Analysis and Applications of Mathematical Fluid Dynamics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: closed (30 September 2023) | Viewed by 24085

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Interests: computational fluid dynamics; heat mass transfer
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Dear Colleagues,

Fluid dynamics studies deal with fluid flow in fluid mechanics. Fluids may be categorized into three forms, namely, liquids, gases, and plasma. Plasma is ionized gas, and much of the universe is thought to consist of plasma. It is often applied in galaxy information and modern plasma television. The study of fluid dynamics has attracted many researchers because of its widespread applications, including, among others, for biological and medical purposes, flow rate and velocity, Bernoulli’s equation: pressure and speed, Poiseuille’s equation and viscosity, blood flow, surface tension, molecular transport phenomena, pumps, and the heart. In addition to the abovementioned research areas, fluid mechanics covers aerodynamics, which is concerned with the study of air in motion, whose applications, among others, include finding and calculating forces acting on airplanes and the design of airplane wings.

This Special Issue aims to bring together academics, engineers, researchers, and scientists to share recent ideas, methods, trends, problems, and solutions in the following areas:

  • Applied, computational, and mathematical physics;
  • Combustion and decomposition theories;
  • Computational thermal engineering;
  • Heat and mass transfer;
  • Magnetohydrodynamics (MHD);
  • Mechanics of fluids.

Dr. Ramoshweu Solomon Lebelo
Guest Editor

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Keywords

  • applied, computational, and mathematical physics
  • combustion and decomposition theories
  • computational thermal engineering
  • heat and mass transfer
  • magnetohydrodynamics (MHD)
  • mechanics of fluids

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Published Papers (19 papers)

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Research

18 pages, 358 KiB  
Article
Periodic Flows in a Viscous Stratified Fluid in a Homogeneous Gravitational Field
by Yuli D. Chashechkin and Artem A. Ochirov
Mathematics 2023, 11(21), 4443; https://doi.org/10.3390/math11214443 - 26 Oct 2023
Viewed by 642
Abstract
The density of a fluid or gas, which depends on the temperature, pressure and concentration of dissolved substances or suspended particles, changes under the influence of a large number of physical factors. We assume that an undisturbed liquid is heterogeneous. The propagation of [...] Read more.
The density of a fluid or gas, which depends on the temperature, pressure and concentration of dissolved substances or suspended particles, changes under the influence of a large number of physical factors. We assume that an undisturbed liquid is heterogeneous. The propagation of periodic flows in viscous, uniformly stratified fluids is considered. The analysis is based on a system of fundamental equations for the transfer of energy, momentum and matter in periodic flows. Taking into account the compatibility condition, dispersion relations are constructed for two-dimensional internal, acoustic and surface linear periodic flows with a positive definite frequency and complex wave number in a compressible viscous fluid exponentially stratified by density. The temperature conductivity and diffusion effects are neglected. The obtained regularly perturbed solutions of the dispersion equations describe the conventional weakly damped waves. The families of singular solutions, specific for every kind of periodic flow, characterize the before unknown thin ligaments that accompany each type of wave. In limited cases, the constructed regular solutions transform into well-known expressions for a viscous homogeneous and an ideal fluid. Singular solutions are degenerated in a viscous homogeneous fluid or disappear in an ideal fluid. The developing method of the fundamental equation system analysis is directed to describe the dynamics and spatial structure of periodic flows in heterogeneous fluids in linear and non-linear approximations. Full article
(This article belongs to the Special Issue Analysis and Applications of Mathematical Fluid Dynamics)
13 pages, 6427 KiB  
Article
Mathematical Modeling of Pseudoplastic Nanofluid Natural Convection in a Cavity with a Heat-Generating Unit and Solid Finned Heat Sink
by Daria S. Loenko and Mikhail A. Sheremet
Mathematics 2023, 11(18), 3868; https://doi.org/10.3390/math11183868 - 11 Sep 2023
Viewed by 728
Abstract
The power-law nanofluid natural convection in a chamber with a thermally generating unit and a solid ribbed structure has been studied in this work. A mixture of carboxymethylcellulose with water and copper nanoparticles is a working fluid illustrating pseudoplastic properties. The effective properties [...] Read more.
The power-law nanofluid natural convection in a chamber with a thermally generating unit and a solid ribbed structure has been studied in this work. A mixture of carboxymethylcellulose with water and copper nanoparticles is a working fluid illustrating pseudoplastic properties. The effective properties of the nanoliquid have been described by experimental correlations reflecting the temperature effect. The governing equations have been formulated on the basis of the conservation laws of mass, momentum and energy employing non-primitive parameters such as stream function and vorticity. The defined boundary value problem has been worked out by the finite difference technique using an independently developed calculation system. The Rayleigh number is fixed for analysis (Ra = 105). The paper analyzes the influence of the nanoparticles volume fraction, an increase in which reduces the temperature in the case of the one edge presence. An analysis of the rib height has shown that its growth leads to a weakening of the convective heat transfer, but at the same time, the source temperature also decreases. Increasing the number of fins from 1 to 3 also helps to reduce the average temperature of the heat-generated element by 15%. Full article
(This article belongs to the Special Issue Analysis and Applications of Mathematical Fluid Dynamics)
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17 pages, 4959 KiB  
Article
Numerical Investigation of a Combustible Polymer in a Rectangular Stockpile: A Spectral Approach
by Adeshina T. Adeosun, Joel C. Ukaegbu and Ramoshweu S. Lebelo
Mathematics 2023, 11(16), 3510; https://doi.org/10.3390/math11163510 - 14 Aug 2023
Viewed by 638
Abstract
Despite the wide application of combustion in reactive materials, one of the challenges faced globally is the auto-ignition of such materials, resulting in fire and explosion hazards. To avoid this unfortunate occurrence, a mathematical model describing the thermal decomposition of combustible polymer material [...] Read more.
Despite the wide application of combustion in reactive materials, one of the challenges faced globally is the auto-ignition of such materials, resulting in fire and explosion hazards. To avoid this unfortunate occurrence, a mathematical model describing the thermal decomposition of combustible polymer material in a rectangular stockpile is formulated. A nonlinear momentum equation is provided with the assumption that the combustible polymer follows a Carreau constitutive relation. The chemical reaction of the polymer material is assumed to be exothermic; therefore, Arrhenius’s kinetic theory is considered in the energy balance equation. The bivariate spectral local linearization scheme (BSLLS) is utilized to provide a numerical solution for the dimensionless equations governing the problem. The obtained results are validated by the collocation weighted residual method (CWRM), and a good agreement is achieved. Dimensionless velocity, temperature, and thermal stability results are presented and explained comprehensively with suitable applications. Some of the obtained results show that thermal criticality increases with increasing power law index (n) and radiation (Ra) values and decreases with increasing variable viscosity (β1) and material parameter (We) values. Full article
(This article belongs to the Special Issue Analysis and Applications of Mathematical Fluid Dynamics)
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17 pages, 3597 KiB  
Article
Convective Heat Transfer and Entropy Generation for Nano-Jet Impingement Cooling of a Moving Hot Surface under the Effects of Multiple Rotating Cylinders and Magnetic Field
by Lioua Kolsi, Fatih Selimefendigil, Samia Larguech, Kaouther Ghachem, Hind Albalawi, Badr M. Alshammari and Taher Labidi
Mathematics 2023, 11(8), 1891; https://doi.org/10.3390/math11081891 - 17 Apr 2023
Cited by 1 | Viewed by 1026
Abstract
In this study, confined slot nano-jet impingement cooling of a hot moving surface is investigated under the combined utilization multiple rotating cylinders and magnetic field. Both convective heat transfer and entropy generation analysis are conducted using a finite element method. Parametric variation of [...] Read more.
In this study, confined slot nano-jet impingement cooling of a hot moving surface is investigated under the combined utilization multiple rotating cylinders and magnetic field. Both convective heat transfer and entropy generation analysis are conducted using a finite element method. Parametric variation of the rotational Reynolds number (Rew between −500 and 500), velocity ratio (VR between 0 and 0.25), Hartmann number (Ha between 0 and 20) and the horizontal location of cylinders (Mx between −8 and 8) are considered. Rotation of the cylinders generally resulted in the degradation of cooling performance while increasing the wall velocity, and the horizontal location of the cylinder was found to positively contribute to this. Heat transfer rate reductions of 20% and 12.5% are obtained using rotations at the highest Rew for the case of stationary (VR = 0) and moving wall (VR = 0.25). When magnetic field at the highest strength is imposed in the rotating cylinder case, the cooling performance is increased by about 18.6%, while it is reduced by about 28% for the non-rotating cylinder case. The hot wall movement contributes, by about 14%, to the overall cooling performance enhancement. Away from the inlet location of the rotating cylinders, thermal performance improvement of 12% is obtained. The entropy generation rises with higher hot wall velocity and higher horizontal distances of the rotating cylinders, while it is reduced with a higher magnetic field for non-rotating cylinders. The best configurations in terms of cooling performance provide 8.7% and 34.2% enhancements for non-rotating and rotating cylinders compared with the reference case of (Rew, VR, Ha, Mx) = (0, 0, 0, 0), while entropy generation becomes 1% and 15% higher. Full article
(This article belongs to the Special Issue Analysis and Applications of Mathematical Fluid Dynamics)
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13 pages, 2821 KiB  
Article
Exergy Analysis for Combustible Third-Grade Fluid Flow through a Medium with Variable Electrical Conductivity and Porous Permeability
by Samuel O. Adesanya, Peace O. Banjo and Ramoshweu S. Lebelo
Mathematics 2023, 11(8), 1882; https://doi.org/10.3390/math11081882 - 15 Apr 2023
Viewed by 1003
Abstract
A mathematical investigation of a thermodynamical system linked with energy management and its impact on the environment, especially climate change, is presented in this study. In this regard, a numerical investigation of the flow and heat transfer of hydromagnetic third-grade liquid through a [...] Read more.
A mathematical investigation of a thermodynamical system linked with energy management and its impact on the environment, especially climate change, is presented in this study. In this regard, a numerical investigation of the flow and heat transfer of hydromagnetic third-grade liquid through a porous medium. The permeability of the medium and electrical conductivity of the fluid are assumed to be temperature functions. The appropriate mathematical formulations for momentum, energy, and entropy equations are presented in both dimensional and dimensionless forms. We obtained the numerical solutions using the spectral version of the Chebyshev collocation method and compared the result with the shooting Runge–Kutta method. Numerical results for velocity, temperature, entropy, and Bejan profiles are communicated through tables and graphs with adequate physical interpretation. The thermal stability of the thermo-fluid system that guarantees the prevention of spontaneous fluid heating that fuels climate change is also included in the analysis. Full article
(This article belongs to the Special Issue Analysis and Applications of Mathematical Fluid Dynamics)
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18 pages, 2445 KiB  
Article
Developments of Electro-Osmotic Two-Phase Flows of Fourth-Grade Fluid through Convergent and Divergent Channels
by Nahid Fatima, Mubbashar Nazeer, Maha M. A. Lashin, M. M. Ghafar, M. R. Gorji and M. K. Hameed
Mathematics 2023, 11(8), 1832; https://doi.org/10.3390/math11081832 - 12 Apr 2023
Cited by 8 | Viewed by 1027
Abstract
This paper discusses the development of two different bi-phase flows. Fourth-grade fluid exhibiting the non-Newtonian fluid nature is taken as the base liquid. Two-phase suspension is obtained by using the spherically homogeneous metallic particle. Owing to the intense application of mechanical and chemical [...] Read more.
This paper discusses the development of two different bi-phase flows. Fourth-grade fluid exhibiting the non-Newtonian fluid nature is taken as the base liquid. Two-phase suspension is obtained by using the spherically homogeneous metallic particle. Owing to the intense application of mechanical and chemical multiphase flows through curved and bent configurations effectively transforms the flow dynamics of the fluid. Differential equations for electro-osmotically driven fluid are modeled and solved with the help of the regular perturbation method. The obtained theoretical solution is further compared with the ones obtained by using two different numerical techniques and found to be in full agreement. Full article
(This article belongs to the Special Issue Analysis and Applications of Mathematical Fluid Dynamics)
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22 pages, 1007 KiB  
Article
Heat and Mass Transfer Analysis for the Viscous Fluid Flow: Dual Approximate Solutions
by Remus-Daniel Ene, Nicolina Pop and Rodica Badarau
Mathematics 2023, 11(7), 1648; https://doi.org/10.3390/math11071648 - 29 Mar 2023
Cited by 1 | Viewed by 1246
Abstract
The aim of this paper is to investigate effective and accurate dual analytic approximate solutions, while taking into account thermal effects. The heat and mass transfer problem in a viscous fluid flow are analytically explored by using the modified Optimal Homotopy Asymptotic Method [...] Read more.
The aim of this paper is to investigate effective and accurate dual analytic approximate solutions, while taking into account thermal effects. The heat and mass transfer problem in a viscous fluid flow are analytically explored by using the modified Optimal Homotopy Asymptotic Method (OHAM). By using similarity transformations, the motion equations are reduced to a set of nonlinear ordinary differential equations. Based on the numerical results, it was revealed that there are dual analytic approximate solutions within the mass transfer problem. The variation of the physical parameters (the Prandtl number and the temperature distribution parameter) over the temperature profile is analytically explored and graphically depicted for the first approximate and the corresponding dual solution, respectively. The advantage of the proposed method arises from using only one iteration for obtaining the dual analytical solutions. The presented results are effective, accurate and in good agreement with the corresponding numerical results with relevance for further engineering applications of heat and mass transfer problems. Full article
(This article belongs to the Special Issue Analysis and Applications of Mathematical Fluid Dynamics)
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15 pages, 3696 KiB  
Article
Turbulent Heat Transfer Augmentation in a Square Channel by Augmenting the Flow Pattern with Novel Arc-Shaped Ribs
by Basma Souayeh and Suvanjan Bhattacharyya
Mathematics 2023, 11(6), 1490; https://doi.org/10.3390/math11061490 - 18 Mar 2023
Cited by 1 | Viewed by 1383
Abstract
Solar water heaters (SWHs) are widely used in HVAC industries as well as in households for different heating purposes. The present numerical simulation focuses on the investigation of the thermo-hydraulic performance of novel semi-arc-rib SWHs. Semi-arc-shaped ribs in the square channel of the [...] Read more.
Solar water heaters (SWHs) are widely used in HVAC industries as well as in households for different heating purposes. The present numerical simulation focuses on the investigation of the thermo-hydraulic performance of novel semi-arc-rib SWHs. Semi-arc-shaped ribs in the square channel of the absorber plates with different pitch and height ratios are investigated in this study. The present novel modification disturbs the boundary layers by generating vortices, and thus, enhanced fluid mixing takes place. Water with a Reynolds number (Re) ranging from 4000 to 25,000 is used as a working fluid, and a 1.0 kW/m2 heat flux is imposed on the tube wall. The results demonstrate a significant increase in the Nusselt number (Nu) as the fluid layers localize behind each rib near the absorber plates, and at the same time, the number of swirls generated inside the tube and the frictional losses both increased noticeably. To ensure the effectivity of the present novel SWH geometry, the thermo-hydraulic performance (η) for each case was calculated, and it was found that in all the cases, it was greater than unity, which signifies that the present semi-arc-rib SWH is promising and can be used in HVAC industrial and household applications. Full article
(This article belongs to the Special Issue Analysis and Applications of Mathematical Fluid Dynamics)
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21 pages, 10520 KiB  
Article
Optimization of MHD Flow of Radiative Micropolar Nanofluid in a Channel by RSM: Sensitivity Analysis
by Reham A. Alahmadi, Jawad Raza, Tahir Mushtaq, Shaimaa A. M. Abdelmohsen, Mohammad R. Gorji and Ahmed M. Hassan
Mathematics 2023, 11(4), 939; https://doi.org/10.3390/math11040939 - 13 Feb 2023
Cited by 20 | Viewed by 1582
Abstract
These days, heat transfer plays a significant role in the fields of engineering and energy, particularly in the biological sciences. Ordinary fluid is inadequate to transfer heat in an efficient manner, therefore, several models were considered for the betterment of heat transfer. One [...] Read more.
These days, heat transfer plays a significant role in the fields of engineering and energy, particularly in the biological sciences. Ordinary fluid is inadequate to transfer heat in an efficient manner, therefore, several models were considered for the betterment of heat transfer. One of the most prominent models is a single-phase nanofluid model. The present study is devoted to solving the problem of micropolar fluid with a single-phase model in a channel numerically. The governing partial differential equations (PDEs) are converted into nonlinear ordinary differential equations (ODEs) by introducing similarity transformation and then solved numerically by the finite difference method. Response surface methodology (RSM) together with sensitivity analysis are implemented for the optimization analysis. The study reveals that sensitivity of the skin friction coefficient (Cfx) to the Reynolds number (R) and magnetic parameter (M) is positive (directly proportional) and negative (inversely proportional) for the micropolar parameter. Full article
(This article belongs to the Special Issue Analysis and Applications of Mathematical Fluid Dynamics)
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29 pages, 2606 KiB  
Article
Artificial Neural Networking Magnification for Heat Transfer Coefficient in Convective Non-Newtonian Fluid with Thermal Radiations and Heat Generation Effects
by Khalil Ur Rehman, Wasfi Shatanawi and Andaç Batur Çolak
Mathematics 2023, 11(2), 342; https://doi.org/10.3390/math11020342 - 9 Jan 2023
Cited by 5 | Viewed by 1355
Abstract
In this study, the Casson fluid flow through an inclined, stretching cylindrical surface is considered. The flow field is manifested with pertinent physical effects, namely heat generation, viscous dissipation, thermal radiations, stagnation point flow, variable thermal conductivity, a magnetic field, and mixed convection. [...] Read more.
In this study, the Casson fluid flow through an inclined, stretching cylindrical surface is considered. The flow field is manifested with pertinent physical effects, namely heat generation, viscous dissipation, thermal radiations, stagnation point flow, variable thermal conductivity, a magnetic field, and mixed convection. In addition, the flow field is formulated mathematically. The shooting scheme is used to obtain the numerical data of the heat transfer coefficient at the cylindrical surface. Further, for comparative analysis, three different thermal flow regimes are considered. In order to obtain a better estimation of the heat transfer coefficient, three corresponding artificial neural networks (ANN) models were constructed by utilizing Tan-Sig and Purelin transfer functions. It was observed that the heat transfer rate exhibits an inciting nature for the Eckert and Prandtl numbers, curvature, and heat generation parameters, while the Casson fluid parameter, temperature-dependent thermal conductivity, and radiation parameter behave oppositely. The present ANN estimation will be helpful for studies related to thermal energy storage that have Nusselt number involvements. Full article
(This article belongs to the Special Issue Analysis and Applications of Mathematical Fluid Dynamics)
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25 pages, 2931 KiB  
Article
Computational Analysis on Magnetized and Non-Magnetized Boundary Layer Flow of Casson Fluid Past a Cylindrical Surface by Using Artificial Neural Networking
by Khalil Ur Rehman, Wasfi Shatanawi and Andaç Batur Çolak
Mathematics 2023, 11(2), 326; https://doi.org/10.3390/math11020326 - 8 Jan 2023
Cited by 6 | Viewed by 1218
Abstract
In this article, we constructed an artificial neural networking model for the stagnation point flow of Casson fluid towards an inclined stretching cylindrical surface. The Levenberg–Marquardt training technique is used in multilayer perceptron network models. Tan–Sig and purelin transfer functions are carried in [...] Read more.
In this article, we constructed an artificial neural networking model for the stagnation point flow of Casson fluid towards an inclined stretching cylindrical surface. The Levenberg–Marquardt training technique is used in multilayer perceptron network models. Tan–Sig and purelin transfer functions are carried in the layers. For better novelty, heat and mass transfer aspects are taken into account. The viscous dissipation, thermal radiations, variable thermal conductivity, and heat generation effects are considered by way of an energy equation while the chemical reaction effect is calculated by use of the concentration equation. The flow is mathematically modelled for magnetic and non-magnetic flow fields. The flow equations are solved by the shooting method and the outcomes are concluded by means of line graphs and tables. The skin friction coefficient is evaluated at the cylindrical surface for two different flow regimes and the corresponding artificial neural networking estimations are presented. The coefficient of determination values’ proximity to one and the low mean squared error values demonstrate that each artificial neural networking model predicts the skin friction coefficient with high accuracy. Full article
(This article belongs to the Special Issue Analysis and Applications of Mathematical Fluid Dynamics)
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13 pages, 1069 KiB  
Article
Radiative MHD Nanofluid Flow Due to a Linearly Stretching Sheet with Convective Heating and Viscous Dissipation
by Haifaa Alrihieli, Mohammed Alrehili and Ahmed M. Megahed
Mathematics 2022, 10(24), 4743; https://doi.org/10.3390/math10244743 - 14 Dec 2022
Cited by 7 | Viewed by 1293
Abstract
This article describes a two-dimensional steady laminar boundary layer flow and heat mass transfer caused by a non-Newtonian nanofluid due to a horizontally stretching sheet. The non-dimensional parameters take into consideration and regulate the effects of convective boundary condition, slip velocity, Brownian motion, [...] Read more.
This article describes a two-dimensional steady laminar boundary layer flow and heat mass transfer caused by a non-Newtonian nanofluid due to a horizontally stretching sheet. The non-dimensional parameters take into consideration and regulate the effects of convective boundary condition, slip velocity, Brownian motion, thermophoresis and viscous dissipation. The thermal radiation, which affects the flow’s thermal conductivity and the nanofluid’s variable viscosity are also taken into consideration. We propose that a hot fluid could exist beneath the stretching sheet’s bottom surface, which could aid in warming the surface via convection. The physical boundary conditions are non-dimensionalized, as are the governing transport set of nonlinear partial differential equations. By using the shooting approach, numerical values for dimensionless velocity, temperature and nanoparticle concentration are achieved. Distributions of velocity, temperature and concentration are plotted against a number of newly important governing factors, and the outcomes are then provided in accordance with those graphs. Additionally, the local skin-friction coefficient, the local Sherwood number and the local Nusselt number are discussed in order to further clarify and thoroughly explain the current problem. In order to validate the numerical results, comparisons are made with previously published data in the literature. There is a really good accord. Additionally, the current work has implications in the nanofluid applications. Full article
(This article belongs to the Special Issue Analysis and Applications of Mathematical Fluid Dynamics)
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15 pages, 3196 KiB  
Article
Numerical Investigation of the Magnetized Reactive Viscous Couple Stress Fluid Flow Down an Inclined Riga Plate with Variable Viscosity
by Samuel Olumide Adesanya, Tunde Abdulkadir Yusuf and Ramoshweu Solomon Lebelo
Mathematics 2022, 10(24), 4713; https://doi.org/10.3390/math10244713 - 12 Dec 2022
Cited by 2 | Viewed by 1077
Abstract
Accurate determination of optimum flow and heat transfer condition is one of the major challenges faced in the application of magnetic fluid in the field of medicine and engineering, especially when applied as ferrofluids for targeted drug deliveries, treatment of hyperthermia, sealants in [...] Read more.
Accurate determination of optimum flow and heat transfer condition is one of the major challenges faced in the application of magnetic fluid in the field of medicine and engineering, especially when applied as ferrofluids for targeted drug deliveries, treatment of hyperthermia, sealants in computer hard drives, lubricants in car shafts. In view of these important applications, a mathematical investigation of the flow and heat transfer behavior of reactive magnetic fluids containing nanostructures is presented based on a couple of stress constitutive models. The reactive fluid is assumed to flow through inclined magnetized solid boundaries for energy conversion. The formulation leads to nonlinear coupled equations. The dimensionless equations are numerically solved using the spectral Chebyshev assumed solution for the weighted residual technique, and the correctness of the solution is confirmed using the shooting Runge–Kutta method. The effects of various fluid parameters on velocity, temperature, skin friction, and heat transfer rates are described in tabular and graphical form, along with suitable physical explanations. Thermal analysis computations are also presented. According to the findings, an enhanced couple of stress fluid and variable viscosity parameters reduced the skin drag and heat transfer rate at the bottom wall. Furthermore, the thermal stability of the flow can be achieved with increasing values modified Hartman number while increasing couple stress parameter encourages thermal instability in the flow domain. Full article
(This article belongs to the Special Issue Analysis and Applications of Mathematical Fluid Dynamics)
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17 pages, 5513 KiB  
Article
Finite Element Analysis of Generalized Thermoelastic Interaction for Semiconductor Materials under Varying Thermal Conductivity
by Aatef Hobiny and Ibrahim Abbas
Mathematics 2022, 10(24), 4676; https://doi.org/10.3390/math10244676 - 9 Dec 2022
Viewed by 837
Abstract
In this work, we consider the problem of a semiconductor half-space formed of varying thermal conductivity materials with and without Kirchhoff’s transforms. Specifically, we deal with one thermal relaxation time within the context of generalized photothermoelastic theory. It is expected that the thermal [...] Read more.
In this work, we consider the problem of a semiconductor half-space formed of varying thermal conductivity materials with and without Kirchhoff’s transforms. Specifically, we deal with one thermal relaxation time within the context of generalized photothermoelastic theory. It is expected that the thermal conductivity of the material will vary with temperature. The finite element method is used to numerically solve this problem. The Laplace transform and the eigenvalues method are used to determine analytical solutions to the linear problem. Various hypotheses are investigated, both with and without the use of Kirchhoff’s transformations, to consider the influence of thermal conductivity change. To verify the accuracy of the proposed approach, we provide a comparison of numerical and analytical results by ignoring the new parameters and investigating the behaviors of physical quantities for numerical outcomes. Full article
(This article belongs to the Special Issue Analysis and Applications of Mathematical Fluid Dynamics)
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16 pages, 507 KiB  
Article
Reduce-Order Modeling and Higher Order Numerical Solutions for Unsteady Flow and Heat Transfer in Boundary Layer with Internal Heating
by Muhammad Bilal, Muhammad Safdar, Safia Taj, Amad Zafar, Muhammad Umair Ali and Seung Won Lee
Mathematics 2022, 10(24), 4640; https://doi.org/10.3390/math10244640 - 7 Dec 2022
Cited by 4 | Viewed by 1338
Abstract
We obtain similarity transformations to reduce a system of partial differential equations representing the unsteady fluid flow and heat transfer in a boundary layer with heat generation/absorption using Lie symmetry algebra. There exist seven Lie symmetries for this system of differential equations having [...] Read more.
We obtain similarity transformations to reduce a system of partial differential equations representing the unsteady fluid flow and heat transfer in a boundary layer with heat generation/absorption using Lie symmetry algebra. There exist seven Lie symmetries for this system of differential equations having three independent and three dependent variables. We use these Lie symmetries for the reduced-order modeling of the flow equations by constructing invariants corresponding to linear combinations of these Lie point symmetries. This procedure reduces one independent variable of the concerned fluid flow model when applied once. Double reductions are achieved by employing invariants twice that lead to ordinary differential equations with one independent and two dependent variables. Similarity transformations are constructed using these two sets of derived invariants corresponding to linear combinations of the Lie point symmetries. These similarity transformations have not been obtained earlier for this flow model. Moreover, the corresponding reduced systems of ordinary differential equations are different from those which exist in the literature for fluid flow and heat transfer that we have been dealing with. We obtain multiple similarity transformations which lead us to new classes of systems of ordinary differential equations. Accurate numerical solutions of these systems are obtained using the combination of an adaptive fourth-order Runge–Kutta method and shooting procedure. Effects of variation of unsteadiness parameter, Prandtl number and heat generation/absorption on fluid velocity, skin friction, surface temperature and heat flux are studied and presented with the help of tables and figures. Full article
(This article belongs to the Special Issue Analysis and Applications of Mathematical Fluid Dynamics)
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21 pages, 846 KiB  
Article
Numerical Investigation of MWCNT and SWCNT Fluid Flow along with the Activation Energy Effects over Quartic Auto Catalytic Endothermic and Exothermic Chemical Reactions
by Yasir Mehmood, Ramsha Shafqat, Ioannis E. Sarris, Muhammad Bilal, Tanveer Sajid and Tasneem Akhtar
Mathematics 2022, 10(24), 4636; https://doi.org/10.3390/math10244636 - 7 Dec 2022
Cited by 20 | Viewed by 1452
Abstract
A mathematical model is created to analyze the impact of Thompson and Troian slip boundaries over a contracting/expanding surface sustaining nanofluid-containing carbon nanotubes along a stagnation point flow. Both multi-wall (MWCNTs) and single-wall (SWCNTs) carbon nanotubes are taken into consideration, with water serving [...] Read more.
A mathematical model is created to analyze the impact of Thompson and Troian slip boundaries over a contracting/expanding surface sustaining nanofluid-containing carbon nanotubes along a stagnation point flow. Both multi-wall (MWCNTs) and single-wall (SWCNTs) carbon nanotubes are taken into consideration, with water serving as the base liquid. The flow is obtained due to the stretching or contracting of the surface. The thermal radiation, activation energy, buoyancy impacts, and chemical processes called quartic autocatalysis are additionally added to the original mathematical model. The MATLAB-constructed bvp4c function involving the three-stage Lobatto IIIa formula for the numerical results of dimensionless velocity, concentration, and temperature profiles are used. By contrasting it against a published paper in this limited instance, it is determined whether the suggested mathematical model is legitimate. In this sense, a remarkable consensus is achieved. Graphical representations are used to depict the behavior of many non-dimensional flow variables, such as the slip velocity parameter, the inertia coefficient, the porosity parameter, and the solid volume fraction. Surface drag force computations are reported to examine the effects at the permeable stretching surface. It has been shown that increasing the slip velocity factor increases the fluid streaming velocity while decreasing the surface drag force. If the endothermic/exothermic coefficient increases, the local thermal transfer efficiency falls. For nanofluids, the changing viscosity factor increases axial velocity while decreasing temperature distribution. Additionally, the solid volumetric fraction improves the temperature distributions by lowering the concentration profile and speed. Full article
(This article belongs to the Special Issue Analysis and Applications of Mathematical Fluid Dynamics)
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18 pages, 426 KiB  
Article
Statistical Descriptions of Inhomogeneous Anisotropic Turbulence
by J. J. H. Brouwers
Mathematics 2022, 10(23), 4619; https://doi.org/10.3390/math10234619 - 6 Dec 2022
Cited by 1 | Viewed by 965
Abstract
Descriptions are given of the Langevin and diffusion equation of passively marked fluid particles in turbulent flow with spatially varying and anisotropic statistical properties. The descriptions consist of the first two terms of an expansion in powers of C01, [...] Read more.
Descriptions are given of the Langevin and diffusion equation of passively marked fluid particles in turbulent flow with spatially varying and anisotropic statistical properties. The descriptions consist of the first two terms of an expansion in powers of C01, where C0 is an autonomous Lagrangian-based Kolmogorov constant: C07. Solutions involve the application of methods of stochastic analysis while complying with the basic laws of physics. The Lagrangian-based descriptions are converted into Eulerian-based fixed-point expressions through asymptotic matching. This leads to novel descriptions for the mean values of the fluctuating convective terms of the conservation laws of continua. They can be directly implemented in CFD codes for calculating fluid flows in engineering and environmental analysis. The solutions are verified in detail through comparison with direct numerical simulations of turbulent channel flows at large Reynolds numbers. Full article
(This article belongs to the Special Issue Analysis and Applications of Mathematical Fluid Dynamics)
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20 pages, 3527 KiB  
Article
Nonlinear Mixed Convection in a Reactive Third-Grade Fluid Flow with Convective Wall Cooling and Variable Properties
by Samuel Olumide Adesanya, Tunde Abdulkadir Yusuf and Ramoshweu Solomon Lebelo
Mathematics 2022, 10(22), 4276; https://doi.org/10.3390/math10224276 - 15 Nov 2022
Cited by 3 | Viewed by 1104
Abstract
Energy management and heat control whenever a reactive viscous fluid is the working medium has been one of the greatest challenges encountered by many in the field of chemical and industrial engineering. A mathematical approach to thedetermination of critical points beyond which the [...] Read more.
Energy management and heat control whenever a reactive viscous fluid is the working medium has been one of the greatest challenges encountered by many in the field of chemical and industrial engineering. A mathematical approach to thedetermination of critical points beyond which the working environment becomes hazardous is presented in the present investigation together with the entropy generation analysis that guarantees the efficient management of expensive energy resources. In this regard, the nonlinear mixed convective flow behavior of a combustible third-grade fluid through a vertical channel with wall cooling by convection is investigated. The mathematical formulation captures the nonlinearities arising from second-order Boussinesq approximation and exponential dependence of internal heat generation, viscosity, and thermal conductivity on temperature. The resulting nonlinear boundary value problems were solved based on the spectral Chebyshev collocation method (SCCM) and validated with the shooting-Runge–Kutta method (RK4). The nonlinear effects on the flow velocity, temperature distribution, entropy generation, and Bejan heat irreversibility ratio are significant. Further analyses include the thermal stability of the fluid. Findings from the study revealed that flow, temperature, and entropy generation are enhanced byincreasing values of the Grashof number, the quadratic component of buoyancy, and the Frank-Kameneskii parameter, but are reducedbyincreasing the third-grade material parameter. Moreover, it was shown that increasing values of the third-grade parameter encourages the thermal stability of the flow, while increasing values of the linear and nonlinear buoyancy parameter destabilizes the flow. The present result is applicable to thick combustible polymers with increased molecular weight. Full article
(This article belongs to the Special Issue Analysis and Applications of Mathematical Fluid Dynamics)
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15 pages, 5684 KiB  
Article
Dynamics of Heat Transfer Analysis of Convective-Radiative Fins with Variable Thermal Conductivity and Heat Generation: Differential Transformation Method
by P. V. Ananth Subray, B. N. Hanumagowda, S. V. K. Varma, A. M. Zidan, Mohammed Kbiri Alaoui, C. S. K. Raju, Nehad Ali Shah and Prem Junsawang
Mathematics 2022, 10(20), 3814; https://doi.org/10.3390/math10203814 - 15 Oct 2022
Cited by 9 | Viewed by 1943
Abstract
The study of convective heat transfer in differently shaped fins with radiation, internal heat generation and variable thermal conductivity was considered. The energy equation of the model was converted into the dimensionless form by adopting the proper variables, which was later solved using [...] Read more.
The study of convective heat transfer in differently shaped fins with radiation, internal heat generation and variable thermal conductivity was considered. The energy equation of the model was converted into the dimensionless form by adopting the proper variables, which was later solved using the differential transformation method. The impact of the parameters on the thermal performance, efficiency and heat transfer of the fins was analyzed graphically and also by performing thermal analysis on the fins. It was noticed that there was a significant effect on the thermal performance of the fins with different shapes, and also the heat transfer rate of the fin increased for improved values of the internal heat generation and radiation parameters. The exponential profile showed better results than other profiles, and the results obtained were supported by thermal analysis using ANSYS software. Full article
(This article belongs to the Special Issue Analysis and Applications of Mathematical Fluid Dynamics)
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