On the effectiveness of viscous dissipation and Joule heating on steady MHD flow and heat transfer of a Bingham fluid over a porous rotating disk in the presence of Hall and ion-slip currents

The combined effects of viscous dissipation and Joule heating on steady magnetohydrodynamics (MHD) flow of an electrically conducting viscous incompressible non-Newtonian Bingham fluid over a porous rotating disk in the presence of Hall and ion-slip currents is studied. An external uniform magnetic field is applied in the z-direction and the fluid is subjected to uniform suction. Numerical solutions are obtained for the governing momentum and energy equations. Results for the details of the velocity as well as temperature are shown graphically and the numerical values of the skin friction and the rate of heat transfer are entered in tables.     

MHD natural convection heat and mass transfer flow over an inclined porous plate with thermophoresis and nonlinear thermal radiation effects

This study examined magnetohydrodynamic natural convection mass and heat transfer flow of an electrically conducting and viscous incompressible fluid over an inclined porous plate with thermophoresis, suction/injection, and uniform magnetic field. The mathematical model governing the fluid behavior surrounding an inclined plate is solved through the Runge–Kutta–Fehlberg fourth–fifth order after utilizing the shooting method. The implication of active dimensionless parameters in the governing equations is fully discussed in detail. The results obtained show that, in the existence of nonlinear thermal radiation and suction/injection, the heat transfer rises with the increase in the angle of inclination but it decreases with the mass transfer and plate shear stress. Furthermore, the heat transfer rate experiences a serious setback due to the increase in the buoyancy force but improves the plate shear stress. The mass transfer is directly proportional to the thermophoresis effect. In addition, Particle suction increases the velocity and temperature curves while it declines the concentration profile, but the opposite is valid for injection. Nonlinear thermal radiation positively affects the temperature, velocity, and concentration profiles. The Lorentz force suppresses the fluid transport and retard the rate of particle concentration, but promotes the fluid temperature distribution. It is also deduced that increasing the rate of particle suction from 0 to 1, accounts for over 76% increase in the particle deposition at the plate surface. However, increasing the rate of particle injection from 0.004 to 0.250 accounts for an over 83% decrease in the particle deposition at the plate surface.     

Effects of mass transfer and free convection on the unsteady mhd flow past a vertical porous plate with constant suction

Effects of free convection currents and mass transfer on the unsteady flow of an electrically conducting and viscous incompressible fluid past an infinite vertical porous plate subjected to uniform suction, in the presence of transverse magnetic field, have been studied taking into account that the external flow velocity varies periodically with time in magnitude but not in direction. The effect of the induced magnetic field has been neglected. Approximate solutions to the transient flow, the amplitude and the phase of the skin-friction and the rate of heat transfer have been derived. During the course of the discussion, the effects of the Grashoff number Gr, the modified Grashoff number Gc (depending on the concentration difference), the Schmidt number Sc, the Eckert number Ec, the magnetic field parameter M, and the frequency ω have been discussed.     

Role of suction/injection and slip flow on hydromagnetic free convective flow in a vertical coaxial cylinder under the influence of radial magnetic field

This investigation attempts to address heat and mass transfer behavior exhibited by a steady fully developed natural convective flow of a viscous, incompressible, and electrically conducting fluid in a vertical porous annulus in the presence of radially applied magnetic field and velocity slip. The motion of the fluid in the annular gap is triggered by the buoyancy forces due to temperature gradient of the inner and outer cylinders. The governing momentum and energy equations responsible for the flow are transformed into dimensionless forms using the appropriate dimensionless parameters. Accordingly, analytical solutions of the energy and momentum fields are derived with the appropriate boundary conditions. The effects of the controlling parameters involved in the flow on the temperature field, velocity field, and drag on the walls of the cylinders are illustrated graphically and with the aid of tables. Findings affirm that fluid temperature can be decreased/increased by increasing suction/injection on the porous wall. Furthermore, the fluid flow in the annular gap can be enhanced by increasing Grashof number, fluid injection, and velocity slip.     

Second law analysis for chemically reacting natural convective second‐grade fluid flow between porous parallel plates with Hall and Ion slip

In this article, we performed the entropy generation of free convective chemically reacting second‐grade fluid confined between parallel plates in the influence of the Hall and Ion slip with heat and mass fluxes. Let there be a periodic suction/injection along with the plates, the governing flow field equations are reduced as a set of coupled nonlinear ordinary differential equations by using appropriate similarity transformations then solved numerically with shooting method based on Runge‐Kutta 4th order scheme. The results are analyzed for velocity in axial and radial directions, temperature distribution, concentration distribution, entropy generation number, Bejan number, mass and heat transfer rates with respect to distinct geometric, and fluid parameters and shown graphically and tables. It is observed that the entropy generation is enhanced with Prandtl number, whereas decreases with a second‐grade parameter, the effects of Hall and Ion slip parameters on velocity components, temperature and entropy generation number are the same. The entropy generation number the fluid is enhanced with the suction‐injection parameter whereas, the concentration of the fluid decreases with the increasing of chemical reaction parameter.     

Mixed convection effects on unsteady flow and heat transfer over a stretched surface

This work focuses on the effects of mixed convection currents on the problem of unsteady, laminar, boundary-layer flow and heat transfer of an electrically-conducting and heat generating or absorbing fluid over a semi-infinite vertical stretched surface in the presence of a uniform magnetic field. The surface is assumed to be permeable so that to account for possible fluid wall suction or injection and that it is maintained at a variable power-law temperature and is being stretched with a linear velocity with the distance along the surface. The governing equations are derived based on the boundary-layer theory and using the Boussinesq approximation. An appropriate transformation is employed and the transformed equations are solved numerically using the finite-difference method. Comparisons with previously published work are performed and the results are found to be in excellent agreement. A comprehensive parametric study is conducted and a representative set of graphical results for the velocity and temperature profiles as well as the time development of the skin-friction and wall heat transfer coefficients are reported and discussed.     

Entropy generation on MHD flow of a Casson fluid over a curved stretching surface with exponential space-dependent heat source and nonlinear thermal radiation

The present model concentrates on entropy generation on a steady incompressible flow of a Casson liquid past a permeable stretching curve surface through chemical reaction and magnetic field effects. The exponential space-dependent heat source cum heat and mass convective boundary conditions are accounted for. The resulting nonlinear boundary layer model is simplified by the transformation of similarity. Chebyshev spectral technique is involved for obtaining numerical results of the converted system of the mathematical models. Behavior of the determining thermo-physical parameters on the profiles of velocity, temperature, concentration, skin friction, heat, mass transfer rate, rate of entropy generation, and finally the Bejan number are presented. The major point of the present investigation show that the curvature term weakens the mass transfer profile as the fluid temperature reduces all over the diffusion regime. A decrease in heat generation strengthens the species molecular bond, which prevents free Casson particle diffusion. Furthermore, the mass transfer field diminishes in suction and injection flow medium.     

The effects of variable viscosity and thermal conductivity on heat transfer for hydromagnetic flow over a continuous moving porous plate with Ohmic heating

A numerical study of heat transfer from boundary layer flow driven by a continuous moving porous plate is proposed. The flow with electrically fluid due to the plate in the presence of a transverse magnetic field and Ohmic heating was molded as a steady, viscous, and incompressible. Both viscosity and thermal conductivity were variable and considered only a function of temperature. Similar analysis with Chebyshev finite difference method (ChFD) was developed to solve the governing equations for momentum and energy and determine the skin-friction coefficient and heat transfer rate. As the magnetic parameter and variable viscosity parameter increase, the fluid temperature and skin-friction coefficient increase and the fluid velocity and heat transfer rate decrease. The fluid temperature increases and heat transfer rate decreases with an increasing Eckert number and thermal conductivity parameter. The skin-friction coefficient and heat transfer rate increase, whereas the fluid velocity and temperature decrease as the wall suction velocity increase.     

HEAT AND MASS TRANSFER FROM A PERMEABLE CYLINDER IN A POROUS MEDIUM WITH MAGNETIC FIELD AND HEAT GENERATION/ABSORPTION EFFECTS

We formulate the problem of coupled heat and mass transfer by natural convection from a horizontal cylinder embedded in a uniform porous medium in the presence of an external magnetic field and internal heat generation or absorption effects. The cylinder surface is maintained at a constant temperature and a constant concentration and is permeable to allow for possible fluid wall suction or blowing. The resulting governing equations are nondimensionalized and transformed into a nonsimilar form and then solved numerically by an implicit, iterative, finite-difference method. Comparisons with previously published work are performed and excellent agreement is obtained. A parametric study of the physical parameters is conducted and a representative set of numerical results for the stream function, temperature, concentration profiles, and the Nusselt and Sherwood numbers is illustrated graphically to show interesting features of the solutions.     

Hydromagnetic flow and heat transfer past a continuously moving porous boundary

The effect of magnetic field on the flow and heat transfer past a continuously moving porous plate in a stationary fluid has been analysed. The governing boundary layer equations have been reduced to a set of nonlinear ordinary differential equations using similarity transformations. The resulting boundary value problem has been solved numerically. The effects of magnetic and suction (or injection) parameters on the velocity and temperature profiles as well as on the skin friction and heat transfer coefficients have been studied. It has been observed that the effect of magnetic field is to increase the wall skin friction while the reverse occurs in the case of Nusselt number.     

Couple stress effects on the MHD oscillatory flow in a fluid-saturated porous layer

In this paper, the oscillatory flow of hydromagnetic couple stress fluid-saturated porous layer with inhomogeneous wall temperatures is studied. The flow is modeled using the modified Darcy equation. The fluid is subjected to a transverse magnetic field and the velocity slip at the lower plate is taken into deliberation. The governing coupled partial differential equations of the flow are transformed to coupled ordinary differential equations and are solved analytically. The impact of the physical parameters such as the Grashof number, Prandtl number, Darcy number, Hartmann number, and couple stress parameters on velocity profiles, temperature, rate of heat transfer, and skin friction are emphasized. The velocity field increased as either the Grashof number, the Darcy number, the suction/injection parameter, and Prandtl number increased nevertheless reverse growth can be seen by increasing the Hartmann number and the couple stress parameter. The temperature field in the channel increases with increasing the suction/injection parameter and Prandtl number but a conflicting development can be seen with increasing the oscillation amplitude. It is interesting to note that skin friction increases on both channel plates as injection increases on the heated plate.     

Magnetohydrodynamic mixed convection in a non-Newtonian third-grade fluid flowing through vertical parallel plates: A semianalytical study of flow and heat transfer

Buoyancy assisted and buoyancy opposed mixed convection of a third-grade fluid, which flows through vertically oriented parallel plates, subjected to uniform and constant wall heat fluxes, under the effect of an externally applied magnetic field, are investigated. The coupled, nonlinear conservation equations of momentum and energy are solved employing the collocation method (CM) and velocity and temperature distributions are solved semianalytically. The results produced by the CM and the results of exact solution are compared for the buoyancy assisted and buoyancy opposed flow of a Newtonian fluid through the vertically oriented parallel plates arrangement without the effect of the externally applied magnetic field. An excellent agreement is exhibited by demonstrating the efficacy of the CM. The effects of the third-grade fluid parameter, Hartmann number, and mixed convection parameter on the dimensionless velocity, temperature, and Nusselt number are studied. The results imply that in the case of buoyancy assisted flow, an increment in the non-Newtonian third-grade fluid parameter causes a decrease in the fluid velocity near the plate walls, which finally causes an increase in the velocity in the central core of the plates. In buoyancy opposed flow, the effect of the same parameter is to oppose the flow reversal near the walls and with higher values of this parameter, it can totally prevent the flow reversal near the walls. The results of the present study can be useful in the fields of flow and heat transfer of various grades of polymers, paints, and food processing.     

Laminar Free Convection in a Square Enclosure Driven by the Lorentz Force

A numerical study is presented of laminar free convection flow driven by magnetic forces. An external magnetic field with one spatially varying component is applied to an electrically conducting fluid in a square enclosure. This magnetically-driven flow is controlled by the intensity and the wave number of the applied magnetic forcing. In addition, when the enclosure is heated laterally in a non-zero gravity environment, the resulting buoyant forces may contribute or resist the magnetically-driven fluid motion. The present results show that a strong magnetic field can even reverse the buoyant flow. The circulation intensity of the flow and the heat transfer from the sidewalls is increased with increasing magnetic field or with decreasing magnetic Reynolds number. The wave number of the magnetic forcing is also an important parameter that determines the vortex patterns and, consequently, the convection heat transfer.     

Heat and mass transfer in a MHD non‐Darcian micropolar fluid over an unsteady stretching sheet with non‐uniform heat source/sink and thermophoresis

The effect of heat and mass transfer in a MHD non‐Darcian flow of a micropolar fluid over an unsteady stretching sheet with thermophoresis and non‐uniform heat source/sink is discussed. The fluid is electrically conducting in the presence of a uniform applied magnetic field. The arising nonlinear problem is solved by the Keller box method. The effects of various physical parameters on skin friction, local Nusselt number, and Sherwood number are presented graphically and in tabular form. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21018     

Impact of thermal diffusion and chemical reaction on oscillatory MHD convective flow of a viscoelastic fluid through a porous medium in a slip flow regime

The purpose of the current investigation is to analyze the influence of thermal diffusion on magnetohydrodynamic viscoelastic fluid flow with concurrent heat and mass transfer near an oscillating porous plate in a slip flow Regime under the influence of a uniform transverse magnetic field. The uniqueness of the present study is to examine the effects of viscoelastic property (Walters B' model) on the flow and heat transfer phenomena when a transverse magnetic field and time-dependent fluctuating suction at the boundary surface are present in a porous medium with a uniform porous matrix. A regular perturbation technique is used to solve the governing equations for small elastic parameters. Graphical representations are used to show how different parameters affect skin friction, temperature, concentration, and velocity. It is observed that concentration distribution as well as the coefficient of friction is enhanced due to the thermal diffusion effect. It is noticed that the visco-elastic parameters reduce the velocity of the fluid. In addition, chemical reactions and suction factors cause the flow field's temperature to drop. Furthermore, the fluid concentration drops under the chemical reaction effect.     

Transient Laminar MHD Natural Convection Cooling in a Vertical Cylinder

A numerical study is presented of transient laminar natural convection cooling of an electrically conductive fluid, placed in a vertical cylinder in the presence of an axial magnetic field. The cylindrical wall is suddenly cooled to a uniform temperature, thus setting the fluid to motion. The cooling process starts with the development of momentum and thermal boundary layers along the cylindrical cold wall, followed by the intrusion of the cooled fluid into the bulk, and finally, by fluid stratification. A range of Hartmann, Rayleigh, and Prandtl numbers are studied for which the flow remains laminar in all stages. It is found that the increase of the magnetic field reduces the heat transfer rate and decelerates the cooling process. This can be attributed to the damping of the fluid motion by the magnetic field, which results in the domination of conduction over convection heat transfer. The increase of the Rayleigh number enhances heat transfer, but the cooling process lasts longer due to the higher temperature of the hot fluid. The flow deceleration and the reduction of heat transfer are less intense for fluids with low Prandtl number.     

Run-up flow of MHD fluid between parallel porous plates in the presence of transverse magnetic field

This paper investigated the run-up flow of magnetohydrodynamics (MHD) incompressible, viscous, Newtonian fluid bounded by two parallel horizontal porous plates in the presence of transverse magnetic field. The fluid flow is initially due to constant pressure gradient, placed parallel to the plates. On attaining steady state, the pressure gradient is suddenly withdrawn and the lower porous plate is set into motion in its own plane, this phenomenon is termed as run-up flow. The transfer of momentum is as a result of the disturbances emanating from the boundary into the fluid. The initial value problem is solved using Laplace transform technique to obtain the closed-form solution for the velocity in the Laplace domain. Semi-analytical result is obtained by an inversion technique based on Riemann-sum approximation to invert the solution for velocity into its corresponding time domain. The mathematical simulation conducted shows that increasing the Hartmann number is observed to decrease the fluid velocity while increasing the pressure gradient is found to enhance the fluid velocity. Furthermore, the opposing effects of suction/injection parameter on the fluid velocity have been established in the research.     

Influence of homogeneous‐heterogeneous reactions and induced magnetic field on the nonlinear thermal convective radiative Jeffrey liquid flow with heat source/sink

An analysis has been carried out to investigate the effect of homogeneous‐heterogeneous reactions and induced magnetic field on the unsteady two‐dimensional incompressible nonlinear thermal convective velocity slip flow of a Jeffrey fluid in the presence of nonlinear thermal radiation and heat source/sink. We assumed that the flow is generated due to injection at the lower plate and suction at the upper plate. We obtained a numerical solution for the reduced nonlinear governing system of equations via the shooting technique with fourth‐order Runge‐Kutta integration. We plotted the graphs for various nondimensional parameters, like Deborah number, heat source/sink parameter, nonlinear convection parameter, nonlinear radiation parameter, magnetic Reynolds number, Strommer's number, velocity slip parameter, strengths of homogeneous, heterogeneous reaction parameters and skin friction over the nondimensional flow, temperature, concentration profiles and magnetic diffusivity fields. Also, we calculated the numerical values of boundary properties, such as the skin friction and heat transfer rate. We noticed that the temperature of the fluid is enhanced with the radiation parameter, whereas the concentration decreases with increase of the magnetic Reynolds number. The present results have good agreement with published work for the Newtonian case.     

Radiation effect on MHD flow past a porous vertical plate in the presence of heat sink

This study investigates heat and mass transfer in MHD convective flow through a vertical plate via porous media in the presence of radiation and a heat source/sink. It is assumed that a uniform magnetic field of strength is imposed perpendicular to the plate and directed into the fluid area. The governing nondimensional equations are solved using the perturbation technique. We further derived the skin friction, Nusselt number, and Sherwood number. The computation of results is performed with the aid of mathematical software and results are presented in graphical and tabular forms for distinct flow impacting parameters. It is observed that fluid motion is retarded due to the application of the magnetic field. Furthermore, the fluid temperature comprehensively falls under the Prandtl number as well as the thermal radiation effect. It is important to note that the heat sink causes fluid velocity and fluid temperature to fall drastically.     

Non-similar analytic solution for MHD flow and heat transfer in a third-order fluid over a stretching sheet

This paper investigates the magnetohydrodynamic (MHD) flow and heat transfer characteristics in the presence of a uniform applied magnetic field. The boundary layer flow of a third-order fluid is induced due to linear stretching of a non-conducting sheet. The heat transfer analysis has been carried out for two heating processes, namely (i) with prescribed surface temperature (PST-case) and (ii) prescribed surface heat flux (PHF-case). The governing non-linear differential equations are solved analytically using homotopy analysis method (HAM). The series solutions are developed and the convergence of these solutions is discussed. Velocity and temperature distributions are shown graphically. The numerical values for the skin friction coefficient and the Nusselt number are entered in tabular form. Emphasis has been given to the variations of the emerging parameters such as third-order parameter, magnetic parameter, Prandtl number and the Eckert number. It is noted that the skin friction coefficient decreases as the magnetic parameter or the third grade parameter increases.