Research

17 pages, 703 KiB

Open AccessArticle

Lithium-Ion Battery Estimation in Online Framework Using Extreme Gradient Boosting Machine Learning Approach

by Sadiqa Jafari, Zeinab Shahbazi, Yung-Cheol Byun and Sang-Joon Lee

Mathematics 2022, 10(6), 888; https://doi.org/10.3390/math10060888 - 10 Mar 2022

Cited by 26 | Viewed by 2869

The battery management system in an electric vehicle must be reliable and durable to forecast the state of charge. Considering that battery degradation is generally nonlinear, state of charge (SOC) estimation with lower degradation can be challenging. Lithium-ion batteries are highly dependent on [...] Read more.

The battery management system in an electric vehicle must be reliable and durable to forecast the state of charge. Considering that battery degradation is generally nonlinear, state of charge (SOC) estimation with lower degradation can be challenging. Lithium-ion batteries are highly dependent on the knowledge of aging, which is usually costly or not available online. In this paper, we suggest the state of charge estimation of lithium-ion battery systems by using an extreme gradient boosting algorithm for electric vehicles application, which acquires the nonlinear relationship model can with offline training. The extreme gradient boosting algorithm is the tree on based learning, which effectively performs and speeds. Voltage-time data used as an input of this system from the partial constant current phase; the proposed algorithm improves the accuracy of predicting the relevant. Additionally, no initial state of charge is required in our proposed method; thus, estimating the state of charge can consider each battery state. Full article

(This article belongs to the Special Issue Modeling and Numerical Analysis of Energy and Environment 2021)

► Show Figures

Figure 1

17 pages, 637 KiB

Open AccessArticle

Modeling and Numerical Simulation of the Thermal Interaction between Vegetation Cover and Soil

by Arturo Hidalgo and Lourdes Tello

Mathematics 2022, 10(3), 338; https://doi.org/10.3390/math10030338 - 23 Jan 2022

Cited by 2 | Viewed by 1818

Abstract

In this work, we propose a mathematical model representing the thermal interaction between vegetation cover and the soil underneath it. This model consists of a one-dimensional reaction–diffusion equation describing the evolution of the temperature in the vegetation cover coupled with a two-dimensional reaction–diffusion [...] Read more.

In this work, we propose a mathematical model representing the thermal interaction between vegetation cover and the soil underneath it. This model consists of a one-dimensional reaction–diffusion equation describing the evolution of the temperature in the vegetation cover coupled with a two-dimensional reaction–diffusion equation to represent the evolution of the temperature in the soil. The thermal interaction between the vegetation cover and the soil is studied and the distribution of temperatures in the soil with depth is also obtained. The vegetation cover acts in this model as a dynamic and diffusive boundary condition for the soil. The developed model takes into account the latent heat of fusion, which appears when the transformation of ice into liquid water or vice versa occurs inside the soil. The numerical approach for the solution of the mathematical model conducted in this work is based on the finite volume method with Weighted Essentially Non-Oscillatory technique for spatial reconstruction and the third-order Runge–Kutta Total Variation Diminishing numerical scheme is used for time integration, which is very efficient to obtain the numerical solution of this type of model. Some numerical examples are solved to obtain the distribution of temperature both in the vegetation cover and the soil. Full article

(This article belongs to the Special Issue Modeling and Numerical Analysis of Energy and Environment 2021)

► Show Figures

Figure 1

42 pages, 19717 KiB

Open AccessArticle

Empirical and Numerical Analysis of an Opaque Ventilated Facade with Windows Openings under Mediterranean Climate Conditions

by Carlos-Antonio Domínguez-Torres, Ángel Luis León-Rodríguez, Rafael Suárez and Antonio Domínguez-Delgado

Mathematics 2022, 10(1), 163; https://doi.org/10.3390/math10010163 - 05 Jan 2022

Cited by 7 | Viewed by 2221

Abstract

In recent years, there has been growing concern regarding energy efficiency in the building sector with energy requirements increasing worldwide and now responsible for about 40% of final energy consumption in Europe. Previous research has shown that ventilated façades help to reduce energy [...] Read more.

In recent years, there has been growing concern regarding energy efficiency in the building sector with energy requirements increasing worldwide and now responsible for about 40% of final energy consumption in Europe. Previous research has shown that ventilated façades help to reduce energy use when cooling buildings in hot and temperate climates. Of the different ventilated façade configurations reported in the literature, the configuration of ventilated façade with window rarely has been studied, and its 3D thermodynamic behavior is deserving of further analysis and modeling. This paper examines the thermal behavior of an opaque ventilated façade with a window, in experimentally and numerical terms and its impact in energy savings to get indoor comfort. Field measurements were conducted during the winter, spring and summer seasons of 2021 using outdoor full scale test cells located in Seville (southern Spain). The modeling of the ventilated façade was carried out using a three-dimensional approach taking into account the 3D behavior of the air flow in the air cavity due to the presence of the window. The validation and comparison process using experimental data showed that the proposed model provided good results from quantitative and qualitative point of view. The reduction of the heat flux was assessed by comparing the energy performance of a ventilated façade with that of an unventilated façade. Both experimental and numerical results showed that the ventilated façade provided a reduction in annual total energy consumption when compared to the unventilated façade, being compensated the winter energy penalization by the summer energy savings. This reduction is about

21 %

for the whole typical climatic year showing the ability of the opaque ventilated façade studied to reduce energy consumption to insure indoor comfort, making its suitable for use in retrofitting the energy-obsolete building stock built in Spain in the middle decades of the 20 century. Full article

(This article belongs to the Special Issue Modeling and Numerical Analysis of Energy and Environment 2021)

► Show Figures

Figure 1

23 pages, 1335 KiB

Open AccessArticle

Mathematical Modeling and Associated Numerical Simulation of Fusion/Solidification Front Evolution in the Context of Severe Accident of Nuclear Power Engineering

by Adrien Drouillet, Guillaume Bois, Romain Le Tellier, Raphaël Loubère and Mathieu Peybernes

Mathematics 2022, 10(1), 116; https://doi.org/10.3390/math10010116 - 31 Dec 2021

Viewed by 1760

Abstract

Considering transient processes where liquid/solid phase change occurs, this paper focuses on the associated modeling and numerical treatment in the frame of “Computational Fluid Dynamics” simulations. While being of importance in many industrial applications involving solidification and melting of mixed materials, including power [...] Read more.

Considering transient processes where liquid/solid phase change occurs, this paper focuses on the associated modeling and numerical treatment in the frame of “Computational Fluid Dynamics” simulations. While being of importance in many industrial applications involving solidification and melting of mixed materials, including power and manufacturing engineering, the first application of this work pertains to the analysis of severe accidents in a nuclear reactor. Indeed, in this context, the molten core materials (a.k.a. corium) can form a high-temperature multiphase liquid pool at the boundary of which fusion and solidification phenomena are of prime importance. In this context, even if materials at play are treated as pure components, it is mandatory to distinguish two different phase change temperatures with a solid fusion temperature and a liquid solidification temperature. Accordingly, in the frame of a sharp interface representation, the paper introduces non-classical heterogeneous conditions at the liquid/solid boundary in such a way that both moving interface (through Stefan conditions associated with fusion or solidification) and static interface (imposing heat flux continuity) are supported at the same time on different spatial locations along this boundary. Within a monolithic resolution of Navier–Stokes and heat conduction equations, this interface is explicitly tracked with combined Front-Tracking and VOF methods. In order to ensure zero velocity in the solid phase, an Immersed Boundary Method and a direct forcing penalization are also introduced. The main relevant features of this combination of numerical methods are discussed along with their implementation in the TrioCFD code taking advantage of the pre-existing code capabilities. Numerical simulations including both verification tests and a case of interest for our industrial application are reported and demonstrate the applicability of the proposed triptych model+methods+code to treat such problems. The numerical tools and the simulation code developed in this work could be used not only in the several accident context but also to simulate melting, solidification and fusion processes occurring in aerodynamics, hypersonic reentry vehicles and laser applications to cite but a few. Full article

(This article belongs to the Special Issue Modeling and Numerical Analysis of Energy and Environment 2021)

► Show Figures

Figure 1

30 pages, 2364 KiB

Open AccessArticle

Well-Balanced High-Order Discontinuous Galerkin Methods for Systems of Balance Laws

by Ernesto Guerrero Fernández, Cipriano Escalante and Manuel J. Castro Díaz

Mathematics 2022, 10(1), 15; https://doi.org/10.3390/math10010015 - 21 Dec 2021

Cited by 5 | Viewed by 2291

Abstract

This work introduces a general strategy to develop well-balanced high-order Discontinuous Galerkin (DG) numerical schemes for systems of balance laws. The essence of our approach is a local projection step that guarantees the exactly well-balanced character of the resulting numerical method for smooth [...] Read more.

This work introduces a general strategy to develop well-balanced high-order Discontinuous Galerkin (DG) numerical schemes for systems of balance laws. The essence of our approach is a local projection step that guarantees the exactly well-balanced character of the resulting numerical method for smooth stationary solutions. The strategy can be adapted to some well-known different time marching DG discretisations. Particularly, in this article, Runge–Kutta DG and ADER DG methods are studied. Additionally, a limiting procedure based on a modified WENO approach is described to deal with the spurious oscillations generated in the presence of non-smooth solutions, keeping the well-balanced properties of the scheme intact. The resulting numerical method is then exactly well-balanced and high-order in space and time for smooth solutions. Finally, some numerical results are depicted using different systems of balance laws to show the performance of the introduced numerical strategy. Full article

(This article belongs to the Special Issue Modeling and Numerical Analysis of Energy and Environment 2021)

► Show Figures

Figure 1

17 pages, 5744 KiB

Open AccessArticle

Numerical Investigation of the Heat Transfer Characteristics of R290 Flow Boiling in Corrugated Tubes with Different Internal Corrugated Structures

by Shenglin Zhu, Jinfeng Wang and Jing Xie

Mathematics 2021, 9(22), 2969; https://doi.org/10.3390/math9222969 - 21 Nov 2021

Cited by 2 | Viewed by 1944

Abstract

The heat transfer and pressure drop characteristics of R290 flow boiling in a corrugated tube were investigated through computational fluid dynamics (CFD) in this study. We established a model of flow boiling in a corrugated tube with different corrugated structures (rectangular and circular [...] Read more.

The heat transfer and pressure drop characteristics of R290 flow boiling in a corrugated tube were investigated through computational fluid dynamics (CFD) in this study. We established a model of flow boiling in a corrugated tube with different corrugated structures (rectangular and circular corrugations) and validated the model using the Liu–Winterton and Xu–Fang empirical equations. The heat transfer coefficient (HTC) and pressure drop were obtained at a mass flow rate of 0.04–0.2 kg/s and a water inlet temperature of 310–330 K. The results show that the HTC and the drop in the pressure of the corrugated tubes both obviously increased compared with a smooth tube as the mass flow rate increased. The HTC decreased for the three tubes as the water inlet temperature increased, while the drop in pressure slightly increased for the three tubes. Moreover, the corrugated structure was found to significantly enhance the heat transfer; the heat transfer enhancement factor (

E_{1}

) of the corrugated tube with the rectangular corrugations and the corrugated tube with the circular corrugations was 2.01–2.36 and 1.67–1.98, respectively. The efficiency index (

I

) for both the rectangular corrugated pipe and the circular corrugated pipe was greater than 1 (1.05–1.24 and 1.13–1.29, respectively). The application of corrugated tubes with round and rectangular corrugations can reduce the heat transfer area required for the exchange of heat and, thus, reduce the cost. Full article

(This article belongs to the Special Issue Modeling and Numerical Analysis of Energy and Environment 2021)

► Show Figures

Figure 1

25 pages, 2217 KiB

Open AccessArticle

Mathematical Modelling of Climate Change and Variability in the Context of Outdoor Ergonomics

by Sergei Soldatenko, Alexey Bogomolov and Andrey Ronzhin

Mathematics 2021, 9(22), 2920; https://doi.org/10.3390/math9222920 - 16 Nov 2021

Cited by 12 | Viewed by 13804

Abstract

The current climate change, unlike previous ones, is caused by human activity and is characterized by an unprecedented rate of increase in the near-surface temperature and an increase in the frequency and intensity of hazardous weather and climate events. To survive, society must [...] Read more.

The current climate change, unlike previous ones, is caused by human activity and is characterized by an unprecedented rate of increase in the near-surface temperature and an increase in the frequency and intensity of hazardous weather and climate events. To survive, society must be prepared to implement adaptation strategies and measures to mitigate the negative effects of climate change. This requires, first of all, knowledge of how the climate will change in the future. To date, mathematical modelling remains the only method and effective tool that is used to predict the climate system’s evolution under the influence of natural and anthropogenic perturbations. It is important that mathematics and its methods and approaches have played a vital role in climate research for several decades. In this study, we examined some mathematical methods and approaches, primarily, mathematical modelling and sensitivity analysis, for studying the Earth’s climate system, taking into account the dependence of human health on environmental conditions. The essential features of stochastic climate models and their application for the exploration of climate variability are examined in detail. As an illustrative example, we looked at the application of a low-order energy balance model to study climate variability. The effects of variations in feedbacks and the climate system’s inertia on the power spectrum of global mean surface temperature fluctuations that characterized the distribution of temperature variance over frequencies were estimated using a sensitivity analysis approach. Our confidence in the obtained results was based on the satisfactory agreement between the theoretical power spectrum that was derived from the energy balance model and the power spectrum that was obtained from observations and coupled climate models, including historical runs of the CMIP5 models. Full article

(This article belongs to the Special Issue Modeling and Numerical Analysis of Energy and Environment 2021)

► Show Figures

Figure 1

17 pages, 2372 KiB

Open AccessArticle

Jet Impingement Cooling of a Rotating Hot Circular Cylinder with Hybrid Nanofluid under Multiple Magnetic Field Effects

by Badreddine Ayadi, Fatih Selimefendigil, Faisal Alresheedi, Lioua Kolsi, Walid Aich and Lotfi Ben Said

Mathematics 2021, 9(21), 2697; https://doi.org/10.3390/math9212697 - 24 Oct 2021

Cited by 9 | Viewed by 1652

Abstract

The cooling performance of jet impinging hybrid nanofluid on a rotating hot circular cylinder was numerically assessed under the effects of multiple magnetic fields via finite element method. The numerical study was conducted for different values of Reynolds number ( [...] Read more.

The cooling performance of jet impinging hybrid nanofluid on a rotating hot circular cylinder was numerically assessed under the effects of multiple magnetic fields via finite element method. The numerical study was conducted for different values of Reynolds number (

100 \leq Re \leq 300

), rotational Reynolds number (

0 \leq Rew \leq 800

), lower and upper domain magnetic field strength (

0 \leq Ha \leq 20

), size of the rotating cylinder (2 w

\leq r \leq

6 w) and distance between the jets (6 w ≤ H ≤ 16 w). In the presence of rotation at the highest speed, the Nu value was increased by about 5% when Re was increased from Re = 100 to Re = 300. This value was 48.5% for the configuration with the motionless cylinder. However, the rotations of the cylinder resulted in significant heat transfer enhancements in the absence or presence of magnetic field effects in the upper domain. At Ha1 = 0, the average Nu rose by about 175%, and the value was 249% at Ha1 = 20 when cases with the cylinder rotating at the highest speed were compared to the motionless cylinder case. When magnetic field strengths of the upper and lower domains are reduced, the average Nu decreases. The size of the cylinder is influential on the flow dynamics and heat transfer when the cylinder is rotating. An optimum value of the distance between the jets was obtained at H = 14 w, where the Nu value was highest for the rotating cylinder case. A modal analysis of the heat transfer dynamics was performed with the POD technique. As diverse applications of energy system technologies with impinging jets are available, considering the rotations of the cooled surface under the combined effects of using magnetic field and nanoparticle loading in heat transfer fluid is a novel contribution. The outcomes of the present work will be helpful in the initial design and optimization studies in applications from electronic cooling to convective drying, solar power and many other systems. Full article

(This article belongs to the Special Issue Modeling and Numerical Analysis of Energy and Environment 2021)

► Show Figures

Figure 1

17 pages, 2384 KiB

Open AccessArticle

Effects of Surface Rotation on the Phase Change Process in a 3D Complex-Shaped Cylindrical Cavity with Ventilation Ports and Installed PCM Packed Bed System during Hybrid Nanofluid Convection

by Lioua Kolsi, Fatih Selimefendigil and Mohamed Omri

Mathematics 2021, 9(20), 2566; https://doi.org/10.3390/math9202566 - 13 Oct 2021

Cited by 1 | Viewed by 1455

Abstract

The combined effects of surface rotation and using binary nanoparticles on the phase change process in a 3D complex-shaped vented cavity with ventilation ports were studied during nanofluid convection. The geometry was a double T-shaped rotating vented cavity, while hybrid nanofluid contained binary [...] Read more.

The combined effects of surface rotation and using binary nanoparticles on the phase change process in a 3D complex-shaped vented cavity with ventilation ports were studied during nanofluid convection. The geometry was a double T-shaped rotating vented cavity, while hybrid nanofluid contained binary Ag–MgO nano-sized particles. One of the novelties of the study was that a vented cavity was first used with the phase change–packed bed (PC–PB) system during nanofluid convection. The PC–PB system contained a spherical-shaped, encapsulated PCM paraffin wax. The Galerkin weighted residual finite element method was used as the solution method. The computations were carried out for varying values of the Reynolds numbers (

100 \leq Re \leq 500

), rotational Reynolds numbers (

100 \leq Rew \leq 500

), size of the ports (

0.1 L 1 \leq d i \leq 0.5 L 1

), length of the PC–PB system (

0.4 L 1 \leq L 0 \leq L 1

), and location of the PC–PB (

0 \leq y p \leq 0.25 H

). In the heat transfer fluid, the nanoparticle solid volume fraction amount was taken between 0 and

0.02 %

. When the fluid stream (Re) and surface rotational speed increased, the phase change process became fast. Effects of surface rotation became effective for lower values of Re while at Re = 100 and Re = 500; full phase transition time (tp) was reduced by about 39.8% and 24.5%. The port size and nanoparticle addition in the base fluid had positive impacts on the phase transition, while 34.8% reduction in tp was obtained at the largest port size, though this amount was only 9.5%, with the highest nanoparticle volume fraction. The length and vertical location of the PC–PB system have impacts on the phase transition dynamics. The reduction and increment amount in the value of tp with varying location and length of the PC–PB zone became 20% and 58%. As convection in cavities with ventilation ports are relevant in many thermal energy systems, the outcomes of this study will be helpful for the initial design and optimization of many PCM-embedded systems encountered in solar power, thermal management, refrigeration, and many other systems. Full article

(This article belongs to the Special Issue Modeling and Numerical Analysis of Energy and Environment 2021)

► Show Figures

Figure 1

41 pages, 24916 KiB

Open AccessArticle

A Massively Parallel Hybrid Finite Volume/Finite Element Scheme for Computational Fluid Dynamics

by Laura Río-Martín, Saray Busto and Michael Dumbser

Mathematics 2021, 9(18), 2316; https://doi.org/10.3390/math9182316 - 18 Sep 2021

Cited by 15 | Viewed by 3458

Abstract

In this paper, we propose a novel family of semi-implicit hybrid finite volume/finite element schemes for computational fluid dynamics (CFD), in particular for the approximate solution of the incompressible and compressible Navier-Stokes equations, as well as for the shallow water equations on staggered [...] Read more.

In this paper, we propose a novel family of semi-implicit hybrid finite volume/finite element schemes for computational fluid dynamics (CFD), in particular for the approximate solution of the incompressible and compressible Navier-Stokes equations, as well as for the shallow water equations on staggered unstructured meshes in two and three space dimensions. The key features of the method are the use of an edge-based/face-based staggered dual mesh for the discretization of the nonlinear convective terms at the aid of explicit high resolution Godunov-type finite volume schemes, while pressure terms are discretized implicitly using classical continuous Lagrange finite elements on the primal simplex mesh. The resulting pressure system is symmetric positive definite and can thus be very efficiently solved at the aid of classical Krylov subspace methods, such as a matrix-free conjugate gradient method. For the compressible Navier-Stokes equations, the schemes are by construction asymptotic preserving in the low Mach number limit of the equations, hence a consistent hybrid FV/FE method for the incompressible equations is retrieved. All parts of the algorithm can be efficiently parallelized, i.e., the explicit finite volume step as well as the matrix-vector product in the implicit pressure solver. Concerning parallel implementation, we employ the Message-Passing Interface (MPI) standard in combination with spatial domain decomposition based on the free software package METIS. To show the versatility of the proposed schemes, we present a wide range of applications, starting from environmental and geophysical flows, such as dambreak problems and natural convection, over direct numerical simulations of turbulent incompressible flows to high Mach number compressible flows with shock waves. An excellent agreement with exact analytical, numerical or experimental reference solutions is achieved in all cases. Most of the simulations are run with millions of degrees of freedom on thousands of CPU cores. We show strong scaling results for the hybrid FV/FE scheme applied to the 3D incompressible Navier-Stokes equations, using millions of degrees of freedom and up to 4096 CPU cores. The largest simulation shown in this paper is the well-known 3D Taylor-Green vortex benchmark run on 671 million tetrahedral elements on 32,768 CPU cores, showing clearly the suitability of the presented algorithm for the solution of large CFD problems on modern massively parallel distributed memory supercomputers. Full article

(This article belongs to the Special Issue Modeling and Numerical Analysis of Energy and Environment 2021)

► Show Figures

Figure 1

9 pages, 269 KiB

Open AccessArticle

On a One-Dimensional Hydrodynamic Model for Semiconductors with Field-Dependent Mobility

by Giuseppe Alì, Francesco Lamonaca, Carmelo Scuro and Isabella Torcicollo

Mathematics 2021, 9(17), 2152; https://doi.org/10.3390/math9172152 - 03 Sep 2021

Cited by 3 | Viewed by 1679

Abstract

We consider a one-dimensional, isentropic, hydrodynamical model for a unipolar semiconductor, with the mobility depending on the electric field. The mobility is related to the momentum relaxation time, and field-dependent mobility models are commonly used to describe the occurrence of saturation velocity, that [...] Read more.

We consider a one-dimensional, isentropic, hydrodynamical model for a unipolar semiconductor, with the mobility depending on the electric field. The mobility is related to the momentum relaxation time, and field-dependent mobility models are commonly used to describe the occurrence of saturation velocity, that is, a limit value for the electron mean velocity as the electric field increases. For the steady state system, we prove the existence of smooth solutions in the subsonic case, with a suitable assumption on the mobility function. Furthermore, we prove uniqueness of subsonic solutions for sufficiently small currents. Full article

(This article belongs to the Special Issue Modeling and Numerical Analysis of Energy and Environment 2021)

24 pages, 9716 KiB

Open AccessArticle

Non-Isothermal Hydrodynamic Characteristics of a Nanofluid in a Fin-Attached Rotating Tube Bundle

by Mashhour A. Alazwari and Mohammad Reza Safaei

Mathematics 2021, 9(10), 1153; https://doi.org/10.3390/math9101153 - 20 May 2021

Cited by 32 | Viewed by 1808

Abstract

In the present study, a novel configuration of a rotating tube bundle was simulated under non-isothermal hydrodynamic conditions using a mixture model. Eight fins were considered in this study, which targeted the hydrodynamics of the system. An aqueous copper nanofluid was used as [...] Read more.

In the present study, a novel configuration of a rotating tube bundle was simulated under non-isothermal hydrodynamic conditions using a mixture model. Eight fins were considered in this study, which targeted the hydrodynamics of the system. An aqueous copper nanofluid was used as the heat transfer fluid. Various operating factors, such as rotation speed (up to 500 rad/s), Reynolds number (10–80), and concentration of the nanofluid (0.0–4.0%) were applied, and the performance of the microchannel heat exchanger was assessed. It was found that the heat transfer coefficient of the system could be enhanced by increasing the Reynolds number, the concentration of the nanofluid, and the rotation speed. The maximum enhancement in the heat transfer coefficient (HTC) was 258% after adding a 4% volumetric nanoparticle concentration to the base fluid and increasing Re from 10 to 80 and ω from 0 to 500 rad/s. Furthermore, at Re = 80 and ω = 500 rad/s, the HTC values measured for the nanofluid were 42.3% higher than those calculated for water, showing the nanoparticles’ positive impact on the heat transfer paradigm. Moreover, it was identified that copper nanoparticles’ presence had no significant effect on the system’s pressure drop. This was attributed to the interaction of the fluid flow and circulated flow around the tubes. Finally, the heat transfer coefficient and pressure drop had no considerable changes when augmenting the rotation speed at high Reynolds numbers. Full article

(This article belongs to the Special Issue Modeling and Numerical Analysis of Energy and Environment 2021)

► Show Figures

Figure 1

22 pages, 4626 KiB

Open AccessArticle

Combination Effect of Baffle Arrangement and Hybrid Nanofluid on Thermal Performance of a Shell and Tube Heat Exchanger Using 3-D Homogeneous Mixture Model

by Mashhour A. Alazwari and Mohammad Reza Safaei

Mathematics 2021, 9(8), 881; https://doi.org/10.3390/math9080881 - 16 Apr 2021

Cited by 52 | Viewed by 2926

Abstract

In this study, thermal performance and flow characteristics of a shell and tube heat exchanger equipped with various baffle angles were studied. The heat exchanger was operated with distilled water, and a hybrid nanofluid at three concentrations of 0.04% and 0.10% of GNP-Ag/water [...] Read more.

In this study, thermal performance and flow characteristics of a shell and tube heat exchanger equipped with various baffle angles were studied. The heat exchanger was operated with distilled water, and a hybrid nanofluid at three concentrations of 0.04% and 0.10% of GNP-Ag/water within Reynolds numbers ranged between 10,000 and 20,000. The thermophysical properties of nanofluid varied with temperature and nanoparticles’ concentration. The baffle angles were set at 45°, 90°, 135°, and 180°. Results showed that the calculated Nusselt number (Nu) could be improved by adding nanoparticles to the distilled water or increasing the fluid’s Reynolds number. At a low Re number, the Nu corresponding to baffle angle of 135° was very close to that recorded for the angle of 180°. At Re = 20,000, the Nu number was the highest (by 35% compared to the reference case), belonging to a baffle angle of 135°. Additionally, results related to friction factor and pressure drop showed that more locations with fluid blocking were observed by increasing the baffle angle, resulting in increased pressure drop value and friction. Finally, the temperature streamlines counter showed that the best baffle angle could be 135° in which maximum heat removal and the best thermal performance can be observed. Full article

(This article belongs to the Special Issue Modeling and Numerical Analysis of Energy and Environment 2021)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Modeling and Numerical Analysis of Energy and Environment 2021

Share This Special Issue

Special Issue Editor

Special Issue Information

Keywords

Published Papers (13 papers)

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI