Research

20 pages, 2876 KiB

Open AccessArticle

Insight into Dynamic of Mono and Hybrid Nanofluids Subject to Binary Chemical Reaction, Activation Energy, and Magnetic Field through the Porous Surfaces

by Qadeer Raza, M. Zubair Akbar Qureshi, Behzad Ali Khan, Ahmed Kadhim Hussein, Bagh Ali, Nehad Ali Shah and Jae Dong Chung

Mathematics 2022, 10(16), 3013; https://doi.org/10.3390/math10163013 - 21 Aug 2022

Cited by 43 | Viewed by 1578

Abstract

The mathematical modeling of the activation energy and binary chemical reaction system with six distinct types of nanoparticles, along with the magnetohydrodynamic effect, is studied in this paper. Different types of hybrid nanofluids flowing over porous surfaces with heat and mass transfer aspects [...] Read more.

The mathematical modeling of the activation energy and binary chemical reaction system with six distinct types of nanoparticles, along with the magnetohydrodynamic effect, is studied in this paper. Different types of hybrid nanofluids flowing over porous surfaces with heat and mass transfer aspects are examined here. The empirical relations for nanoparticle materials associated with thermophysical properties are expressed as partial differential equations, which are then interpreted into ordinary differential expressions using appropriate variables. The initial shooting method converts the boundary condition into the initial condition with an appropriate guess and finally finds out an accurate numerical solution by using the Runge–Kutta method with numerical stability. Variations in nanoparticle volume fraction at the lower and upper walls of porous surfaces, as well as the heat transfer rate measurements, are computed using the controlling physical factors. The effects of the flow-related variables on the axial velocity, radial velocity, temperature, and concentration profile dispersion are also investigated. The Permeable Reynolds number is directly proportional to the regression parameter. The injection/suction phenomenon associated with the expanding/contracting cases, respectively, have been described with engineering parameters. The hybrid nanoparticle volume fraction (1–5%) has a significant effect on the thermal system and radial velocity. Full article

(This article belongs to the Special Issue Nonlinear Partial Differential Equations in Mathematical Fluid Dynamics)

► Show Figures

Figure 1

17 pages, 861 KiB

Open AccessArticle

Insight into Significance of Bioconvection on MHD Tangent Hyperbolic Nanofluid Flow of Irregular Thickness across a Slender Elastic Surface

by Muhammad Zeeshan Ashraf, Saif Ur Rehman, Saadia Farid, Ahmed Kadhim Hussein, Bagh Ali, Nehad Ali Shah and Wajaree Weera

Mathematics 2022, 10(15), 2592; https://doi.org/10.3390/math10152592 - 25 Jul 2022

Cited by 74 | Viewed by 2047

Abstract

This numerical investigation effectively establishes a unique computing exploration for steady magnetohydrodynamic convective streams of tangent hyperbolic nanofluid traveling across a nonlinearly elongating elastic surface with a variable thickness. In addition, the importance of an externally imposed magnetic field of tangent hyperbolic nanofluid [...] Read more.

This numerical investigation effectively establishes a unique computing exploration for steady magnetohydrodynamic convective streams of tangent hyperbolic nanofluid traveling across a nonlinearly elongating elastic surface with a variable thickness. In addition, the importance of an externally imposed magnetic field of tangent hyperbolic nanofluid is comprehensively analyzed by considering the substantial impact of thermal conductivity and thermal radiation consequences. The governing PDEs (partial differential equations) are transmuted into a nonlinear differential structure of coupled ODEs (ordinary differential equations) using a series of variable similarity transformations. Furthermore, these generated ODEs (ordinary differential equations) are numerically set using a novel revolutionary Runge-Kutta algorithm with a shooting approach constructed in a MATLAB script. In this regard, extensive comparison studies are carried out to validate the acquired numerical results. The interactions between the associated profiles and the relevant parameters are rationally explored and shown using graphs and tabular forms. The velocity distribution declined with improving Weissengberg number

W e

and power-law index m, while the reverse performance can be observed for temperature. As enhancement in Brownian motion, Thermophoretic and radiation parameters significantly rise in temperature distribution. The use of many different technological and industrial systems, including nano-bioconvective systems, nano-droplet evaporation, nano-ink jet printing, and microbial fuel cells, would benefit this research study. Full article

(This article belongs to the Special Issue Nonlinear Partial Differential Equations in Mathematical Fluid Dynamics)

► Show Figures

Figure 1

28 pages, 8405 KiB

Open AccessArticle

Numerical Study of MHD Natural Convection inside a Cubical Cavity Loaded with Copper-Water Nanofluid by Using a Non-Homogeneous Dynamic Mathematical Model

by Mohamed Sannad, Ahmed Kadhim Hussein, Awatef Abidi, Raad Z. Homod, Uddhaba Biswal, Bagh Ali, Lioua Kolsi and Obai Younis

Mathematics 2022, 10(12), 2072; https://doi.org/10.3390/math10122072 - 15 Jun 2022

Cited by 15 | Viewed by 1760

Abstract

Free convective flow in a cubical cavity loaded with copper-water nanofluid was examined numerically by employing a non-homogeneous dynamic model, which is physically more realistic in representing nanofluids than homogenous ones. The cavity was introduced to a horizontal magnetic field from the left [...] Read more.

Free convective flow in a cubical cavity loaded with copper-water nanofluid was examined numerically by employing a non-homogeneous dynamic model, which is physically more realistic in representing nanofluids than homogenous ones. The cavity was introduced to a horizontal magnetic field from the left sidewall. Both the cavity’s vertical left and right sidewalls are preserved at an isothermal cold temperature (T_c). The cavity includes inside it four isothermal heating blocks in the middle of the top and bottom walls. The other cavity walls are assumed adiabatic. Simulations were performed for solid volume fraction ranging from (0 ≤ ϕ ≤ 0.06), Rayleigh number varied as (10³ ≤ Ra ≤ 10⁵), the Hartmann number varied as (0 ≤ Ha ≤ 60), and the diameter of nanoparticle varied as (10 nm ≤ d_p ≤ 130 nm). It was found that at (d_p = 10 nm), the average Nusselt number declines when Ha increases, whereas it increases as (Ra) and (ϕ) increase. Furthermore, the increasing impact of the magnetic field on the average Nusselt number is absent for (Ra = 10³), and this can be seen for all values of (ϕ). However, when (d_p) is considered variable, the average Nusselt number was directly proportional to (Ra) and (ϕ) and inversely proportional to (d_p). Full article

(This article belongs to the Special Issue Nonlinear Partial Differential Equations in Mathematical Fluid Dynamics)

► Show Figures

Figure 1

31 pages, 7778 KiB

Open AccessArticle

MHD Natural Convection and Radiation over a Flame in a Partially Heated Semicircular Cavity Filled with a Nanofluid

by Obai Younis, Milad Alizadeh, Ahmed Kadhim Hussein, Bagh Ali, Uddhaba Biswal and Emad Hasani Malekshah

Mathematics 2022, 10(8), 1347; https://doi.org/10.3390/math10081347 - 18 Apr 2022

Cited by 11 | Viewed by 1652

Abstract

The numerical analysis of MHD-free convective heat transfer and its interaction with the radiation over a heated flame inside a porous semicircular cavity loaded with SWCNTs–water nanofluid was explored for the very first time in the present work. The two circular arcs of [...] Read more.

The numerical analysis of MHD-free convective heat transfer and its interaction with the radiation over a heated flame inside a porous semicircular cavity loaded with SWCNTs–water nanofluid was explored for the very first time in the present work. The two circular arcs of the upper wall of the enclosure were preserved at a constant cold temperature, whereas the middle region of it was considered adiabatic. The midland region of the lower wall was heated partially, while other regions were also assumed adiabatic. An internal hot flame was included inside the cavity, while the cavity was exposed to a magnetic field. The results were illustrated for Hartmann number (0 ≤ Ha ≤ 100), Rayleigh number (10⁴ ≤ Ra ≤ 10⁶), heated region length (0.1 ≤ L ≤ 0.3), solid volumetric fraction (0 ≤ φ ≤ 0.04), Darcy number (10⁻³ ≤ Da ≤ 10⁻⁵) and radiation parameter (0 ≤ Rd ≤ 1). It was found that decreasing L is the best option for enhancing natural convection. Moreover, it was noted that (Nu_out) is directly proportion to (Ra), (

ϕ

), (Rd) and (Da) increase. In contrast, it was in reverse proportion to (Ha). Furthermore, the results showed that augmentation of about (4%) and a decrement of (56.55%) are obtained on the average (Nu) on the heated length by increasing the radiation and the Hartmann number, respectively. Moreover, raising the radiation number from (0 to 1) causes an augmentation of about (73%) in the average (Nu) of the heated flame. Results also indicated that increasing the Hartmann number will cause a decrement of about (82.4%) of the maximum velocity profile in the vertical direction. Full article

(This article belongs to the Special Issue Nonlinear Partial Differential Equations in Mathematical Fluid Dynamics)

► Show Figures

Figure 1

18 pages, 12932 KiB

Open AccessArticle

Double Diffusive Natural Convection in a Square Cavity Filled with a Porous Media and a Power Law Fluid Separated by a Wavy Interface

by Lioua Kolsi, Shafqat Hussain, Kaouther Ghachem, Muhammad Jamal and Chemseddine Maatki

Mathematics 2022, 10(7), 1060; https://doi.org/10.3390/math10071060 - 25 Mar 2022

Cited by 9 | Viewed by 1971

Abstract

This study deals with the influence of a wavy interface separating two layers filled with power law fluid and porous media, respectively. The governing equations are solved using the Finite Element Method (FEM) and the numerical model is validated by comparing with experimental [...] Read more.

This study deals with the influence of a wavy interface separating two layers filled with power law fluid and porous media, respectively. The governing equations are solved using the Finite Element Method (FEM) and the numerical model is validated by comparing with experimental findings. The parameters governing the studied configuration are varied as: Rayleigh number (10³ ≤ Ra ≤ 10⁶), power law index (0.6 ≤ n ≤ 1.4), Darcy number (10⁻² ≤ Da ≤ 10⁻⁶), buoyancy ratio (0.1 ≤ N ≤ 10) and Lewis number (1 ≤ Le ≤ 10). It is inferred that the temperature gradient increases by augmenting the Rayleigh number, as the flow is observed from the vertical to horizontal direction in both layers. Constant enhancement in the heat and mass transfer is also observed by enriching the buoyancy effect. Moreover, the average Nusselt and Sherwood numbers decline by increasing the width of the porous layer. Full article

(This article belongs to the Special Issue Nonlinear Partial Differential Equations in Mathematical Fluid Dynamics)

► Show Figures

Figure 1

17 pages, 5730 KiB

Open AccessArticle

Generalized Exp-Function Method to Find Closed Form Solutions of Nonlinear Dispersive Modified Benjamin–Bona–Mahony Equation Defined by Seismic Sea Waves

by Muhammad Shakeel, Attaullah, Essam Roshdy El-Zahar, Nehad Ali Shah and Jae Dong Chung

Mathematics 2022, 10(7), 1026; https://doi.org/10.3390/math10071026 - 23 Mar 2022

Cited by 23 | Viewed by 1777

Abstract

Using the new generalized exp-function method, we were able to derive significant novel closed form solutions to the nonlinear dispersive modified Benjamin–Bona–Mahony (DMBBM) equation. The general framework of the new generalized exp-function method has been given. Many novel closed form solutions have been [...] Read more.

Using the new generalized exp-function method, we were able to derive significant novel closed form solutions to the nonlinear dispersive modified Benjamin–Bona–Mahony (DMBBM) equation. The general framework of the new generalized exp-function method has been given. Many novel closed form solutions have been obtained in the form of hyperbolic, trigonometric, and rational function solutions. Using the computer application Wolfram Mathematica 10, we plotted 2D, 3D, and contour surfaces of closed form solutions found in this work. In the form of a table, the acquired results are compared to the known solutions in the existing literature. Full article

(This article belongs to the Special Issue Nonlinear Partial Differential Equations in Mathematical Fluid Dynamics)

► Show Figures

Figure 1

14 pages, 98376 KiB

Open AccessArticle

Mixed Convection inside a Duct with an Open Trapezoidal Cavity Equipped with Two Discrete Heat Sources and Moving Walls

by Fateh Mebarek-Oudina, Hanane Laouira, Ahmed Kadhim Hussein, Mohamed Omri, Aissa Abderrahmane, Lioua Kolsi and Uddhaba Biswal

Mathematics 2022, 10(6), 929; https://doi.org/10.3390/math10060929 - 14 Mar 2022

Cited by 23 | Viewed by 1771

Abstract

The current research presents a numerical investigation of the mixed convection inside a horizontal rectangular duct combined with an open trapezoidal cavity. The region in the bottom wall of the cavity is heated by using two discrete heat sources. The cold airflow enters [...] Read more.

The current research presents a numerical investigation of the mixed convection inside a horizontal rectangular duct combined with an open trapezoidal cavity. The region in the bottom wall of the cavity is heated by using two discrete heat sources. The cold airflow enters the duct horizontally at a fixed velocity and a constant temperature. All the other walls of the duct and the cavity are adiabatic. Throughout this study, four various cases were investigated depending on the driven walls. The effects of the Richardson number and Reynolds number ratio are studied under various cases related to the lid-driven sidewalls. The results are presented in terms of the flow and thermal fields and the average Nusselt number. The yielded data show that the average Nusselt number rises as the Richardson number and Reynolds number ratio increases. Furthermore, the Reynolds number ratio and the movement of the cavity sidewall(s) have a significant effect on the velocity and temperature contours. By the end of the study, it is shown that the maximum rates of heat transfer are related to Case 1 where the left sidewall moves downward and heater 2, which is placed near the left sidewall. Full article

(This article belongs to the Special Issue Nonlinear Partial Differential Equations in Mathematical Fluid Dynamics)

► Show Figures

Figure 1

18 pages, 40157 KiB

Open AccessArticle

MHD Hybrid Nanofluid Mixed Convection Heat Transfer and Entropy Generation in a 3-D Triangular Porous Cavity with Zigzag Wall and Rotating Cylinder

by Aissa Abderrahmane, Naef A. A. Qasem, Obai Younis, Riadh Marzouki, Abed Mourad, Nehad Ali Shah and Jae Dong Chung

Mathematics 2022, 10(5), 769; https://doi.org/10.3390/math10050769 - 28 Feb 2022

Cited by 66 | Viewed by 3164

Abstract

The purpose of this work was to conduct a numerical examination of mixed convective heat transfer in a three-dimensional triangular enclosure with a revolving circular cylinder in the cavity’s center. Numerical simulations of the hybrid Fe₃O₄/MWCNT-water nanofluid are performed [...] Read more.

The purpose of this work was to conduct a numerical examination of mixed convective heat transfer in a three-dimensional triangular enclosure with a revolving circular cylinder in the cavity’s center. Numerical simulations of the hybrid Fe₃O₄/MWCNT-water nanofluid are performed using the finite element approach (FEM). The simulation is carried out for a range of parameter values, including the Darcy number (between 10⁻⁵ and 10⁻²), the Hartmann number (between 0 and 100), the angular speed of the rotation (between −500 and 1000), and the number of zigzags. The stream function, isotherms, and isentropic contours illustrate the impact of many parameters on motion, heat transfer, and entropy formation. The findings indicate that for enhancing the heat transfer rates of hybrid nanofluid in a three-dimensional triangular porous cavity fitted with a rotating cylinder and subjected to a magnetic field, Darcy number > 10⁻³, Hartmann number < 0, one zigzag on the hot surface, and rotation speed >500 in flow direction are recommended. Full article

(This article belongs to the Special Issue Nonlinear Partial Differential Equations in Mathematical Fluid Dynamics)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Nonlinear Partial Differential Equations in Mathematical Fluid Dynamics

Share This Special Issue

Special Issue Editor

Special Issue Information

Keywords

Published Papers (8 papers)

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI