Vertical Permeable Plate Research Articles

Nusselt number and skin‐friction coefficients of a micropolar flow over a flat plate under constant wall temperature conditions in a porous medium

AbstractThis study examines the forced convection of a micropolar fluid (MPF) flow across a vertical permeable plate inside a porous medium. A similar solution is derived for a scenario involving a constant surface temperature. The system of transformed governing equations is addressed by employing a finite‐difference method. Notably, a parametric analysis is conducted to demonstrate how the Prandtl number, micropolar parameters, Darcy number, inertia coefficient (ξ), skin friction (Cf), and Nusselt number (Nu) impact the system. The results are then presented graphically, while the physical aspects of the issue are assessed. Although a larger Nu produced a high wall heat transfer, the Cf values are decreased as ξ increases. The ξ also reduces the local Nu. Compared with Newtonian fluids, the MPF increases Cf and reduces the heat transfer rate. The outcomes are validated by comparing the current results with other related studies. The results of this study are useful for improving the efficiency of solar panels by enhancing their cooling rate. It is also found that increasing the inertia of MPF leads to an increase in the friction coefficient (Cf) while increasing porosity, microrotation parameter n and Fs decreases (Cf).

MHD Mixed Convection Flow Over a Permeable Vertical Flat Plate Embedded in a Darcy–Forchheimer Porous Medium

The purpose of this paper is to describe the stead MHD mixed convection flow over a permeable vertical flat plate embedded in a Darcy–Forchheimer porous medium. Using appropriate similarity variables, the partial differential equations are transformed into ordinary (similar) differential equations, which are numerically solved using the bvp4c function in MATLAB. The numerical results are used to present graphically and in tables, illustrations of the reduced skin friction, reduced Nusselt number, velocity, and temperature profiles. Dual (upper and lower branch) solutions are discovered in this exciting analysis. Although numerous studies on the mixed convection past a vertical plate embedded in a fluid-saturated porous medium exist, none of the researchers have focused on the Darcy–Forchheimer flow with asymptotic solutions. The behavior of the flow and heat transfer has been thoroughly analyzed with the variations in governing parameters, such as Darcy–Forchheimer G,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$G,$$\\end{document} suction/injection S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S$$\\end{document}, MHD M,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M,$$\\end{document} and mixed convection λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document} parameters.

A finite difference study of radiative mixed convection MHD heat propagating Casson fluid past an accelerating porous plate including viscous dissipation and Joule heating effects

A finite difference numerical simulation scrutiny is executed to evaluate the combined impacts of heat generation, buoyancy forces, viscous dissipation and Joule heating in unsteady hydro-magnetic mixed convective chemically reactive and radiative Casson fluid flowing along an exponentially accelerating permeable vertical plate engrossed in a porous media by considering ramp surface concentration and temperature. The dimensionless non-linear coupled PDEs describing the flow model are dealt numerically by adopting the competent implicit Crank-Nicolson finite difference procedure. The variance of velocity, temperature, and concentration distributions are exposed via graphical representations due to the dissimilarity of the flow restrained parameters. Computational outcomes of the skin-friction, Nusselt and the Sherwood numbers are portrayed in the tabular pattern. The final outcomes of the research exposed that the impacts of thermal radiation, viscous dissipation, and heat production parameters enlarges the temperature and velocity distributions. The fluid motion deflates for growing Casson parameter and magnetic field intensity. The rising chemical reaction parameter suppresses the concentration and velocity distributions. Very importantly it is distinguished that fluid momentum, temperature, and concentration are quicker in the instance of isothermal plate temperature than ramp wall temperature. This kind of research may find specific industrial and medical utilizations such as glass manufacturing, crude oil purification, lubrication, paper production, blood transport study in cardiovascular design, etc.

The effects of magnetic field and thermal radiation on the mixed convection of Al2O3-Cu/water hybrid nanofluid over a permeable vertical flat plate

This study comprehensively investigates the effect of magnetic fields and thermal radiation on mixed convection in a hybrid alumina–copper/water nanofluid flowing over a permeable vertical flat plate. The study aims to model conventional nanofluid behavior accurately by considering the hybridization of two types of nanoparticles. Conventional similarity transformations and Akbari–Ganji’s method are employed to simplify the governing equations, resulting in ordinary differential equations. Among the dual solutions obtained, only one stable solution is identified. The key findings reveal that boundary layer separation can be avoided by reducing the copper concentration volume and increasing the magnetic and radiation parameters. The mixed convection parameters induce counter-flow, enhancing heat transfer when the magnetic and radiation parameters increase and the copper concentration volume decreases. Conversely, increasing the concentration volume of copper leads to accelerated boundary layer separation and reduced measured physical quantities. Overall, the mixed convection parameter enhances skin friction and heat transfer rates, particularly in the achievable solution. The accuracy of the proposed method is validated through a comparison with the finite element method (FEM). The graphical presentation of the results facilitates a clearer interpretation of the study’s findings.

Insight of mixed convectional heat transport in molybdenum disulfide-water nanofluid flow on moving vertical permeable plate with homogeneous-heterogeneous reactions

This analysis is framed to take care of the high heat transfer demand from various application prospects and in this context nanofluid may be in consideration because nanofluids are well-known liquids with higher heat transfer capabilities. Here, a mixed convection flow of Molybdenum disulfide-water (MoS2-H2O) nanofluid on a moving vertical plate is examined when there are chemical reactions. Nanofluid problem is investigated using Tiwari and Das model, and numerically solved by “bvp4c” method. For the considered effects in the study, overshoots in temperature profile of nanofluid are observed. Momentum and thermal layer thicknesses become thinner with suction and thicker with blowing. Temperature overshoot is higher for blowing cases. Enhanced homogeneous–heterogeneous reactions lead to rise of the concentration boundary layer’s thickness. Also, magnitude of surface-drag force decays and cooling rate enhances with MoS2-H2O nanofluid mixed convection. For weaker suction and for blowing, cooling of nanofluid is faster with larger volume fraction of nanoparticles, but contrast results are obtained for greater suction. Importantly, compared to the homogeneous reaction, the heterogeneous reaction exhibits more impactful influences on flow and heat-mass transport characters.

Numerical and statistical analyses of a natural convection radiative hybrid nanofluid flow on a vertical permeable plate

Numerical and statistical analyses of a natural convection radiative hybrid nanofluid flow on a vertical permeable plate

Control of radiating heat on the heat transfer of polar hybrid nanofluid flow through a vertical permeable plate

The recent applications in industrial products and engineering need high thermal efficiency for the betterment of the shape of the products, the concept of hybrid nanofluid is significant in comparison to nanofluid and pure fluid. Therefore, this analysis focuses on the flow of a micropolar hybrid nanofluid over a vertical permeable plate. The study considers free convection of an electrically conducting fluid, incorporating metal and oxide components with a water-based hybrid nanofluid. Further, the conjunction of dissipative and radiating heat with generative/absorptive heat enhances the thermal properties. The use of standard transformation rules gives rise to converting the nondimensional form of concerned PDEs to ODEs. Moreover to get rid of the solution, for the nondimensional set of equations, a shooting-based numerical technique like Runge–Kutta (RK)-fourth-order is adopted for the standard values of several components within their range. The effectiveness of these parameters is studied and displayed through graphs. The computed result of the rate coefficients at the surface is depicted in tabular form. The comparative analysis with earlier work studied by considering the base liquid shows a good correlation in particular cases. However, the important outcomes are, the magnetized nano as well as hybrid nanoparticles produces a thicker momentum boundary layer thickness whereas it enhances the fluid temperature.

MHD dissipative flow past a permeable vertical plate in a porous medium in the presence of constant heat, mass flux, and diffusion‐thermo effect

AbstractAn analytical study of heat and mass transport in magnetohydrodynamic convective flow over an indefinitely long porous plate, which is vertically immersed in the porous medium, is investigated when heat sink, diffusion‐thermo, and thermal radiation are present. A magnetic field with uniform strength has been applied transversely directed into the fluid region. Analysis of diffusion‐thermo impact within the flow problem with constant heat and constant mass flux in the presence of thermal radiation and heat sink is the novelty of the current work. By using the Eckert number E as the perturbation parameter, the regular perturbation approach is used to solve nondimensional governing equations. On the flow and transport characteristics, the effects of Prandtl number, Grashof number, Eckert number, Dufour number, Schmidt number, radiation, magnetic field, and heat sink parameter have been investigated graphically and in tabular form, respectively. The innovative aspect of the current study is the inclusion of the Dufour effect, in addition to constant heat and mass flux at the plate. The Dufour effect can be utilized to improve separation processes, such as distillation, extraction, and chromatography. When the Dufour number and radiation parameter increase, the fluid velocity increases, and while the heat sink parameter increases, it decreases. As dissipation increases, the velocity of the fluid also increases. The concentration of the fluid is enhanced as mass diffusivity increases. When the heat absorption sink grows, the temperature of the fluid decreases.

Inherent irreversibility in unsteady magnetohydrodynamic nanofluid flow past a slippery permeable vertical plate with fractional-order derivative

Abstract This study focuses on fractional-order derivatives for the unsteady flow of magnetohydrodynamic (MHD) methanol-iron oxide (CH3OH-Fe3O4) nanofluid over a permeable vertical plate. The utilization of fractional-order derivatives provides a mathematical representation of the flow model. The concluding model, consisting of a system of fractional-order transient partial differential equations, has been solved using the finite difference method, and graphical illustrations demonstrate the effects of key parameters on the flow field. Velocity and temperature profiles provide insights into nanofluid behavior. Additionally, essential quantities such as skin friction coefficient, Nusselt number, Bejan number, and entropy generation rate have been depicted graphically. Comparison with previous studies authenticates the accuracy of the anticipated model, contributing to new intuitions into MHD nanofluid flow over a permeable vertical plate. It is worth noting that the current model, incorporating fractional-order derivatives, contributes to understanding the physical characteristics of MHD CH3OH-Fe3O4 nanofluid flow over a permeable vertical plate, research that has not been extensively explored before.

Magnetohydrodynamic conjugate heat transfer analysis on a viscous fluid past a vertical permeable plate

The influence of conjugate heat transfer based on radiation and magnetohydrodynamic utilization is an attractive research area, with progressive features; it has many applications in thermal engineering, heat exchangers, cooling phenomenon, magnetic cell separation, energy production, hyperthermia, etc. Following the motivating significances of the current research topic, this paper explores the influences of an electrically conducting and radiating fluid with internal friction, heat generation and thermal radiation embedded in a porous medium past a flat permeable plate. The boundary layer equations are dimensionally transformed and solved numerically using implicit finite difference technique called the Keller-box method. The effect of various fluid obeying parameters such as magnetic field, viscous dissipation and heat generation on the flow factors such as velocity and temperature are graphed and discussed in this paper. Growing heat source, energy inside the fluid boosts, thereby increasing the energy of the flow. Increase in generation of energy reduces the viscosity of the flow reduces thereby increasing the velocity of the flow particles.

A Model on Free Convective Casson Fluid Flow Past a Permeable Vertical Plate with Gyrotactic Microorganisms

This study focused on free convective MHD Casson fluid flow past a permeable vertical plate with microorganisms and Soret-Dufour mechanisms. The physical model is governed by system of partial differential equations (PDEs). The set of PDEs were overhaul into a nonlinear ordinary differential equation by considering acceptable similarity variable. The spectral relaxation method (SRM) was utilized to obtain solution to the overhaul nonlinear ordinary differential equations. This study examined critically the significant of the Gyrotactic microorganisms on Casson fluid locomotion Also, the significance of parameters such as thermal radiation, Soret-Dufour mechanisms, Brownian motion, Joule heating and so on are examined on velocity, concentration, motile microorganism and temperature profiles. The Casson parameter was found to intensify the velocity contour and the hydrodynamic boundary layer thickness. A higher magnetic parameter gives rise to Lorentz force which declines the motion of the fluid. There is higher temperature within the boundary layer because of the presence of thermal radiation.

Study of nonlinear radiative heat transfer with magnetic field for non-Newtonian Casson fluid flow in a porous medium

This paper studies the effect of thermo-diffusion, electrical field, and nonlinear thermal radiation. Thermal radiant heat transfer has several industrial applications, and the analysis of radiation heat transfer in non-Newtonian fluids under different conditions has been widely studied. To better understand the problem of thermal nonlinear radiation heat transfer flow in non-Darcy Casson fluid on stretched surfaces, this research examines such a phenomenon. The Hybrid Analytical and Numerical Method (The HAN Method) is used to precisely analyze the steady flow of incompressible Newtonian electrically conducting non-Darcy Casson fluid on a vertical permeable stretchable plate with the presence of the magnetic field. The governing equations of this problem are reduced from the system of nonlinear partial differential equations (PDEs) into a system of nonlinear ordinary differential equations (ODEs) using similarity transformations. The results showed that Casson's parameter has a small and indirect effect on temperature and mass transfer, but it affects the velocity significantly and directly. Also, the magnetic field has a direct and significant effect on temperature and velocity but an indirect and significant effect on concentration. The electric field has a direct and significant effect on temperature and velocity but an indirect and significant effect on concentration. Also, the effects of parameters such as thermal buoyancy, inertial, porous permeability, Eckert number, Prandtl number, chemical reaction, Schmidt and Soret numbers, and porosity on velocity, temperature, and concentration have been studied.

A Numerical Assessment of Time-Dependent Magneto-Convective Thermal-Material Transfer over a Vertical Permeable Plate

The objective of this work is to investigate the influences of thermal radiation, heat generation, and buoyancy force on the time-dependent boundary layer (BL) flow across a vertical permeable plate. The fluid is unsteady, incompressible, viscous, and electrically insulating. The heat transfer mechanism happens due to free convection. The nondimensional partial differential equations of continuity, momentum, energy, and concentration are discussed using appropriate transformations. The impressions of thermal radiation and buoyancy forces are exposed in the energy and momentum equation, respectively. For numerical model, a set of nonlinear dimensionless partial differential equations can be solved using an explicit finite difference approach. The stability and convergence analyses are also established to complete the formulation of the model. The thermophysical effects of entering physical parameters on the flow, thermal, and material fields are analyzed. The variations in local and average skin friction, material, and heat transfer rates are also discussed for the physical interest. The analysis of the obtained findings is shown graphically, and relevant parameters pointedly prejudice the flow field. Studio Developer FORTRAN 6.2 and Tecplot 10.0 are applied to simulate the schematic model equations and graphical presentation numerically. The intensifying values of the magnetic field are affected decreasingly in the flow field. The temperature profiles decrease within the BL to increase the value of radiation parameters. The present study is on the consequences for petroleum engineering, agriculture engineering, extraction, purification processes, nuclear power plants, gas turbines, etc. To see the rationality of the present research, we compare these results and the results available in the literature with outstanding compatibility.

Effects of higher order chemical reaction and slip conditions on mixed convection hybrid ferrofluid flow in a Darcy porous medium

Many researchers have been captivated by the ability of hybrid ferrofluid to increase heat and mass transmission, leading them to further examine the working fluid. This study is essential for figuring out how Fe3O4-CoFe2O4/H2O hybrid ferrofluid would behave thermally and massively when physical factors like a greater degree of chemical reaction (n) and slip boundary conditions are present through mixed convection stagnation point flow in Fe3O4-CoFe2O4/H2O hybrid ferrofluid toward a permeable vertical flat plate embedded in Darcy porous medium. The complexity of the partial differential equation for heat, flow, as well as mass transfer is reduce through similarity transformation into a system of ordianry differential equation, before being numerically solved using the built-in solver bvp4c in MATLAB for various values of the governing parameters. Dual solutions (first and second solution) are obtained as result produced in regions of opposing and assisting flow. Hybrid ferrofluids with additional CoFe2O4 nanoparticles have a higher heat transfer rate than ferrofluids and base fluid (water). Furthermore, a different order of chemical reaction greatly influences the mass transfer rate. Note that the presence of thermal and concentration slips reduce the heat transfer and mass transfer rate, accordingly, and delay the boundary layer separation.

Parabolic form of casson fluid flow based on angle of inclination in conducting field

A considerable analysis has been performed to draw out the flow properties of MHD Casson fluid in parabolic movement with several parameters. The novelty in the examination is the angle of inclination with the permeable vertical plate. The purpose of the work is to analyze the impact of some parameters on the flow in two cases namely, obtuse angle and acute angle. The solution of the flow governed equations is attained by the utilization of the finite divergence technique in explicit type. The nature of the fluid velocity is observed in the cases of acute angle and obtuse angle and described accordingly with the use of graphs and tables. One of the major findings is that for increasing values of porosity the velocity enhances in the case of acute angle and falls down in the case of obtuse angle.

Numerical Solution of Magnetized Williamson Nanofluid Flow over an Exponentially Stretching Permeable Surface with Temperature Dependent Viscosity and Thermal Conductivity.

This research work describes and investigates Williamson nanofluid flow over an exponentially stretching permeable vertical plate with temperature-dependent thermal conductivity and viscosity. The governing non-linear partial differential equations (PDEs) are metamorphosed into coupled non-linear ordinary differential equations (ODEs) by using similarity transformation. The succeeding equations were numerically solved using MATLAB function bvp4c for various values of parameters. For velocity, temperature, concentration, the skin friction coefficient, and the local Nusselt number, data are presented in the form of graphs and tables. It is noted that for increasing values of magnetic parameter , Williamson parameter and viscosity parameter , the boundary layer thickness of the velocity profile decreases, while it increases for the temperature profile. The findings of the present work are validated through the published results.

MHD flow pattern in a parabolic mode based on the angle of inclination under cross‐diffusion

AbstractA considerable effort has been made to draw out the flow properties of the magnetohydrodynamic fluid in parabolic movement with several parameters under cross‐diffusion. The novelty in the examination is the angle of inclination with a permeable vertical plate. The purpose of the work is to analyze the impact of some parameters on the flow in two cases, namely, obtuse angle and acute angle. The solution of the flow‐governed equations is attained by the utilization of the finite divergence technique in explicit type. The nature of the fluid velocity is observed in the cases of acute angle and obtuse angle and described accordingly with the use of graphs and tables. The validation of the method is checked with the published outcomes and pointed out a fine agreement with it. One of the major findings is that for increasing values of porosity the velocity enhances in the case of an acute angle and falls in the case of an obtuse angle.

Significance of Casson dissipative fluid and spanwise cosinusoidally fluctuating temperature on unsteady MHD free convective flow past a hot vertical permeable plate with radiation absorption and chemical reaction

AbstractThe current analysis concentrated on the consequence of Casson dissipative fluid and spanwise consinusoidally fluctuation temperature on unsteady magnetohydrodynamics free convective flow past a moving hot vertical permeable plate with heat generation, radiation absorption, and chemical reaction. It has imperative practical applications in plentiful fields like physiological processes, biomedical science, food processing, pharmaceutical, chemical material processing engineering, manufacturing systems, and so on. The governing partial differential equations are evaluated analytically by employing a multiple regular perturbation method. The influence of assortment physical estimators on fluid velocity, temperature, concentration, skin friction, Nusselt number, and Sherwood number was illustrated quantitatively through graphs. Eventually, it was revealed that velocity, concentration, and Sherwood number declined with the progressive values of the chemical reaction parameter. Velocity and temperature were enhanced with incremental values of Prandtl number, while the contradictory impact occurred in Nusselt number and skin friction. Meanwhile, velocity and skin friction lessened with the incremental values of the magnetic parameter and Casson fluid parameter.

FEM to study the radiation, Soret, Dufour numbers effect on heat and mass transfer of magneto-Casson fluid over a vertical permeable plate in the presence of viscous dissipation

In this paper, the impact of Dufour number along with viscous dissipation on the non-steady stream of heat together with the mass transfer of Casson fluid, on vertical permeable laminate is studied with chemical reaction. Dimensionless governing equations of temperature, velocity as well as concentration have been resolved by the finite element method (FEM). The tables of skin friction, Sherwood along with the Nusselt number are explained numerically in the tables. Effects of various physical quantities such as Dufour, Soret numbers, Eckert number, radiation, chemical reaction parameters, and so on are discussed in detail through figures and tables. A comparison with previously published work reveals extremely excellent agreement.

An impact on non-Newtonian free convective MHD Casson fluid flow past a vertical porous plate in the existence of Soret, Dufour, and chemical reaction

The objective of this research is to explore the heat and mass transfer properties of an unsteady MHD natural convective Non-Newtonian, Casson fluid flow through a permeable vertical plate in the existence of Soret, Dufour, and chemical reaction. The aspects of heat and radiation absorptions are also factored in. Applications of the present study would be useful in magnetic material processing and chemical engineering systems. Mathematically, the flow field situation is expressed in terms of partial differential equations. The transformed flow-narrating partial differential equations of momentum as well as energy and species concentration were numerically solved using the finite element technique. Non-dimensional flow parameters were used to extract the numerical outcomes of velocity, temperature, and concentration, and the outcomes are envisioned graphically. The significance of the factors determining, Nusselt number, Sherwood number, and skin friction is also considered. The outcomes reveal that raising the permeability parameter causes the velocity to improve while enhancing the Casson parameter causes the velocity distribution to reduce.