The flow and heat transfer of an incompressible viscous electrically conducting fluid over a continuously moving vertical infinite plate with uniform suction and heat flux in porous medium, taking account of the effects of the variable viscosity, has been considered. The solutions are obtained for velocity, temperature, concentration and skin friction. It is found that the velocity increases as the viscosity of air or porous parameter increases whereas velocity decreases when Schmidt number increases. The skin friction coefficient is computed and discussed for various values of the parameters.

The problem of heat and mass transfer in the boundary layer induced by a moving surface in a quiescent fluid is important in many engineering applications. For examples, in the extrusion of polymer sheet from a dye, the cooling of an infinite metallic plate in a cooling path, glass blowing continuous casting and spinning of fibers. Sakiadis [

Many transport processes exist in nature and in Industrial applications in which the simultaneous heat and mass transfer occurs as a result of combined buoyancy effects of diffusion of chemical species. Chemical reaction effects on heat and mass transfer laminar boundary layer flow have been discussed by various authors [14-18] in various situations.

In this paper, the effects of variable viscosity on hydromagnetic boundary layer flow along a continuously moving vertical plate with uniform suction and heat flux has been studied.

Consider a steady boundary layer convective flow through porous medium of an electrically conducting visco-elastic fluid on a continuous surface, issuing from a slot and moving vertically with a uniform velocity in a fluid and heat is supplied from the plate to the fluid at a uniform rate, in the presence of a uniform magnetic field of strength. Let the x-axis be taken along the direction of motion of the sheet and the y-axis be normal to the surface. The induced magnetic field is assumed to be negligible. It is assumed that there exists a first order chemical reaction between the fluid and the fluid species concentration. The physical model of the problem is shown in

Under the above assumption, the equations for boundary layer flow are as follows:

Equation of heat transfer:

Equation of concentration:

The corresponding boundary conditions are

where are the velocities along coordinates, respectively, is the acceleration due to gravity, is the coefficient of thermal expansion, is the concentration coefficient, is the fluid temperature, is the temperature of the fluid far away from the plate, is the electrical conductivity, is the ambient density, is the fluid viscosity, is the heat flux, is the thermal conductivity, is the specific heat at constant pressure, is the radiative heat transfer, is the normal velocity at the plate, is the concentration, is the concentration in the fluid far away from the plate, is the permeability of the porous medium.

From the Equation (1), we get

By using Rosseland approximation, takes the form [

where is the mean absorption coefficient and is the Stefan-Boltzmann constant.

The temperature differences within the fluid assumed sufficiently small such that may be expressed as a linear function of the temperature. Expanding in Taylor series about and neglecting the higher order terms, we get

By using Equations (6)-(8) then Equation (3) gives

Introducing the following non-dimensional quantities:

In view of Equation (10), Equations (2), (9), and (4) reduce to the following non-dimensional form:

The corresponding boundary conditions are

where the prime denote differentiation with respect to and is the thermal Grashof number, is the solutal Grashof number, is the Prandtl number, is the Hartmann number, is the Schmidt number, is the porous parameter, the radiation parameter.

The fluid viscosity was assumed to obey the Reynolds model [

where is a parameter depending on the nature of the fluid.

Using, Equation (13) in the Equation (11) we obtain,

1) Case of constant viscosity:

For, from Equation (16), we have

Solving (17) under boundary condition (14), we get

where

2) Variable viscosity case:

On taking into account the solution for temperature and concentration, we solved numerically the Equation (16) under the boundary conditions (14) using the RungeKutta fourth order technique with guessing by shooting technique.

The skin friction coefficient is defined as

In order to see the physical impact of the variable viscosity on the velocity field, the graphical representation of results is important. For the purpose of discussing the effect of variable viscosity on the flow profiles within the boundary layer, numerical calculations have been carried out for various values involved in the problem with fixed values of. The value of is taken to be for air. The effect of on dimensionless velocity are illustrated in Figures 2-4 with

It is observed from the

The effect of the porous parameter on velocity profile is shown in

It is seen from the

The governing equations for boundary layer flow and mass transfer of a steady viscous, incompressible elec-

trically conducting fluid with variable viscosity over a continuously moving vertical porous plate in the presence of magnetic field and radiation has been investigated. It was found that when viscosity parameter and porous parameters were increased, the fluid velocity increased. However, velocity decreases as the Schmidt number decrease. In addition, it was found that the skin-friction coefficient increased due to increase in the viscosity parameter, the radiation parameter, thermal Grashof number or solutal Grashof number. But the increasing of the magnetic parameter, Schmidt number or porous parameter leads to a decrease in the skin-friction.