation (Equation (11)) demonstrates a high level of accuracy, with a minimum error of 0.08% and a maximum error of 9.93%. These findings suggest that the correlation has significant potential for future use.

$$\overline{Nu}=1.04+\frac{0.57}{1+{\left(\frac{Ra}{12499.08}\right)}^{-0.76}}, 3\times {10}^3\le \mathrm{Ra}\le 2\times {10}^4$$

(11)

Figure 9 presents the variation of Nu_avg with different nanoparticle concentrations (C) for Al₂O₃ nanofluid. It is observed that Nu_avg slightly decreases with the increase in C. The decrease in Nu_avg with increasing C may be due to several factors, such as the nanoparticles may aggregate at high concentrations, leading to a decrease in effective surface area and, thus, a decrease in convective heat transfer.

Based on the outcomes presented in Figure 9, a new correlation is suggested for computing Nu_avg. This correlation (Equation (12)) demonstrates a robust concurrence with the results of earlier studies, with an error range of 0.01% to a maximum of 5.41%.

$$\overline{Nu}=27.06+\frac{4.38}{1+{\left(\frac{C}{0.03}\right)}^{4.9}},1\%\le \mathrm{C}\le 3\%$$

(12)

Figure 10 shows that the Nu_avg increases with increasing Ra for a fixed Pr = 100, which indicates an enhancement of convective heat transfer. However, the rate of increase depends on the power-law index n. It is also seen that Nu_avg slightly increases with the increase in n. It indicates that the non-Newtonian behavior of the fluid has a small effect on the convective heat transfer in the fluid.

Based on the data depicted in Figure 10, two correlations (Equations (13) and (14)) are proposed with minimum and maximum errors of 0.06% and 3.41%, and 0.01% and 7.69%, respectively. These correlations demonstrate excellent agreement with the provided data.

$$\overline{Nu}=\frac{0.01105\ast Pr}{1+{\left(\frac{n}{4.3431}\right)}^{1.5247}},0.1\le n\le 2.0, \mathrm{Ra}={10}^4, \mathrm{Pr} =100$$

(13)

$$\overline{Nu}=\frac{0.061826\ast Pr}{1+{\left(\frac{n}{0.1494}\right)}^{0.851}},0.1\le n\le 2.0, \mathrm{Ra}={10}^5, \mathrm{Pr} =100$$

(14)

5. Heat Transfer Analysis

According to the above-mentioned literature, the flow behavior inside the cavities can be classified into the following categories: effect of the applied boundary conditions to walls such as temperature difference, localized heat sources, magnetic field, or inlet flow to the cavity through a specific port(s). The other types of cavities use internal fins or cylinders to drive the flow inside the cavity. Some of the above-mentioned references (Given in Table 1) are discussed below:

5.1. Square Cavity

In the study by Abbas et al. [181], the effect of using Cu-water nanofluid on heat transfer enhancement was investigated inside a square cavity, using two circular heated obstacles and applying a constant magnetic field. They found that Nu_avg improved with the rise of Ra up to a certain point and then showed a negligible variation. However, for lower values of Ra, Nu decreased with Ha. Additionally, the increase in nanoparticle concentration resulted in a decrease in the heat transfer rate for each value of Ha. The study also found that the increase in magnetic field intensity led to a decrease in the rate of heat transfer because of the high sensitivity of Cu nanoparticles to the applied magnetic field. In the study by Roy et al. [197], the flow behavior inside a square cavity filled with MHD hybrid Cu-Al₂O₃/H₂O nanofluid was investigated. A cold elliptical block and a hot square block were inserted inside the cavity, and all four walls were set at the same temperature as the elliptical object. The results of the study confirmed that the local Nu increased with Ra and decreased with an applied magnetic field. Additionally, the presence of nanoparticles enhanced the heat transfer rate. The study also found that Ha had a stronger effect on local and average Nu at high values of Ra. Furthermore, high Rd led to an improvement in the rate of heat transfer. In the study by Zarei et al. [201], the flow of a Cu-H₂O nanofluid inside a square cavity with a wavy left wall and straight other walls was investigated, with a uniform heat flux applied to the left vertical wall and a constant temperature on the right vertical wall, while the other boundaries were adiabatic. They found that increasing the nanoparticles concentration and decreasing the wavelength and amplitude of the wavy wall led to an increase in Nu_avg. In the study by Akhter et al. [7], the flow of a hybrid nanofluid Cu-Al₂O₃/H₂O inside a square cavity was investigated. A heat-conductive circular solid was placed at the center of the cavity. The bottom and top boundaries of the cavity were partially heated and cooled, respectively. Their results confirmed that the heat transfer was enhanced with the Ra and decreased with the Ha. They also found that the thermal performance increased linearly with an increase in χ. For the nanoparticles volume fraction of 1% and 5%, there was an increase in heat transfer by 47.74% and 106.78%, respectively, as compared to the base fluid.

5.2. Rectangular Cavity

The study by Wee et al. [2] found that the rate of heat transfer in a rectangular cavity full of air is significantly higher when the cavity is in a vertical position with upwards transfer compared to a horizontal position with the downward transfer. Al-Farhany & Turan [39] found that using a rectangular porous cavity with left and right boundaries at various temperatures and insulated top and bottom walls, the flow inside the cavity was driven by buoyancy, and the results showed that the highest Nu_avg occurred at zero inclination for high Ra, while for low Ra, the maximum Nu_avg was found at 60 degrees inclination. Additionally, the results showed that as the aspect ratio and Le increase, Nu_avg decreases and Sh increases. Elsherbiny & Ragab [51] studied an inclined rectangular cavity with a hot spot at the bottom wall and insulated surfaces. They found that as the aspect ratio increases, Nu_avg decreases, and when the local heat source position was at the middle or quarter position of the bottom wall, the maximum Nu_avg occurred at specific aspect ratio values. Moreover, they found that Nu_avg increases with increasing tilt angle (φ) from 0 to 75 degrees, then starts to decrease until 150 degrees and remains constant up to 180 degrees. Elsherbiny & Ismail [69] studied an oblique rectangular cavity with two local heat sources at the bottom wall and insulated surfaces. They found that Nu_avg increases until φ’s reaches 60 degrees and then starts to decrease until it reaches a minimum value at 180 degrees. They also found that at a tilt angle of 150 degrees, the effect of Ra on Nu_avg is very low, and at 180 degrees, Nu_avg becomes independent of Ra. Additionally, they observed that Nu_avg decreases by 23% when the aspect ratio reaches 10. Hatami [6] numerically investigated the free convection and flow of nanofluids in a rectangular cavity with two heated fins installed on the cold lower and upper walls while the vertical walls were insulated. They found that Nu_avg was higher for higher volume fractions of Al₂O₃ and similarly for lower volume fractions of TiO₂. Additionally, they observed that Nu_avg increases as the height of the fins increases. Yu et al. [3] studied numerically the effect of the magnetic field and electric source on the flow characteristics and heat and mass transfer of electrically conducting fluid inside a rectangular cavity. It was found that with the increase in the density of the magnetic field, the oscillatory flow became more stable, and heat transfer by convection and mass transfer was reduced. Moreover, it was also found that the magnetic field had no effect on Nu_avg, which only varied with dimensionless heat generation or absorption coefficient, while Sh remained equal to one.

Jiang and Zhou’s [4] study examined the impact of nanofluids on surface tension in a rectangular cavity. They applied a temperature difference across the vertical walls and a free surface on the upper surface. They found that for distilled water-Al₂O₃ nanofluid, a rise in nanoparticles volume fraction led to convective flow being dominated by the fluid’s thermophysical properties and the surface tension temperature coefficient. For PGW-ZnO nanofluid, an increase in nanoparticle concentration resulted in convective flow being mainly controlled by the surface tension temperature coefficient. Karatas and Derbentli’s [138] study investigated free convection flow in a partially heated rectangular cavity with various aspect ratios. They kept the temperature of the vertical cold boundary constant, and the temperature of the hot boundary was a time-periodic temperature. They observed that Nu_avg increased from 2.64 to 16.44 as the aspect ratio decreased from 6 to 1. Thiers et al. [158] explored the impact of local thermal disturbances (one on the cold side and the other on the hot side) on the flow instability in a rectangular enclosure with an aspect ratio of 4.0. They considered the left boundary as a hot boundary, while right boundary as a cold boundary, and the top and bottom walls as adiabatic. Their research showed that the highest heat transfer enhancement occurred when the local disturbance area was located at L_h= 0.7 and/or L_c = 0.3. Hasnaoui et al. [164] studied thermo-solutal convection in a rectangular cavity. They found that the flow became unstable for Sr = 0 and −0.5 and remained unstable until R = 20. They also observed that the rate of heat transfer was strongly impacted by thermo-diffusion in the range of R, leading to instabilities. Alqaed et al. [5] performed a numerical simulation to study the natural convection heat transfer and entropy generation of alumina-water nanofluid flow in a rectangular cavity. They installed two hot triangular blades on the bottom wall, and the two sidewalls were adiabatic, whereas the upper wall was set at a low temperature and the bottom wall was set at a high temperature. They found that a rise in Ra led to an increase in Nu_avg and entropy generation, but it decreased Be, and the increment in Ha also led to reducing Be for higher Ra. They reported that the maximum values of Nu_avg, entropy generation, and Be occurred at a cavity inclination of 30 degrees. Liu [191] examined the convection heat transfer behavior inside a rectangular cavity with an adiabatic fin fixed on each of the side walls. The top and bottom boundaries were adiabatic, while the left boundary was cold, and the right boundary was hot. The study found that Nu_avg increased by 5% for the finned cavity as compared to the non-finned one. Additionally, Nuavg for both cases increased with the angle of inclination until 5 degrees and then decreased.

Sasaguchi et al. [14] studied the heat transfer analysis numerically in a rectangular cavity containing water. All boundaries were insulated and cold (−10 °C), including the internal presence of single or double cylinder inside the cavity. The study found that the solidification speed for a single cylinder was faster than double cylinders for a temperature equal to 0 °C, while the solidification was faster for the double cylinders for a temperature higher than 4 °C. Liu & Huang [153] investigated the effect of adding thin fins to the middle of the high and low-temperature walls of a rectangular cavity, with the top and bottom walls being considered as insulated walls. They applied a linear temperature distribution to the hot and cold side walls. The study found that the effect of the adiabatic horizontal thin fin led to a change in the convective flow attached to the middle of the sidewall. Nu_avg correlated well with Ra^0.25 for all three thermal heating conditions examined. However, when the slope of the applied linear temperature distribution was negative to both the right and left walls, Nu_avg was lower than the other two heating conditions.

Joe and Perumal [169] studied the influences of rotating cylinders on the mixing and distribution of temperature within a rectangular cavity. They found that the best results were obtained when the cylinders were close to the middle line and rotated in the same direction. This resulted in improved mixing and a more uniform temperature distribution. Saha et al. [172] studied free convection flow inside a rectangular cavity with isothermally heated baffles. They concluded that the flow velocity and heat transfer interaction efficiency were highest for the case of plane baffles, where fluid was blended more effectively as the length of the baffles increased. They also found that the maximum value of Nuavg was achieved at Re = 250 for plane baffles. Additionally, they found that the heating efficiency increased with Re and Ri and decreased as the length of the baffles increased. Velkennedy et al. [179] investigated the air-flow behavior inside a ventilated rectangular cavity with two outlets and one inlet. The inlet vent was positioned on the bottom of the right wall, and the outlets were put on the top wall. Both vertical walls were considered hot walls, and the bottom wall was adiabatic. They found that the rate of heat transfer to the right wall was reduced at the upper part of the cavity due to the introduction of a cold partition. However, they also found that the heat transfer rate increased significantly with the introduction of the cold partition for lower Ra, and this difference was reduced for higher Ra. Ait-Taleb et al. [58] studied the flow behavior inside a building block that generally contains three air cavities in the horizontal orientation and two in the vertical orientation. They found that by keeping the temperatures of the upper and lower walls the cold outside and hot inside, respectively, the hollow block with two air cells deep in the vertical direction allowed for a significant reduction in heat transfer between the inside and outside of the building. Charqui et al. [186] numerically investigated the heat transfer and free convection flow inside a tall thin partitioned cavity, where the left and right parts were filled with air and water, respectively. They found that even though the partition was thin, air and water behaved differently. The temperature of the inside wall had less effect by solar flux than the heat flux through the partition. The wall opposite to sunlight was kept at 20 degrees Celsius, and the temperature of the other surface was varied between 0 degrees Celsius to 50 degrees Celsius. The other surfaces were assumed to be adiabatic.

5.3. Other Cavity Types

Alam et al. [8] investigated the effect of various types of nanofluids on thermal behavior inside a semicircular cavity that was exposed to a periodic magnetic field. They used nanoparticles such as ZnO, Fe₃O₄, Co, Al₂O₃, and Ag and base fluids such as water and kerosene. The bottom surface was exposed to non-uniform parabolic heating, while the circular surface was set at a fixed cold temperature. They found that the highest value of Nu_avg was obtained for Co-kerosene nanofluid by 588.197% for χ = 5%. They also found that for a specific value of χ, there was a slight rise in Nu with the augmentation of Ra. The study also revealed that the variable magnetic field and the Brownian motion of nanoparticles had a significant effect on heat transmission enhancement. Additionally, the findings indicated that a non-uniform magnetic field showed higher heat transmission than a uniform case. Acharya & Chamkha [184] studied the thermal and fluid flow behavior of Al₂O₃-H₂O nanofluid inside a hexagonal enclosure. The enclosure had three parallel fins inside, with the right and left fins being cooled and the middle one being heated. The top lid was partially heated, while the bottom boundary was fully heated, and the other boundaries were assumed to be adiabatic. The study also applied a horizontal magnetic field to the cavity. The results presented that the local Nu and Nu_avg increased with the increase in Ra, and the u-shaped fins gave the highest outcomes. Additionally, local Nu and Nu_avg decreased with Ha. The study found that the increase in the fin’s height led to an increase in the rate of heat transfer, and the central position of the fins was the optimized position that gave the highest rate of heat transfer. Esfe et al. [9] studied the effect of using Al₂O₃-H₂O nanofluid in a U-shaped porous cavity on heat transfer and fluid flow. They found that Nu_avg reduced with the increase in Ra and χ. However, Nu_avg decreased when Da increased from 0 to 60, indicating that the porous structure had an impact on the heat transfer enhancement. Overall, the study provided insights into the utilization of nanofluids and porous structures to improve heat transfer in U-shaped cavities. Geridonmez & Oztop [10] studied the influence of an oblique partial periodic magnetic field on the free convection of hybrid Al₂O₃-Cu/H₂O nanofluid inside an isosceles triangular cavity. They considered three cases with different wall temperatures and magnetic field orientations and found that the heat transfer rate was reduced with an increase in Ha and that a horizontal magnetic field provided a higher rate of heat transfer than the other cases. Hirpho and Ibrahim [189] studied the mixed convection of a hybrid nanofluid (Al₂O₃-Cu/H₂O) in a trapezoidal cavity with a partially heated bottom wall, cold left and right walls, and an adiabatic top lid. They found that the local Nu number increased with the rise of χ, the Casson fluid parameter, and Ri. This indicates that the rate of heat transfer in the cavity is improved by the presence of nanoparticles, the non-Newtonian behavior of the fluid, and the buoyancy forces.

Khalil et al. [190] examined the free convection in a trapezoidal cavity with a wavy bottom wall filled with pure water and saturated metal foam as a porous medium. The top and side boundaries were kept at a cold temperature while the bottom surface was heated. The study found that Nu_avg increased as the number of waves and amplitude of the bottom wall’s waves increased. Additionally, Nuavg improved when the cold temperature of the sides and top walls was decreased. Furthermore, an increase in Ha resulted in an increase in Nu_avg. Nouraei et al. [193] explored mixed convection of an H₂O-Cu nanofluid in an open semicircular cavity. The circular section was partially heated along 45 degrees at four different angles, and all other positions were insulated. The study found that the local Nu number increased from the inlet to the outlet along the curved surface for a Re of 100. Additionally, the results showed that the maximum Nu_local was obtained for χ = 0.06 for all cases. Prince et al. [195] investigated the conjugate natural convection inside a trapezoidal cavity with a thick base and different surface corrugations, such as flat, sinusoidal, and triangular surfaces. The base was made of different materials, such as pinewood, plexiglas, dry concrete, and glass fiber. The base was set isothermally hot while the top wall was kept isothermally cold, and the side walls were adiabatic. The study found that there was a considerable improvement in convection heat transfer for high Ra up to the value of Ra > 10⁴. Moreover, the glass fiber showed the highest Nu_avg and the lowest dimensionless fluid temperature. For Ra ≤ 10⁴, the conduction heat transfer mode would be dominant. This suggests that the corrugated surface of the cavity base and the material of the base can significantly enhance the heat transfer rate, but the effect becomes less significant for lower Ra. Rahaman et al. [196] studied the natural convection of air inside a valley-shaped trapezoidal cavity, where the top and bottom walls were considered hot and cold, respectively, and both the side walls were adiabatic. The study found that Nu was small at the beginning for stratified air and gradually increased in the transitional phase when the stratification was broken and became fixed for Ra ≤ 10⁶. After that, Nu exhibited oscillatory behavior for Ra ≥ 10⁷.

He et al. [203] discussed the effect of a magnetic field on a phase change nanocomposite inside a cubical cavity filled with. The nanocomposites were obtained by adding Fe₃O₄ nanoparticles into paraffin. The left wall was set as a hot boundary while the other walls were insulated. The study found that, without applying a magnetic field and with a uniform distribution of the nanoparticles in the paraffin, the rate of heat transfer was increased. However, when a magnetic field was applied, the melting rate of paraffin was reduced. Ikram et al. [204] studied the heat transfer behavior inside a hexagonal enclosure equipped with different types of rotating modulators. A uniform heat flux was applied to the bottom inclined wall while the top was exposed to ambient temperature. The other two vertical walls were insulated. The results presented that the increase in Re from 100 to 1000 improved heat transfer by 57.1%. An inverse relationship between thermal storage capacity and thermal effectiveness was also observed, which means that as the thermal storage capacity increases, the thermal effectiveness decreases. Ouri et al. [205] studied the effect of convective heat transfer in an L-shaped vented cavity that contained an inner rotating cylinder. The cold fluid entered the cavity through the top lid, while the lower wall was hot, and the remaining boundaries were adiabatic. Their findings showed that Nuavg, the average Nusselt number, increased by 180% for the highest Re and 19% and 8% for cylinder rotational speeds of 1000 and −1000, respectively. In addition, the spatial Nuavg, which is the Nusselt number at different points within the cavity, showed an increase by varying the cylinder size up to 86% and 33.5% at cylinder rotational speeds of 1000 and −1000, respectively.

5.4. Lid-Driven Cavity

5.4.1. Square Cavity

In a study by Moallemi & Jang [11], the hydraulic and thermal behaviors in a square cavity were examined when a shearing force was applied by moving a glass sheet on the top wall and combined with the buoyancy force from heating the bottom wall. The results showed that the influence of buoyancy was clearer on heat transfer for higher values of Pr with constant Re and Gr. Additionally, for a minimum level of buoyancy, forced convection heat transfer was dominant and independent of Ri. The study also found that as buoyancy increased, the heat transfer mechanism transitioned from forced convection to mixed convection, with Nu_avg being a function of Pr. In a study by Chamkha & Abu-Nada [42], the mixed convection of a water-Al₂O₃ nanofluid flow in single and double lid-driven square cavities was examined using different nanofluid viscosity approaches. The top lid-driven wall was kept at a constant hot temperature, while the bottom lid-driven wall was set at a cold temperature. The results showed that at moderate and large Ri, the increase in χ led to an improvement in the rate of heat transfer for single and double-lid-driven cavities for both the Pak and Cho correlation and the Brinkman model. Additionally, in the single lid-driven cavity and for small Ri, Pak and Cho’s correlation predicted a reduction in Nu_avg. However, for other conditions, an increase in Nu_avg was predicted by the Pak and Cho correlation, which was larger than the Brinkman model for all values of χ. In a study by Ahmed et al. [48], a numerical examination of MHD mixed convection flow in an oblique lid-driven square enclosure with an opposite temperature gradient was conducted. The sinusoidal temperature distribution was applied to the right and left walls, the top wall was considered as a moving boundary, and a zero velocity was considered for the bottom wall. The results showed that the increase in Ha had no effect on heat transfer on both vertical walls. Additionally, the rate of heat transfer enhanced with Ha and ϕ increased in the case of opposing buoyancy-driven convection. For forced convection, Nu_local increased on the left wall while it decreased on the right wall when the amplitude ratio of the sinusoidal temperature increased. In the study by Muthtamilselvan & Doh [63], the authors numerically investigated the heat transfer behavior of a Cu-H₂O nanofluid flowing in a lid-driven square cavity. They found that Ri had a small effect on heat transfer except for Ri = 4, where a non-linear relationship between the Nusselt number and the volumetric solid fraction was observed. They also found that for non-uniform heating, a sinusoidal behavior of local heat transfer was attained, and a maximum heat transfer occurred in the middle of the bottom wall. In the study by Pekmen & Tezer-Sezgin [209], the authors investigated the mixed convection flow behavior inside a lid-driven square cavity filled with porous media with the application of a magnetic field. The top wall was hot and moving, the bottom wall was cold and fixed, and the vertical walls were adiabatic. They found that as Ha increased, Nu_avg decreased due to the retarding effect of the Lorentz force. Additionally, they observed that as Da decreased, the heat transfer became more conductive even as Re increased.

In the study by Ray & Chatterjee [65], the authors discussed the influences of an external magnetic field on an electrically conducting fluid inside a lid-driven square cavity with a conducting cylindrical body inserted. The top wall was moving and fixed at a cold temperature. They found that a rise in Ri led to an enhancement in the rate of heat transfer and fluid temperature, while the presence of a magnetic field reduced the heat transfer rate. Moumni et al. [71] conducted a study on heat transfer and mixed convection flow and behavior in a square cavity with double lid-driven filled with different types of nanofluids. They found that adding nanoparticles to the fluid led to an improvement in the heat transfer rate, with copper and silver nanoparticles showing the highest heat transfer rate due to their high thermal conductivity. They also found that the rate of heat transfer raised with the increase in Ri and Re for constant nanoparticles concentration. Selimefendigil and Öztop [210] conducted a study on the effect of two rotating cylinders on mixed convection of ferrofluid flow inside a square cavity. They found that the enhancement of the Nu_avg was 181.5% for a negative angular speed ratio (Ω = −400) and 181.6% for a positive angular speed ratio (Ω = 400). They also found that the rise in the angular speed ratio caused an increase of 91.7% in Nu_avg and that an 88.9% enhancement in Nu_avg was achieved when the diameter ratio of the cylinders was changed from 2 to 0. Sheremet and Pop [73] conducted a numerical analysis on the mixed convection of a nanofluid flow inside a lid-driven square cavity where both the top and bottom walls were moving in opposite directions. The top and bottom walls were considered hot and cold walls, respectively. Their results showed that the heat transfer mechanism depends strongly on Ri and the moving parameter. They also found that Nu slightly increased with Le except in the counter-direction of moving horizontal walls, where Nu decreased with Le. Jmai et al. [76] conducted research on the effect of a partially heated wall on mixed convection Cu/H₂O nanofluid flow inside a lid-driven square cavity. Each vertical side wall contains a heat source of high temperature, and both the upper and lower boundaries can move in the same and opposite directions and are considered cold. Their results showed that for all speed ratios, Nu increased as Ri decreased. The maximum value of Nu = 54.41 was observed when the speed ratio = −2 and Ri = 0.01.

Rashad et al. [12] conducted a study on MHD mixed convection Cu–water nanofluid flow in a lid-driven square cavity. The upper and lower walls were moving opposite to each other and were considered adiabatic. The right vertical wall was partially heated, and the left wall was partially cold; the other parts of the vertical boundaries were adiabatic. Their results revealed that the highest heat transfer occurred when the size of the heat source was as small as possible and placed at the middle position of the walls. They also concluded that heat transfer decreased with the increase in Ri. The presence of a magnetic field was found to reduce the convective heat transfer, and the presence of nanoparticles led to a decrease in the Nu. Selimefendigil et al. [84] conducted a numerical analysis to study the effect of Ri, Ha, magnetic field inclination angles, and the combination of upper and lower diagonal domains on the hydraulic and thermal behavior inside a lid-driven square cavity. They found that Nu_avg decreased by 80.14% when Ri increased from 0.01 to 100 for inclinations angles of 90 and 0 degrees. They also found that increasing the magnetic inclination angle of the upper triangular domain led to a higher average heat transfer compared to increasing the magnetic field in the lower triangular domain. Selimefendigil & Öztop [82] studied the mixed convection inside a lid-driven square cavity with nanofluid. The cavity had elastic side walls, where the left boundary was moving upward and fixed at a constant temperature, while the right wall was a hot one. They concluded that the rate of heat transfer is increased with increasing Ri, Ha, and nanoparticles concentration. However, the rate of heat transfer is decreased with the increasing inclined angle of the magnetic field. Additionally, the study found that the influence of elasticity on the heat transfer rate is considerable, where it increased with increasing elasticity. In the study by Gangawane [93], mixed convection heat transfer was numerically explored in a top lid-driven square cavity with a triangular heated block and constant heat flux. The top wall was moving while the other walls were kept stationary, and the upper and lower boundaries were adiabatic while the vertical boundaries were at ambient temperature. Nu_avg increased up to a Re_cr between 190–220 and then began to decrease, particularly for Gr greater than 50. In the study by Gibanov et al. [95], Al₂O₃-H₂O nanofluid flow was numerically studied in a lid-driven square cavity. The upper wall was hot and moving, while the bottom wall was fixed and cold. Nu_avg was found to decrease with an increase in Ri and the backward step ratio.

The study by Khanafer and Aithal [102] investigated the effects of a rotating cylinder on mixed convection flow in a lid-driven square cavity. Their results demonstrated that the presence of the cylinder led to an increase in Nu_avg and that clockwise rotation led to an increase in Nu_avg, while counter-clockwise rotation led to a decrease in Nu_avg with an increase in rotational speed. The study by Selimefendigil et al. [105] examined the effects of the magnetic field, Ri, E, Ha, nanoparticle concentration, and the presence of a flexible wall on the MHD flow of a nanofluid inside a square cavity. They found that Nu_avg increased with the increase in Ri and observed 74.35% of heat transfer enhancement for Ri = 5. They also found that 66.5% heat transfer enhancement was obtained for E = 10⁴ N/m² as compared to the case E = 2.5 × 10⁵ N/m². Additionally, if Ha is reduced from 50 to 0, there will be an improvement in the rate of heat transfer by 54.55%. If the nanoparticles concentration increased from 0 to 0.04, there would be an improvement in heat transfer by 33.87%. The existence of a flexible wall led to an enhancement in heat transfer by 13.2%. Gibanov et al. [96] investigated mixed convection ferrofluid flow in a square cavity with a lid-driven with a moving, cold upper wall and a hot bottom wall and found that Nuavg at the heated wall increases with the increase in Ha and the thickness of porous media. Hussain et al. [99] examined the effect of an inclination angle on the heat transfer in a double lid-driven square cavity filled with Al₂O₃-H₂O nanofluid, with two fixed heat sources at the bottom wall. They confirmed that heat transfer is improved with the increase in nanoparticles concentration and Ri. Additionally, an increase in inclination angle caused an increase in Nuavg because of the left heat source, but the inverse behavior was noticed for the right heat source. Alsabery et al. [111] studied the conjugate mixed convection of H₂O-Al₂O₃ nanofluid flow inside a square cavity with a double lid driven containing a solid inner object. The top wall was kept at a constant cold temperature and moved to the right, while the bottom wall moved to the left and was kept at a fixed high temperature. The vertical walls were insulated. The study found that the presence of nanofluid enhanced the rate of heat transfer, but at low Re and high Ri, it had an inverse effect on the Nu.

Astanina et al. [110] studied mixed convection of Al₂O₃-H₂O nanofluid flow in a square cavity with a lid-driven, including two layers of porous media at the bottom with different thermal properties, permeability, and porosity. The lower wall was kept at a hot temperature, and the top moving wall was considered cold. The other walls were adiabatic. The study found that heat transfer enhanced with an increase in Ri for constant Re. It also found that Nu_avg reduced for different ranges of porous layer thicknesses when Ri > 1. Gangawane et al. [115] studied mixed convection flow in a square cavity containing a heated triangular block placed at the center of the cavity. The top wall was moving and insulated, while the lower wall was fixed and insulated as well, and the vertical wall was exposed to ambient temperature. The triangular block was considered isothermal and at a higher temperature than the ambient temperature. The results showed that there was a 50% increase in heat transfer when the size of the block increased from 10% to 30%. Gibanov et al. [116] studied the effect of Ri, the thickness of the lower wall, thermal conductivity ratio, and nanoparticle concentrations of Al₂O₃-H₂O nanofluid flow inside a lid-driven square cavity. The top lid was moving and hot, while the bottom wall was considered cold. The other vertical walls were insulated. The study found that the increase in thermal conductivity ratio and nanoparticle ratio led to an increase in heat transfer rate, while the increase in Ri and thickness of the bottom wall reduced heat transfer. Razera et al. [123] studied the effect of a fin on mixed convection flow inside a lid-driven square cavity. A lower wall was considered as the first position for the fin and then located on the side walls. The fin surface was considered a hot spot with high temperature, while the vertical and lower walls were set to be adiabatic. The upper moving surface was considered to be cold. The results showed that the fins on the right wall gave the highest Nusselt number while the fins on the lower wall gave an intermediate performance between the three cases. Hussain et al. [117] investigated the influence of an inclined magnetic field on the mixed convection H₂O-Al₂O₃ nanofluid flow inside a double-lid driven square cavity. The top and bottom walls were moving in opposite directions, and both walls were insulated. The left vertical wall was at a hot temperature, and the right one was considered to be cold. The results presented that Nu_avg increased with the increase in χ and decreased with the increase in Ri. Furthermore, Nu_avg reduced with the increase in Ha and the inclination angle of the magnetic field.

Taghizadeh & Asaditaheri [127] studied heat transfer by convection through an inclined lid-driven square cavity containing a circular porous cylinder placed at the center of the cavity. The lower and upper walls were considered hot and cold walls, respectively, and the vertical walls were considered adiabatic. The upper wall was moving at a steady speed, and the other walls remained fixed. They found that for all inclination angles, the increase in Da enhanced heat transfer when Ri = 0.01. For Ri ≥ 1, the rate of heat transfer decreased. For Ri = 5 and 10, heat transfer was more affected by the angle of inclination of the cavity, which weakens buoyancy forces and decreases the Nusselt number. Barnoon et al. [132] studied entropy generation and mixed convection of nanofluid flow in a lid-driven square cavity. The cavity was subjected to a magnetic field from the bottom wall, and a velocity was applied to the upper lid. They examined the effect of insulated and isothermal two rotating cylinders inside the cavity. They found that the increase in Ha led to reducing the heat transfer rate. The presence of an isothermal cylinder gave a higher rate of heat transfer than the existence of an insulated cylinder. However, in general, the cylinders inside the cavity-enhanced the rate of heat transfer, and the increase in angular speed of the cylinder led to a rise in the rate of heat transfer. Additionally, the fraction of nanofluid equal to 3% with a tilt angle of 0 of the cavity produces a higher rate of heat transfer. Lamarti et al. [139] explored mixed convection flow inside a square cavity with a periodically oscillating top lid. They discovered that the local Nusselt number starts high for high Re and drops rapidly. They also found that for a constant Gr, Re had a large effect on Nu_avg and that forced convection became dominant. Alsabery et al. [145] investigated the influence of a magnetic field on mixed convection of nanofluid flow in a square cavity with a lid driven with a thick triangular wall placed in the lower left corner. They found that the rate of heat transfer increased with the increase in Re and Ri. The maximum Nu occurred at Re = 500 and χ = 0.02. Alsabery et al. [160] studied the influence of hybrid nanofluid H₂O-Cu-Al₂O₃ flow inside a square lid-driven cavity with two vertical wavy walls containing a square block. The left wall was kept at a high temperature, the right wall was cold, and the top and bottom walls were adiabatic. They found that Nu_avg increased with the increase in Ri and that Nu increased with the increase in χ.

Hussain et al. [165] explored the effect of fins and inclined magnetic fields on square cavities filled with H₂O-Cu nanofluid with single and double-lid driven. The upper lid had a hot temperature, and the lower wall had a cold temperature, while the other walls were insulated. Two adiabatic vertical fins were installed on the upper wall, and an inclined magnetic field was applied to both cavities. They found that with the presence of fins, the convective heat transfer decreased with an increase in Ha and Ri. Additionally, Nu_avg decreased with an increase in the number of fins. Ahmed et al. [182] studied the flow and heat transfer behavior in a porous lid-driven square cavity filled with Al₂O₃-Cu/water hybrid nanofluid. The horizontal walls were moving at a constant speed, considered adiabatic, and the vertical walls were stationary. The left wall was hot, and the right one was cold. They found that the thermophoresis parameters had a very small effect on Nu_avg. Furthermore, Le had no effect on heat transfer enhancement, and Da had very little effect on the variation of Nu_avg. Ali et al. [183] examined mixed convection nanofluid flow inside a square cavity with lid-driven. The top wall was cold and moving horizontally in both directions, while the hot bottom wall was fixed and partially heated. A rotating flat plate was inserted in the cavity, and a magnetic field was subjected to the cavity. The other remaining parts of the walls were set to be adiabatic. The results confirmed that the highest rate of heat transfer occurred when the flat plate length was a quarter of the length of the cavity side (L). The improvement is more than 137.04% as compared to the case of 0.15 L, and it will be 208.89% for the case without the plate. It was also discovered that the heat transfer rate increased by 123.02% for rotational speed = 100, plate length 0.25 L, and nanoparticles concentration = 0.05, as compared with base fluid water. Batool et al. [185] studied heat and mass transfer analysis of a square cavity with lid-driven containing micropolar nanofluids under the influence of magnetic field and buoyancy force. A speed was applied to the upper wall, and the bottom wall was considered hot. The rate of heat transfer became faster at the maximum vortex viscosity parameter. Moreover, an optimized heat transfer mechanism was noticed from the bottom to the top wall, reducing the Brownian motion parameter. Dahani et al. [188] studied mixed convection and surface radiation in a square cavity with double lid-driven. One of the moving walls was considered hot, and the other was set to be cold, while the stationary walls were considered adiabatic. At Ri = 100, the contribution of radiation to the total Nu far outweighs that of convection. To minimize heat transfer, a combined effect of large Ri and angle of inclination close to 180° and non-emissive walls should be considered.

5.4.2. Rectangular Cavity

The study by Balootaki et al. [112] investigated the influence of mixed convection flow in a lid-driven rectangular cavity with a hot-moving upper surface and insulated other surfaces. The presence of a cold obstacle inside the cavity was also considered. The results demonstrated that rising the cavity inclination improves the heat transfer rate under forced convection, and the Nusselt number increases with increasing Rayleigh number for different inclination angles. The study by Louaraychi et al. [140] examined mixed convection flow in horizontal rectangular cavities with single- and double-lid driven using both numerical and analytical methods. It was found that the mixed convection parameter Ra/Pe³ can be used to distinguish between three convection regimes: natural, mixed, and forced convection. The results showed that when forced convection is dominant, Nu_avg remained constant for small values of Ra and slightly increased during mixed convection heat transfer. Beyond this range, a fast linear increase in Nu_avg was observed for dominant natural convection heat transfer. Additionally, Nu_avg increased with the Peclet number (Pe) due to the shear effect. Tizakast et al. [178] conducted a numerical and analytical study on the double-diffusive mixed convection of a non-Newtonian power-law fluid in a closed rectangular cavity. The study found that the flow intensity and heat and mass transfer were insensitive to an increase in the parameter A for values of A greater than or equal to 24. The results also showed that non-Newtonian double-diffusive mixed convection is controlled by the parameters Ra_T, Pe, Le, and power-law index n. Additionally, the study found that an increase in Le had no effect on heat transfer, while a high buoyancy ratio increased both heat and mass transfer. Tizakast et al. [199] conducted a numerical and analytical study on the Rayleigh-Bénard double-diffusive mixed convection flow inside horizontal rectangular cavities subjected to uniform heat and mass fluxes along the sliding horizontal walls, with the other walls fixed and insulated. They confirmed that the heat and mass transfer and flow intensity became insensitive to the aspect ratio, A, for values of A greater than or equal to 28. For a Prandtl number greater than or equal to 10, the flow behavior became independent of Pr. The study concluded that Newtonian Rayleigh–Bénard double-diffusive mixed convection is controlled by the parameters Pe, Ra_T, Le, buoyancy ratio N, and power-law index n.

5.4.3. Triangular Cavity

Selimefendigil & Öztop [107] conducted research on the mixed convection of nanofluid flow in a triangular cavity with lid-driven. They found that for negative and positive x-direction motion, Nu_avg decreased by 41.02% and 38.77% for Ri, equal to 50 and 0.05, respectively. Additionally, Nu_avg decreased by 55% when Ra increased from 10⁴ to 10⁷. Furthermore, the study found that an enhancement of 22.95% was obtained for Nu_avg for the highest nanoparticle concentration. Soomro et al. [157] conducted a study on the convection heat transfer inside a lid-driven triangular cavity subjected to a horizontal constant magnetic field. The upper moving wall was set as hot, while the side inclined walls were adiabatic, and a cold temperature cylinder was placed at the center of the cavity. The study found that Nu_avg increased with the increase in Ri at a high flow shear rate. Additionally, Nuavg increased with the increase in Re when high viscous forces were present. Shahid et al. [175] conducted a study on the mixed convection flow inside a heated lid-driven right-angle isosceles triangular cavity. The horizontal top side of the cavity was moving horizontally and kept adiabatic, the vertical wall was hot, and the inclined wall was cold. The results of the study showed that natural convection became more dominant than forced convection as Gr increased, and this led to an increase in Nu_avg. Additionally, for small values of Ri, the forced convection was more dominant due to the effect of shear forces generated by the moving lid. Xiong et al. [180] studied mixed convective heat transfer of MHD fluid flow in a lid-driven triangular cavity subjected to heating by a thick triangular wall. The top wall was moving to the right with a high temperature, while the inclined sidewalls were adiabatic. Cold obstacles were placed near the side walls and along the left and right side inclined walls with a temperature lower than the top wall temperature. The results showed that the expansion of Ha led to a reduction in heat transfer. Additionally, for higher Ri, the heat transfer was enhanced due to the increase in shear rate. The study also found that for the left side obstacle, the heat transfer rate increased due to an increase in Re, while the opposite behavior was observed for Ha and Ri. For the right obstacle, the heat transfer rate was strengthened along the upper wall due to the emergence of Re, while a reverse process was followed for Ha and Ri.

5.4.4. Cubical Cavity

The study by Karbasifar et al. [119] focused on the heat transfer process of mixed convection Al₂O₃-H₂O nanofluid flow in a lid-driven cubical cavity containing a hot elliptical centric cylinder. The results showed that Nu_avg decreased as Ri increased for fixed χ and ϕ. Additionally, Nu_avg raised with the increase in χ for constant Ri and ϕ. It was also found that Nu_avg increased slightly when ϕ increased for constant Ri. The study also found that Nu_avg increased with the increase in Re and χ. In the study by Kareem & Gao [120], they explored the effect of a SiO₂-H₂O nanofluid on turbulent mixed convection inside a cubical cavity with a heated top wall and a cold bottom wall. They found that the presence of the nanofluid improved the heat transfer effectiveness, with the highest Nu_avg being observed for a rotational speed of −5. Additionally, the rotational velocity of the cylinder had a stronger effect on the bottom wall than on the top wall. Al-Rashed et al. [131] studied the flow of H₂O-Al₂O₃ nanofluid in an oblique lid-driven cubical cavity, including a hot elliptical centric cylinder. They found that raising the concentration of nanoparticles led to an increase in heat transfer coefficients, and Nu decreased with the increase in Ri for constant χ and inclination angle. Additionally, increasing the inclination angle slightly increased Nu for constant Ri. Alsabery et al. [146] investigated the mixed convection H₂O-Al₂O₃ nanofluid flow inside a cubical chamber containing a heat-conducting cylinder. The right vertical wall was partially heated, the left vertical wall was considered cold, and the other walls were insulated. They found that increasing χ led to an improvement in heat transfer for a fixed Re = 10.

5.4.5. Other Types of Cavities

Abu-Nada and Chamkha [57] numerically investigated the mixed convection flow of CuO-H₂O nanofluid in a cavity with a wavy wall with a lid-driven. The top wall was hot and moving, while the cold bottom wall was wavy. They found that for all values of Ri, Nu was maximum at the left top corner of the cavity and then decreased along the heated lid until it reached zero at the middle position of the lid. After that, Nu increased slightly at the second half of the wall and then vanished at the right side of the cavity. Hatami et al. [98] investigated the behavior of nanofluid flow inside a T-shaped lid-driven porous cavity. The top moving wall was cold, while the bottom wall was hot, and the other walls were insulated. They found that both Nu_local and Nu_avg increased with the increase in Ri and Re. Additionally, they observed that increasing Da and χ led to an increase in Nu_avg. Selimefendigil et al. [106] studied mixed convection nanofluid flow inside a trapezoidal cavity with an adiabatic stationary cylinder. Both the left and right walls were flexible walls. The top wall was moving and considered cold, while the bottom was stationary and considered hot. The other walls were considered adiabatic. They found that heat transfer increased by 9.8% when the value of elastic modulus was raised from 10³ to 10⁵ when the elastic wall inclination was equal to 0 degrees. Additionally, they observed that Nu_avg increased linearly with the increase in χ, and the heat transfer was enhanced by 25.30% at the highest χ as compared to the base fluid. Cho [134] analyzed heat transfer and entropy generation of Cu-H₂O nanofluid in a lid-driven cavity and subjected it to an oblique magnetic field. The left wall was a hot moving wall, the right wavy wall was cold, and the other walls were insulated. Their results showed that Nu increased with the increase in χ or wave amplitude of the wavy surface. Additionally, during the natural convection-dominated regime, Nu had a higher value for the magnetic field inclination of 90° and 270°, while the opposite behavior was observed for the inclination of 0° and 180°. During the forced convection-dominated regime, Nu had a higher value for the magnetic field inclination of 135° and 315°, while the opposite behavior was observed for the inclination of 90° and 270°. Hadavand et al. [136] studied mixed convection H₂O-Ag nanofluid flow inside a semi-circular cavity with a lid-driven. The left side of the cavity was heated by injecting hot water, while the upper lid was cold and moving. Other surfaces were considered adiabatic. Their results showed that the best heat transfer behavior was observed for Ri = 1, χ = 0.06, and ϕ = −45°, 0°, −90°, 45°, and 90°.

Selimefendigil and Öztop [142] conducted a study on the influence of a magnetic field on mixed convection nanofluid flow in an oblique L-shaped cavity. They found that Nu_avg increased by 42.2% and 39.9% for water and nanofluid, respectively, when the cavity inclination angle was changed from 180° to 150°. They also found that Nu_avg was reduced by 11% when an elastic wall was used instead of a solid wall at a specific Ri = 0.03. Additionally, Nu_avg was reduced by approximately 42% for both fluid and nanofluid for the lowest and highest Ra. Haq et al. [150] examined the heat transfer behavior in a hexagonal cavity filled with water and subjected to a magnetic field. They discovered that the heat transfer could be improved by using a cylinder with variable thermal conditions in the middle of the cavity and by increasing Ha. The Nusselt number at the heated surface decreased as Ri decreased for a specific Re = 300 and Ha = 10. Noor et al. [192] studied the forced convection of MHD flow inside a trapezoidal cavity with a circular object inside. They found that Nu decreased near the heated top lid and remained constant along the horizontal direction of the top lid. Additionally, they found that at low Ri, Nu had a higher value at the top hot-moving wall. Conversely, at high Ri, Nu decreased abruptly along the heated part of the top lid for both heated and cold conditions of the circular object. Polasanapalli and Anupindi [194] studied the mixed heat transfer behavior in an air-filled concentric annular cavity with the inner surface being hot and the outer surface being cold. They considered four different rotational conditions of cylinders: counter-rotating cylinders, co-rotating cylinders, outer rotating cylinders, and inner rotating cylinders. They found that the rate of heat transfer is lower for the differentially heated cavity, regardless of the rotational velocity of the cylinders. Shah et al. [198] studied the mixed convection flow of CuO-H₂O nanofluid in a lid-driven corrugated porous cavity with a cylindrical object inside. The object had three different surface conditions: adiabatic, cold, and hot. Internal heat generation/absorption and uniform heat were applied to the vertical wall, and the bottom was insulated. They found that Nu increased as Re increased. The highest Nu was attained for χ = 0.05. Xia et al. [200] studied the mixed convection flow of H₂O-Al₂O₃ nanofluid inside a T-shaped lid-driven cavity with a hot obstacle at different positions. The top lid was moving to the right and had a cold temperature, while all the other walls were adiabatic except the hot obstacle, which was considered hot. Their results showed that as Ri increased, the heat transfer decreased. Additionally, they found that an increase in χ helped to increase the rate of heat transfer. Furthermore, an increase in aspect ratio caused a reduction in the rate of heat transfer. Zhang et al. [202] investigated Ag-water nanofluid flow inside a semi-elliptic lid-driven cavity. The top moving lid was cold, while the curved bottom wall was hot. Their results showed that the presence of nanoparticles with high circulation led to an increase in the rate of heat transfer. Additionally, the heat transfer rate enhanced with the increase in Gr for lower Ri.

6. Conclusions

Heat transfer analysis inside cavities has been investigated by many authors. Different geometries have been adopted for the enclosed cavity in order to enhance heat transfer and improve the flow behavior inside the cavity. A high percentage of published articles worked on rectangular and square cavities, while the other geometries were triangular, trapezoidal, semi-circular, etc. Furthermore, some articles discussed the flow behavior of two adjacent rectangular domains that are used in building blocks or some types of windows. Two main hydraulic boundary conditions are applied: fixed and moving boundaries (lid-driven), while several thermal boundary conditions are applied, starting with temperature difference, heat flux, cold and hot fins, and other types of objects, etc. Moreover, the effect of sinusoidal and triangular surfaces and flexible boundaries are also considered. In addition, several articles have studied the influence of magnetic fields and different fluids types on heat transfer.

Through the review of natural convection, the findings revealed that Nu increased with the rise of Ra and nanoparticles concentration. Moreover, Nu decreased with the increase in Ha. The effect of objects inside the cavity varied with the boundary conditions applied to the surface of the object and conditions of it whether it was fixed or moving. Moreover, Nu decreased with the increase in Da considering porous material inside the cavity. The cavity with forced convection is discussed by many authors. In addition to the previous mentioned boundary conditions and types of cavities, a moving boundary is applied (lid-driven cavity). This type of condition will move the flow inside the cavity from natural convection to forced convection or mixed convection between two types.

During the lid-driven cavity, there will be an interchange relationship between forced, and natural convection depending on the applied boundary conditions and types of fluids that have been used. Some results demonstrate that buoyancy will be dominant for high values of Pr while forced convection controls the flow process inside the cavity. The influence of adding different nanoparticles led to an increase in Nu and rate of heat transfer with the rise in nanoparticles concentration. In a few cases, nanofluid had an inverse effect on Nu at low Re when Ri is high. The majority of published articles demonstrated that the increase in Ri led to a decrease in Nu and the rate of heat transfer. In the case of elastic boundaries, some results presented that the heat transfer raised with an increase in Ri. In most cases, the rate of heat transfer improved with the increase in Ha. Some articles referred to a rise in Nu with the increase in Ha, with some boundaries being elastic and the cavity being filled with porous media. The existence of some objects inside the cavity had helped to increase in heat transfer rate. For example, rotating cylinders, flat plates, triangular blocks, rectangular blades, etc., led to an increase in Nu.

Finally, this configurative systematic review focuses on the importance of heat transfer enhancement or degeneration in relation to various factors such as the shape of the cavity, the presence of fins/cylinders/blocks/blades, and the use of fluids/nanofluids/hybrid-nanofluids and/or porous media. The review also proposes future research directions based on an extensive literature review. The review includes details of the flow domain, dimensions, type of flow, parameters and their ranges, meshing, CFD methods, and algorithms, which are presented in tabular form. Additionally, the review provides extensive details on CFD validation. The authors believe that this is the first time such detailed information has been presented in a review and that it will be valuable for future researchers.

7. Future Work

In conclusion, research on heat transfer behavior in cavities has been highlighted since around 1965, and much research is still being carried out by researchers. However, several key points are not highlighted yet and can be considered as future research, and such key points are mentioned below:

• Most of the studies focused on laminar natural/mixed/forced convection flow, but very few studies considered turbulent flow regimes.
• Most recently, rotating blades or plates inside the cavity received attention from researchers. Still, no work is conducted considering the design, shape, and aerodynamic behavior of blades.
• Will it be possible to develop a general form of correlation for the average Nusselt number?
• Very little research is found considering the LES and DNS modeling in cavities for transient/turbulent flow regimes. This area should be considered a high-interest area in the future.
• The choice of turbulence models has not been highlighted yet by researchers. It can be an important study.
• Different types of shapes are considered in the literature, but more research is suggested to find an optimum design of the physical domain that can give maximum heat transfer enhancement.
• Very little or limited research work is conducted considering the presence of nanoplastic or microplastic in fluids inside a cavity. It is highly considered research for future studies.
• Study the hydraulic and thermal behavior of two immiscible fluids (for example, air and water) inside a cavity.