Effects of chemical reaction and thermal radiation on MHD free convective flow of micro polar fluid past an infinite moving vertical porous plate with viscous dissipation

This article discusses the impact of chemical reaction and radiation on an unstable two-dimensional laminar flow around a viscous fluid over a semi-infinite, vertical absorbent surface that moves progressively. The governing classification of partial differentiation was converted into an ordinary differentiation system in this case. To get numerical solutions, the Galerkin finite element technique is applied to nondimensional velocity, micro-rotation, temperature, and concentration profiles. The consequences of skin friction, the combined pressure quantity, the mass, and heat assignments at the boundary are formed using different fluid properties and flow conditions. Physical quantities and their effects Graphs depict the radiation parameter R, thermal conductivity k, Eckert number Ec, and other velocities, micro-rotation, temperature, and concentration factors. The main findings of this current problem is showing the chemical reaction effects on velocity and concentration. It is observed that both the velocity and concentration of the fluid decrease when Kr increases.     

Transient natural convective flow of a radiative viscous incompressible fluid past an exponentially accelerated porous plate with chemical reaction species

The present study deals with an unsteady magnetohydrodynamic natural convective flow of a viscous, incompressible fluid past an exponentially accelerated porous plate surrounded by a porous medium with suction or injection. The novelty of the current research is to analyze the behavior of the flow due to mass transfer with first-order chemical reaction in the presence of a heat source in the energy equation. The existence of suction/injection and radiation parameters in the flow enhances the utility of the research as they are an integral part of nuclear reactors, thermal and chemical engineering processes, and many more. The Laplace transform technique (via Bromwich contour) is applied to solve exactly the governing equations. The nature of the flow velocity, temperature, and concentration profiles due to the impact of pertinent flow parameters are presented graphically. The numerical outcomes of coefficient of skin friction, rate of heat transfer, and mass transfer are obtained in tabular form. The results indicate that the skin friction increases slowly with the reaction parameter and largely with the suction parameter, whereas the concentration gradient increases at a much higher rate with the reaction parameter. The fluid injection has a negative impact on the velocity gradient. It is seen that the heat source enhances both velocity and temperature profiles throughout the flow field, whereas the first-order chemical reaction acts reversely on the velocity and mass transfer process. The current research can be applied to identify the cause behind the drag force produced in seepage flow due to the heated or cooled accelerated plate.     

MHD mass transfer flow past an inclined plate with variable temperature and plate velocity embedded in a porous medium

An exact solution of unsteady MHD free convective mass transfer flow past an infinite inclined plate embedded in a saturated porous medium with variable plate velocity, temperature, and mass diffusion has been presented. An attempt has been made to analyze the Soret effect and the influence of the angle of inclination on the flow and transport properties, in the presence of thermal radiation, heat source, and chemical reaction. The equations governing the flow, heat, and mass transfer are solved by employing the Laplace transform technique, in closed form. The variations in fluid velocity, temperature, and concentration profiles are shown graphically whereas the numerical values of shear stress, the rate of heat transfer, and the rate of mass transfer from the plate to the fluid are presented in tabular form for various values of the flow parameters. The results show that the flow is accelerated due to the Soret effect while the angle of inclination sustains a retarding effect on fluid velocity. Further it is observed that the viscous drag at the plate and the mass diffusion from the plate to the fluid decrease under the influence of thermal diffusion.     

Non-similar solution of an unsteady mixed convection flow over a vertical cone with suction or injection

Non-similar solution of an unsteady mixed convection flow over a vertical cone in the presence of surface mass transfer has been obtained when the axis of the cone is inline with the flow. The time dependent free stream velocity varying arbitrarily with time introduces unsteadiness in the flow field. The results have been obtained for accelerating and decelerating free stream velocities. The numerical difficulties arising at the starting point of the stream wise coordinate and for time dependent flow field are overcome by applying an implicit finite difference scheme in combination with the quasilinearization technique. Numerical results are reported here to account the effects of Prandtl number, buoyancy and mass transfer (injection and suction) parameters at different streamwise locations for various times on velocity and temperature profiles, and skin friction and heat transfer coefficients.     

Analytical study of heat and mass transfer effects on unsteady Casson fluid flow over an oscillating plate with thermal and solutal boundary conditions

In this study, the impacts of heat and mass transfer characteristics on an isotropic incompressible Casson fluid flow over an oscillatory plate with the incidences of solutal and thermal boundary conditions have been investigated. Exact solutions of the fundamental equations governing the fluid flow are determined by using the Laplace transform technique. Numerical results based on analytical solutions are presented in graphical and tabular illustrations to clarify the behaviors of the fluid. Most interestingly, both fluid velocity and species concentration increase with an increment of mass transfer coefficient, whereas the fluid velocity diminishes as oscillating frequency increases near the surface of the plate. This happens due to the presence of high fluctuation of the plate in the flow system. Finally, this investigation is helpful to the scientific community, and the obtained results can be used as benchmark solutions for solving nonlinear flow governing problems fully via various numerical methods.     

Combined effects of homogeneous and heterogeneous reactions on peristalsis of Ree-Eyring liquid: Application in hemodynamic flow

This research examines the influence of homogeneous and heterogeneous chemical reactions on the peristaltic flow via an inclined permeable channel. The current investigation emphasizes on modeling the flow of blood in narrow arteries by taking convective and wall properties into account. The Ree-Eyring non-Newtonian model is used to govern the fluid flow due to its significance in understanding the behavior of dilatant, pseudoplastic, and viscous liquids. The variation in variable viscosity and thermal conductivity is considered for analyzing the complex rheological behavior of blood. The similarity transformations are used in the process of nondimensionalization. The series solution procedure is adopted to solve the governing nonlinear differential equations. The expressions for velocity, temperature, concentration, and trapped bolus are obtained. The computational results are analyzed with the help of graphs for shear thickening, shear thinning, and Newtonian fluid models. One of the significant findings of the current model is that an introduction of variable liquid properties improves the temperature and velocity profiles for Newtonian and pseudoplastic fluid models. Compared with the other theoretical models developed, the rheological and flow properties of various biological fluids can be derived from the model used in the present investigation.     

Finite element Soret Dufour effects on an unsteady MHD heat and mass transfer flow past an accelerated inclined vertical plate

The present study is focused on the Soret and Dufour effects on magnetohydrodynamics unsteady fluid flow over an accelerated inclined vertical plate with thermal radiation and heat source. Solution of the nondimensional governing differential equations are worked out by the efficient Galerkin finite element method. The influence of several relevant flow parameters on velocity, temperature, and concentration distributions, as well as the numerical results, are studied and graphically displayed. The nondimensional skin friction and the rate of heat and mass transfer parameters are presented in the Tables 1-3 below. Raising the Soret number results in growing concentrations, but the converse is true for the Schmidt number. Skin friction reduces when Soret and Dufour numbers increase. The present simulations apply to the processing of magnetic materials in the chemical and metallurgical industries.     

Rotation,electromagnetic field,and variable thermal conductivity effects on free convection flow past an eternity vertical porous plate

The present research may facilitate the reduction of the number of conversion steps required to include the low output voltages in an electrokinetic biomass process. Variable thermal conductivity and electroosmosis flow have already established great potential in the thermo-elastic models of various manufacturing industries and have been widely used in energy technologies. As a result, the current framework investigates the characteristics of natural convection flow with the influence of variable thermal conductivity and electroosmosis over an eternity vertical porous plate. Coriolis forces and Hall current effects are considered in the momentum equations, and also thermal radiation and variable thermal conductivity are taken as energy equations. A linear chemical reaction parameter is used in the concentration equation. The equation of Poisson–Boltzmann is exploited to depict the electric potential characteristics within the accelerated plate medium. The pdepe command in Matlab software is used to figure out the numerical solutions to equations about momentum, energy, and concentration. The expressions of fluid transverse velocity, fluid axial velocity, fluid temperature, and concentration profiles are presented as numerical results and also derived vital relevant stream parameters diagrammatically, whereas the numerical values of primary skin friction, secondary skin friction, and Nusselt number are presented in tabular form for various values of pertinent flow parameters. The temperature rises as the strength of the thermal conductivity variable parameter increases. Also, as the values of the Taylor number and the thermal conductivity variable parameter go up, the primary velocity goes down. Similarly, secondary velocity increases in the opposite direction as the Taylor number and thermal conductivity variable parameter increase.     

Thermosolutal convective non-Newtonian radiative Casson fluid transport over a vertical plate propagated by Arrhenius kinetics with heat source/sink

In the current study, a mathematical formulation is developed by combining the non-Newtonian (Casson) fluid model to simulate the thermosolutal free convection radiative flow over a vertical surface. The current flow model is formulated with a heat sink/source and radiation driven by Arrhenius kinetics. The basic flow equations are transmuted into a nondimensional form via similarity transformations for which numerical simulations are performed utilizing the Runge-Kutta-Fehlberg method with shooting technique. The results obtained for velocity, energy, and species mass concerning various flow parameters are presented graphically. Computed results for skin friction, Nusselt number, and Sherwood number are tabulated. The results have been verified for limited cases by comparing with various investigations, revealing excellent accuracy. The detailed geometry reveals that an increase in the activation energy enhances the flow velocity and heat transport in the Casson fluid system due to exothermic heat reaction. With the increase of the Frank-Kamenetskii term, there is a substantial rise in temperature distribution and a decrease in concentration profiles due to high Arrhenius exothermic process, which revealed that the presence of Arrhenius kinetics is more effective to improve heat transportation phenomenon. Enhancement of the heat source/sink term completely boosts heat distribution. Rise in Radiation parameter, temperature field increases by reducing heat dissipation to the ambient.     

Solidification of PCM around a curved tube

This paper presents the results of an experimental and numerical investigation on the solidification of PCM around a curved cold tube to determine the effects of the Dean number, cooling fluid flow rate and its temperature on the interface velocity, the time for complete solidification and the solidified mass. To formulate the solidification process around a curved tube a conduction model was used together with the immobilization technique and the Landau transform. The energy equation and the associated boundary conditions were discretized by the finite control volumes method. The computational program was optimized by numerical experiments and the optimized form was used to validate the model. Comparisons of the numerical predictions and experiments to investigate the effects the Dean number on the solidified mass showed agreement within 1% while the interface velocity and the time for complete solidification showed agreements of about 8% and less than 6%, respectively. The effects of the flow rate of the working fluid could be predicted within less than 8% for the solidified mass and to less than 4% for both the interface velocity and the time for complete solidification. The effects of the temperature of the working fluid are predictable to within less than 8% for the time for complete solidification and the interface velocity.     

Entropy analysis of MHD flow of Jeffrey fluid in an inclined channel

This study is aimed at investigating the influence of entropy analysis of magnetohydrodynamic flow of Jeffrey fluid in an inclined micro-channel in the presence of thermal radiation and field suction/injection. We have improved the mathematical model of the physical problem under consideration. The designed equations have been solved by applying the shooting-based fourth-order, Runge–Kutta method with the boundary conditions, which describe velocity slip and temperature jump conditions at the fluid–wall inter-face. Numerical efforts are described graphically and mentioned quantitatively concerning different parameters such as Jeffery parameter, Bejan number, and entropy generation embedded in the problem. The numerical results for the expression of the irreversibility ratio are obtained. It is observed that the wall inclination strengthens the entropy production rate in the micro-channel, and the thermal buoyancy layer induces an increase in fluid velocity as suction.     

Thermo‐solutal convection in an inclined porous cavity with various aspect ratios under mixed thermal and species boundary conditions

The problem of laminar thermo‐solutal convective flow of a binary fluid mixture in an inclined rectangular cavity filled with a uniform porous medium is considered. Mixed heat and mass fluxes and uniform temperature and concentration conditions are applied on two opposing walls of the cavity while the other two walls are kept adiabatic and impermeable to mass transfer. The problem is put in terms of the stream function‐vorticity formulation. A numerical solution based on the finite‐difference methodology is obtained. Representative results illustrating the effects of the inclination angle of the cavity, buoyancy ratio, Darcy number, and the cavity aspect ratio on the contour maps of the streamline, temperature, and concentration as well as the profiles of velocity, temperature, and concentration at mid‐section of the cavity are reported. In addition, numerical results for the average Nusselt and Sherwood numbers as well as some useful correlations are presented for various parametric conditions and discussed. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20369     

Hall current,radiation absorption,and diffusion thermoeffects on unsteady MHD rotating chemically reactive second-grade fluid flow past a porous inclined plate in the presence of an aligned magnetic field,thermal radiation,and chemical reaction

In this paper, we analyze the effects of Hall current, radiation absorption and diffusion thermo on unsteady magnetohydromagnetic free convection flow of a viscous incompressible electrically conducting and chemically reacting second-grade fluid past an inclined porous plates in the presence of an aligned magnetic field, thermal radiation, and chemical reaction. An exact analytical solution of the governing equations for fluid velocity, fluid temperature, and species concentration subject to appropriate initial and boundary conditions is obtained using the perturbation technique. Expressions for shear stress, rate of heat transfer, and rate of mass transfer at the plate are derived. The numerical values of primary and secondary fluid velocities, fluid temperature and species concentration are displayed graphically, whereas those of shear stress and rate of mass transfer at the plate are presented in tabular form for various values of pertinent flow parameters. In addition, the skin friction on the boundary, the heat flux expressed in terms of the Nusselt number, and the rate of mass transfer described in the Sherwood number are all derived, and their behavior is studied computationally. It can be deduced that an increase in radiation absorption and hall current parameters over the fluid region increases the velocity produced. The resulting velocity continually increases to a very high level, with contributions coming from thermal and solutal buoyancy forces. Skin friction may decrease by manipulating the rotation parameter, but the Hall effect can worsen it. When the parameter for the chemical reaction increases, there is a concomitant rise in the mass transfer rate.     

Modeling and simulation of a proton exchange membrane fuel cell using computational fluid dynamics

An isothermal, three dimensional, single phase model was presented to evaluate a proton exchange membrane fuel cell (PEMFC) with serpentine flow. The mass, momentum and electrochemical equations were solved simultaneously for the steady state condition using computational fluid dynamics (CFD) software based on the finite element method. The model considered reactions as mass source/sink terms, and electron transport in the catalyst layers and GDLs. To validate the model, the numerical results were compared to the experimental data collected from the fabricated membrane electrode assemblies. The exchange current density parameter of the catalysts was fitted by the model to calibrate the results. The model showed good agreement with experimental data and predicted a higher current density for the catalyst with a higher surface area and Pt content. The oxygen, hydrogen and water mass fraction distribution, velocity magnitude and pressure distribution were estimated by the model. Moreover, the effect of pressure and temperature, as two important operating conditions, on the current density was predicted by the validated model.     

Second-order slip and Newtonian cooling impact on unsteady mixed convective radiative chemically reacting fluid with Hall current and cross-diffusion over a stretching sheet

The aim of the current study is to develop a mathematical model for unsteady mixed convective radiative chemically reactive fluid flow with Hall current, cross-diffusion, Newtonian cooling impacts and boundary conditions are influenced by second-order slip velocity. Effectively a viscous formulation combining different novel effects model is deployed. The basic Navier–Stokes derived flow equations are transformed into dimensionless form via particular similarity transformations for which numerical simulations utilize the finite element method. The numerical results for velocity components, temperature, and concentration on various flow parameters are sketched. For validation of the present results a comparison with previously published studies are conducted for some limiting conditions and reveals an excellent accuracy. Engineering items of interest like shear stresses, Nusselt number, and Sherwood number are computed and discussed extensively with the foremost parameters. Our analysis explores the fact that the physical parameters have a substantial influence upon boundary layer profiles.     

Simulation of fourth-grade magnetized fluid flow due to motile cilia in a heated curved channel

This research aims to investigate the main features of the ciliary flow of fourth-grade fluid in a curved channel. The fluid is considered electrically conducting with a radial magnetic field effect. The constitutive relation for energy is formulated with the addition of viscous dissipation and thermal radiation. The governing system of coupled partial differential equations with extremely nonlinear expressions is simplified using the long wavelength and low Reynolds number approximations. The numerical outcomes of simplified normalized equations are obtained using the finite difference method incorporating the relaxation algorithm. The numerical outcomes regarding the influences of several physical parameters on the temperature, velocity, pumping characteristics, and stream function are examined through graphs. The outcomes reveal that fluid velocity diminishes by enhancing the magnetic parameter. Also, the temperature is enhanced by enhancing the values of the Brickman number. The current model has been used in bioengineering processes, microfluidics, and drug delivery systems.     

Finite Element Analysis of Radiative Mixed Convection Magneto‐Micropolar Flow in a Darcian Porous Medium with Variable Viscosity and Convective Surface Condition

A mathematical study is presented for the collective influence of the buoyancy parameter, convective boundary parameter and temperature dependent viscosity on the steady mixed convective laminar boundary flow of a radiative magneto‐micropolar fluid adjacent to a vertical porous stretching sheet embedded in a Darcian porous medium. The fluid viscosity is assumed to vary as an inverse linear function of temperature. Using appropriate transformations, the governing equations of the problem under consideration are transformed into a system of dimensionless nonlinear ordinary differential equations, which are then solved with the well‐tested, efficient finite element method. The results obtained are depicted graphically to illustrate the effect of the various important controlling parameters on velocity, microrotation, and temperature functions. The skin friction coefficient, wall couple stress, and the rate of heat transfer have also been computed and presented in tabular form. Comparison of the present numerical results with earlier published data has been performed and the results are found to be in good agreement, thus validating the accuracy of the present numerical code. The study finds applications in conducting polymer flows in filtration systems, trickle bed magnetohydrodynamics in chemical engineering, electro‐conductive materials processing, and so on.     

Finite element analysis of couple stress micropolar nanofluid flow by non‐Fourier's law heat flux model past stretching surface

Numerical analysis has been done to investigate magnetohydrodynamics nonlinear convective flow of couple stress micropolar nanofluid with Catteneo‐Christov heat flux model past stretching surface with the effects of heat generation/absorption term, chemical reaction rate, first‐order slip, and convective boundary conditions. The coupled highly nonlinear differential equation governing the steady incompressible laminar flow has been solved by a powerful numerical technique called finite element method. The impacts of diverse parameters on linear velocity, angular velocity (microrotation), temperature, concentration profile, local skin friction coefficient, local wall couple stress, local Nusselt number, and Sherwood number are presented in graphical and tabular form. The result pointed out that the enhancement in material parameter β increases the velocity of the fluid while the couple stress parameter K has quite opposite effect. Heat and mass transfer rate of the fluid are enhanced by increasing material parameter while couple stress parameter shows the opposite influence. Moreover, heat and mass transfer rate are higher with the Catteneo‐Christov heat flux model than Fourier's law of heat conduction. The accuracy of the present method has been confirmed by comparing with previously published works.     

Fluid properties of an unsteady MHD free stream flow over a stretching sheet in presence of radiation

Variable fluid properties with thermal radiation in an unsteady magnetohydrodynamics free stream incompressible flow over a stretching sheet has been considered. The thermal diffusivity and viscosity of the fluid varies linearly with temperature. The governing partial differential equations are moulded to ordinary differential equations using time-dependent similarity variables and the stream function. RKF technique with shooting method has been implement to find the solution numerically. In the current analysis the impact of unsteadiness, magnetic field, radiative parameter, variable fluid viscosity and thermal diffusivity parameter on heat and flow behavior with the free stream parameter have been studied. Transition point observed in the velocity profiles with an change in unsteadiness parameter and the effect of magnetic field is reduced in the presence of free stram velocity. The velocity and the temperature gradient are computed on the surface and their outcomes with different parameters have been analyzed in the results shown graphically and in tabular form.