Viscous Dissipation Effects on MHD Free Convective Effects of Unsteady Flow Over a Vertical Porous Plate with Effects of Radiation

Abstract

In this paper, Hall Effects with Radiation effects on unsteady free convection flow and mass transfer over an infinite vertical porous plate which is embedded in porous medium with heat source. The basic governing equations of the problem are transformed into a system of non dimensional differential equations, which are then solved analytically by using Perturbation techniques. The dimensionless Velocity, temperature and concentration profiles are displayed graphically showing the effects fluid flow for the different values of the parameters involving in this problem like permeability parameter Kp,Grashof numbers Gr, Gc for heat and mass transfer, Heat Source parameter (S),Schmidt Number(Sc),Prandtl Number (Pr),Radiation Parameter(R) Second Order Chemical reaction parameter () etc.,. It is interesting to note that an increase of Grashof number(Gr),Permeability parameter(Kp)  Grashof Number (Gc)  accelerates the transient velocity of fluid.But increase of Heat Source parameter (S)retards the velocity profile of fluid flow.Further, it is observed that the temperature profile of the fluid flow decrease while increasing of prandtl number(Pr) and Radiation Parameter(R).But increase of Grashof number(Gr),shows the reverse process.The effect of increasing Schmidt number(Sc) and Chemical reaction parameter ( is to decrease the concentration boundary layer thickness of the flow field.Further, a growing of Magnetic Parameter  (M) and Hall Parameter (m) increasing the skin friction at the wall expect (Pr=5) and growing of Magnetic Parameter  (M) and Hall Parameter (m) leads to increase the magnitude of the rate of heat transfer at the wall expect (Pr=0.71).The investigated results showed graphically that the flow field is notably influenced by the considering parameters.

Introduction:. The Influence of Magnetic field on viscous incompressible flow of electrically conductor fluid has its important in many application such as extrustion of plastics in manufacture of rayon and nylon, purification of crude oil,paper industry, textile industry,etc.,. In Engineering in MHD pumps, MHD bearing etc., at high temperature attained   in some Engineering devices, gas, for example can be ionized  and so become an electrical conductor. However, in the presence of strong electric field, the electrical conductive is affected by magnetic field. Consequently, the conductivity parallel to electric field is reduced. Hence, the current is reduced to the direction normal to both electric and magnetic fields.

Objectives: Our Objective is to analyze the effects of hall current on unsteady MHD free convective heat and mass transfer flow past an infinite vertical porous plate embedded in porous medium with second order chemical reaction and heat source.

Methods: The method of  Problem is governed  by the system of coupled non-linear partial differential equations whose exact solutions are difficult to obtain, so we use Perturbation Techniques for obtained solution, which is more economical from computational point of view.

Results: Our results showns that, the behavior of Velocity, temperature, Concentration, shearing stress, Nusselt Number and Sherwood Number has been discussed for variation in the govering parameters.

Conclusions.        In this paper clearly shows effects of the parameters in the flow fluid. The velocity, temperature and concentration profiles are shown graphically with various values of parameters.

• Permeability parameter(Kp) accelerates the transient velocity of the fluid flow.


• Growing of Grashof Number (Gr) and Grashof Number (Gc) accelerates the transient velocity of the fluid flow but growing Radiation Parameter (R) and Heat Source (S) retards the transient velocity.


• Growing of Heat Source (S) accelerates the temperature but the reverse process if Prandtl Number (Pr) and Radiation Parameter (R) retards the Temperature of the fluid flow.


• Grashof Number (Gr) accelerates the Temperature profile of the fluid flow.


• Chemical Reaction Parameter (and Schmidt Number (Sc) are retards Concentration of Mass while both are grown.


• Permeability parameter(Kp) accelerates the transient velocity of the fluid flow.


• Using various parameters to analysis the nature of velocities, temperature and concentration over the fluid flow over a vertical porous plate.