Infinite Vertical Porous Plate Research Articles

The Combined Effect of Chemical Reaction, Thermal Radiation on steady free convection and mass transfer flow in a porous medium considering Soret and Dufour effects

In the present analysis, we study the two-dimensional, steady, free convection and mass transfer flow past a continuously moving semi infinite vertical porous plate in a porous medium in the presence of thermal radiation, chemical reaction, Dufour and Soret effects. The governing nonlinear partial differential equations have been reduced to the coupled nonlinear ordinary differential equations by the similarity transformations. The resulting equations are then solved numerically using finite difference method. The non-dimensional velocity, temperature and concentration profiles are displayed graphically for various interesting parameters entering into the problem and discussed in detail.

Transient magnetohydrodynamic (MHD) flow of a visco-elastic fluid past an infinite vertical porous plate embedded in a porous medium with Hall current and slip condition in a rotating system

An attempt is made to present a theoretical analysis of a transient magnetohydrodynamic (MHD) flow of a visco-elastic fluid (Walter’s B’) past an infinite vertical porous plate embedded in a porous medium with constant permeability in a rotating system in the presence of Hall current when the plate temperature varies periodically with time. The expressions for the non-dimensional velocity field, temperature field, and the coefficient of skin friction and Nusselt number at the plate are obtained and the effects of various physical parameters on these fields are demonstrated graphically with physical interpretation. Comparison of some of the numerical results obtained from the analytical solution of the present work is made with previously published results under special cases and it shows a good agreement. Key words: Magnetohydrodynamics (MHD), visco-elastic, Hall current, rotation, slip-flow regime.

Three-Dimensional Mixed Convection Flow past an Infinite Vertical Plate with Constant Surface Heat Flux

The present paper contains a mathematical analysis of the mixed convection three dimensional steady lami- nar flow of a viscous incompressible fluid past an infinite vertical porous plate. The three-dimensional flow is caused by the transverse sinusoidal suction at the plate. A constant heat flux is prescribed at the plate. Assuming the plate velocity to be uniform, analytical solutions are obtained for the flow field, the temperature field and the skin-friction. Effects of Prandtl number and Grashof number on the flow characteristics are explored and illustrated graphically. In view of the importance of the problems of laminar flow control (LFC), especially in the field of aeronautical engineering, various theoretical and experimental studies of different arrangements and configurations of suction holes and slits have been compiled by Lachmann(1). The suction of the fluid is also an acknowledged technique for control- ling the undesirable features in the boundary layer theory. Further, from the technological point of view, free convec- tion flow and heat transfer problems are always important, for they have many practical applications. The phenomenon of free-convection arises when the difference between the plate temperature and the free stream temperature apprecia- bly large which causes density variations leading to buoyancy forces acting on the fluid elements. This process of heat transfer is encountered in cooling of nuclear reactors, providing heat sinks in turbine blades and aeronautics. Free convection flow past vertical plate has been studied exten- sively by many researchers and some of them are Os- trach(2-3), Stewartson et. al.(4), Sparrow et. al.(5-6), Ma- buchi(7), Riley et. al.(8), Berezovsky et.al.(9), Na(10), Dey et al (11), Kawase et al(12), Martynenko et.al.(13), Weiss et.al.(14) and Pantokratoras(15-16) in numerous ways to include various physical effects. In their work they have restricted themselves to two-dimensional flow only. There may arise situations where the flow fields may be essential- ly three-dimensional, for example when variations in the suction velocity distribution is transverse to the flow direc- tion. Gersten and Gross(17) have studied the effect of such

Hydromagnetic Unsteady Mixed Convection Flow Past an Infinite Vertical Porous Plate

An approximate analysis of unsteady mixed convection flow of an electrically conducting fluid past an infinite vertical porous plate embedded in porous medium under constant transversely applied magnetic field is presented here. The periodic transverse suction velocity is applied to the surface due to which the flow becomes unsteady. The surface is kept at oscillating wall temperature. Analytical expressions for the transient velocity, temperature, amplitude and phase of the skin-friction and the rate of heat transfer are obtained and discussed in detail with the help of graphs, under different parameter values.

Unsteady/Steady Free Convective Couette Flow of Reactive Viscous Fluid in a Vertical Channel Formed by Two Vertical Porous Plates

This paper presents unsteady as well as steady-state free convection Couette flow of reactive viscous fluid in a vertical channel formed by two infinite vertical parallel porous plates. The motion of the fluid is induced due to free convection caused by the reactive nature of viscous fluid as well as the impulsive motion of one of the porous plates. The Boussinesq assumption is applied, and the nonlinear governing equations of motion and energy are developed. The time-dependent problem is solved using implicit finite difference method, and steady-state problem is solved by applying regular perturbation technique. During the course of computation, an excellent agreement was found between the well-known steady-state solutions and transient solutions at large value of time.

Finite Element Solution of Heat and Mass Transfer in MHD Flow of a Viscous Fluid past a Vertical Plate under Oscillatory Suction Velocity

The study of hydromagnetic heat and mass transfer in MHD flow of an incompressible, electrically conducting, viscous fluid past an infinite vertical porous plate along with porous medium of time dependent permeability under oscillatory suction velocity normal to the plate has been made. It is considered that the influence of the uniform magnetic field acts normal to the flow and the permeability of the porous medium fluctuate with the time. The problem is solved, numerically by Galerkin finite element method for velocity, temperature, concentration field and the expressions for skin – friction, Nusselt number and Sherwood number are also obtained. The results obtained are discussed for Grashof number (Gr > 0) corresponding to the cooling of the plate and (Gr < 0) corresponding to the heating of the plate with the help of graphs and tables to observe the effects of various parameters.

Variable fluid properties and thermal radiation effects on flow and heat transfer in micropolar fluid film past moving permeable infinite flat plate with slip velocity

This work deals with the influence of thermal radiation on the problem of the mixed convection thin film flow and heat transfer of a micropolar fluid past a moving infinite vertical porous flat plate with a slip velocity. The fluid viscosity and the thermal conductivity are assumed to be the functions of temperature. The equations governing the flow are solved numerically by the Chebyshev spectral method for some representative value of various parameters. In comparison with the previously published work, the excellent agreement is shown. The effects of various parameters on the velocity, the microrotation velocity, and the temperature profiles, as well as the skin-friction coefficient and the Nusselt number, are plotted and discussed.

Radiative Mixed Convection Mass Transfer Flow past an Iso-Thermal Porous Plate Embedded in a Permeable Medium in Presence of Thermal Diffusion and Heat Generation

paper an exact analysis to study the combined effects of thermal diffusion (Soret) and heat generation on a mixed convection flow past an infinite vertical porous plate in presence of thermal radiation has been made. The governing system of partial differential equations subject to favorable boundary conditions is being solved analytically. Cogly- Vincentine-Gilles equilibrium approximations have been used to describe the radiative heat flux in the energy equation. Closed form of solutions for the velocity field, the temperature field and the concentration field are obtained and discussed graphically for various values of the physical parameters such as radiation parameter, Soret number, Grashof number, modified Grashof number, Prandtl number, Schmidt number and heat generation parameter. Moreover, expressions for the skin-friction, heat transfer co-efficient and mass transfer co-efficient are discussed with graphs and tables.

MHD Three Dimensional Couette Flow past a Porous Plate with Heat Transfer

In this paper a steady three dimensional flow of a viscous - incompressible fluid through highly porous medium bounded by a vertical infinite porous plate under the influence of a transverse applied magnetic field, with periodic suction velocity is considered. Governing equations are solved by using perturbation technique and obtained the expressions for velocity and temperature. The above flow quantities are discussed through the graphs for different physical parameters. Also the expressions for shear stress and the rate of heat transfer co-efficient are derived and discussed.

Hall Effect on Oscillatory Hydromagnetic Free Convective Flow of a Non-Newtonian Fluid past an Infinite Vertical Porous Flat Plate with Heat Sources / Sink and Constant Suction

This paper deals with the hall effect on oscillatory hydromagnetic free convective flow of non-Newtonian fluid past an infinite vertical porous flat plate with heat sources/sinks. In the formulation part, equations of continuity, motion and energy have been developed. These equations have been made dimensionless with the introduction of non-dimensional parameters concerned and solved applying complex variable technique under the boundary conditions employed. Profiles of primary velocity, secondary velocity and temperature have been plotted after computerization with the numerical values of the non-dimensional parameters. The values of skin frictions and the rates of heat transfer have been entered in the tables. It is observed that both the primary and secondary velocity increase with the increase of the non-Newtonian parameters (Rc) as well as the reciprocal of the porosity parameters (1/K*). The temperature of the fluid falls with the Prandtl number (Pr).

Soret and Dufour Effects on Unsteady MHD Mixed Convection Flow past a Radiative Vertical Porous Plate Embedded in a Porous Medium with Chemical Reaction

The Soret and Dufour effects on unsteady MHD mixed convection flow past an infinite radiative vertical porous plate embedded in a porous medium in the presence of chemical reaction have been studied. A uniform magnetic field acts perpendicular to the porous surface. The Rosseland approximation has been used to describe the radiative heat flux in energy equation. The governing equations are solved numerically by applying explicit finite difference Method. The effects of various parameters on the velocity, temperature and concentration fields have been examined with the help of graphs.

Magnetic Hydrodynamic Free Convective Flow past an Infinite Vertical Porous Plate

A study of magnetic hydrodynamic free convective flow past an infinite vertical porous plate in an incompressible electrically conducting fluid is considered. The investigation of the effect of viscous dissipation on the velocity profiles and temperature distribution of the fluid in the presence of a transverse magnetic field subject to a constant suction velocity is conducted. The ordinary differential equations governing the flows are analyzed using an explicit finite-difference scheme and computer generated programs. The results are presented in graphical form showing the effects of the various parameters arising in the flow. The numerical results of the study show that an increase in the viscous dissipation causes an increase in the velocity profiles and temperature distribution of the fluid.

Radiation and thermal diffusion effects on an unsteady MHD free convection mass-transfer flow past an infinite vertical porous plate with the hall current and a heat source

An analysis is performed to study the effects of radiation and thermal diffusion on an unsteady MHD free convection heat- and mass-transfer flow of an incompressible, electrically conducting, viscous fluid past an infinite vertical porous plate with the Hall current and a heat source. The flow is considered under the influence of a constant suction velocity and a uniform magnetic field applied normally to the flow. The dimensionless governing equations are solved numerically by the Galerkin finite element method. The effects of the flow parameters on the primary and secondary velocities, temperature, species concentration, shearing stresses, Nusselt number, and Sherwood number are calculated and presented in figures and tables. The results obtained show that a decrease in the temperature boundary layer thickness occurs when the Prandtl number and radiation parameter are increased and an increase in the Schmidt number leads to a decrease in the concentration boundary layer thickness.

Magnetohydrodynamic Free Convective Flow Past an Infinite Vertical Porous Plate with Magnetic Induction

The steady two-dimensional magnetohydrodynamic free convective laminar flow of an electrically conducting, viscous and incompressible fluid with finite electrical conductivity past an infinite heated vertical porous plate has been investigated. The coupled ordinary differential equations governing the velocity, the temperature and induced magnetic field distributions are solved analytically. The effects of Prandtl number (P r ), Grashof number (Gr), magnetic field parameter (M), and suction parameter ( $$ \overline{V}_{0} $$ ) on the flow field are analysed using graphs. The study reveals that the increase of the Prandtl number (Pr) and the suction velocity ( $$ \overline{V}_{0} $$ ) lead to a decrease in the temperature, velocity and the induced magnetic field in the boundary layer region whereas increase in Grashof number and magnetic field parameter lead to increased induced magnetic field.

Fluctuating Heat and Mass Transfer on Unsteady MHD Free Convection Flow of Radiating and Reacting Fluid past a Vertical Porous Plate in Slip- Flow Regime

In this paper, an analytical study on unsteady MHD free convective viscous incompressible flow of electricallyconducting fluid with periodic heat and mass transfer past an infinite vertical porous flat plate in slip flow regime is presented. A uniform magnetic field perpendicular to the plate is applied. The effects of thermal radiation and chemical reaction are included. The effects of flow parameters and thermo physical properties on the flow, temperature and concentration fields across the boundary layer are investigated. The forms of the wall shear stress, Nusselt number and Sherwood number are derived. The results are shown in figures and tables followed by a quantitative discussion.

Mass Transfer Effects on Unsteady Hydromagnetic Convective Flow past a Vertical Porous Plate in a Porous Medium with Heat Source

The objective of this paper is to analyze the effect of mass transfer on unsteady hydromagnetic free convective flow of a viscous incompressible electrically conducting fluid past an infinite vertical porous plate in presence of constant suction and heat source. The governing equations of the flow field are solved using multi parameter perturbation technique and approximate solutions are obtained for velocity field, temperature field, concentration distribution, skin friction and the rate of heat transfer. The effects of the flow parameters such as Hartmann number M, Grashof number for heat and mass transfer Gr, Gc; permeability parameter Kp, Schmidt number Sc, heat source parameter S, Prandtl number Pr etc. on the flow field are analyzed with the help of figures and tables. It is observed that a growing Hartmann number or Schmidt number retards the mean velocity as well as the transient velocity of the flow field at all points. The effect of increasing Grashof number for heat and mass transfer or heat source parameter is to accelerate both mean and transient velocity of the flow field at all points. The mean velocity of the flow field increases with an increase in permeability parameter while the transient velocity increases for smaller values of Kp (≤1) and for higher values the effect reverses. A growing Hartmann number decreases the transient temperature of the flow field at all points while a growing permeability parameter or heat source parameter reverses the effect. The Prandtl number increases the transient temperature for small values of Pr (≤1) and for higher values the effect reverses. The effect of increasing Schmidt number is to reduce the concentration boundary layer thickness of the flow field at all points. The problem has some relevance in the geophysical and astrophysical studies.

Thermo-diffusion and diffusion-thermo effects on a three dimensional MHD mixed convection flow past an infinite vertical porous plate with thermal radiation

Thermo-diffusion and diffusion-thermo effects on a three dimensional MHD mixed convection flow past an infinite vertical porous plate with thermal radiation

Unsteady MHD free convective heat and mass transfer from a vertical porous plate with Hall current, thermal radiation and chemical reaction effects

AbstractAn analysis is presented to investigate the effects of chemical reaction, thermal radiation and heat generation or absorption on unsteady free convective heat and mass transfer along an infinite vertical porous plate in the presence of a transverse magnetic field and Hall current. The governing partial differential equations are formulated and transformed by using a similarity transformation into a system of ordinary differential equations. The resulting equations are solved numerically using a fourth‐order Runge–Kutta scheme along with the shooting method. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. Numerical results for the velocity, temperature and concentration distributions are shown graphically for different parametric values. The effects of parameters on the local friction coefficients, the Nusselt number and Sherwood numbers are depicted in tabulated form. Copyright © 2009 John Wiley &amp; Sons, Ltd.

Chemical reaction effect on an unsteady MHD free convection flow past an infinite vertical porous plate with constant suction

This paper focuses on the effects of chemical reaction on an unsteady magneto hydrodynamic free convection fluid flow past an infinite vertical porous plate with constant suction has been analyzed. The dimensionless governing equations are solved numerically by a finite element method. The effects of the various parameters on the velocity, temperature and concentration profiles are presented graphically and values of skin-friction coefficient, Nusselt number and Sherwood number for various values of physical parameters are presented through tables.

Chemical reaction and radiation effects on the transient MHD free convection flow of dissipative fluid past an infinite vertical porous plate with ramped wall temperature

A finite-difference analysis is performed to study the effects of thermal radiation and chemical reaction on the transient MHD free convection and mass transform flow of a dissipative fluid past an infinite vertical porous plate subject to ramped wall temperature. The fluid considered here is a gray, absorbing/emitting radiation but a non-scattering medium. The dimensionless governing equations are unsteady, coupled and non-linear partial differential equations. An analytical method fails to give a solution. Hence an implicit finite difference scheme of Crank-Nicolson method is employed. The effect of the Magnetic parameter (M), Chemical reaction parameter (K), Radiation parameter (F), Buoyancy ratio parameter (N), Schmidt number (Sc) on the velocity field and skin friction for both air (Pr=0.71) and water(Pr=7) in the presence of both aiding (N&gt;0) and opposing (N&lt;0) flows are extensively discussed with the help of graphs.