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The objective of the present study is to investigate diffusion-thermo (Dufour effect) and radiation effects on unsteady MHD free convection flow past an impulsively started infinite vertical plate with variable temperature and uniform mass diffusion in the presence of transverse applied magnetic field through porous medium. At time t > 0, the plate is given an impulsive motion with constant velocity in the vertical upward direction against to the gravitational field. At the same time the plate temperature is raised linearly with time t and the level of concentration near the plate is raised to . A magnetic field of uniform strength is applied normal to the direction to the flow. The dimen- sionless governing equations are solved in closed form by Laplace-transform technique. The effect of flow parameters on velocity, temperature, concentration, the rate of heat transfer and the rate of mass transfer are shown through graphs.

In nature, there exist flows which are caused not only by the temperature differences but also the concentration differences. These mass transfer differences do affect the rate of heat transfer. In industries, many transport processes exist in which heat and mass transfer takes place simultaneously as a result of combined buoyancy effect in the presence of thermal radiation. Hence, radiative heat and mass transfer play an important role in manufacturing industries for the design of fins, steel rolling, nuclear power plants, gas turbines and various propulsion device for aircraft, missiles, satellites, combustion and furnace design, materials processing, energy utilization, temperature measurements, remote sensing for astronomy and space exploration, food processing and cryogenic engineering, as well as numerous agricultural, health and military applications. If the temperature of surrounding fluid is rather high, radiation effects play an important role and this situation does exist in space technology. In such cases, one has to take into account the combined effect of thermal radiation and mass diffusion.

Boundary layer flow on moving horizontal surfaces was studied by Sakiadis [

England and Emery [

Free convection flows that occurs in nature and in engineering practice is very large and has been extensively considered by many authors. When heat and mass transfer occurs simultaneously between the fluxes the driving potentials are more intricate in nature. An energy flux is generated not only by temperature gradients but by composition gradients as well. Temperature gradients can also create mass fluxes and this is the Soret or Thermal-diffusion effect. Generally, the thermal-diffusion and diffusion-thermo effects of smaller order magnitude than the effects prescribed by Fourier’s or Fick’s laws and are often neglected in heat and mass transfer processes. Due to the importance of thermal-diffusion and diffusionthermo effects for the fluids with very light molecular weight as well as medium molecular weight many investtigators have studied and reported results for these flows and the contributors such as Eckert and Drake [

In this paper, it is proposed to study diffusion-thermo and radiation effects on MHD free convection flow past an impulsively started infinite vertical plate with variable temperature through porous medium in the presence of transverse applied magnetic field. The dimensionless governing equations are solved using Laplace transform technique. And the solutions are expressed in terms of exponential and complementary error functions.

Diffusion-thermo and radiation effects on unsteady MHD free convection of flow of a viscous incompressible, electrically, conducting, radiating fluid past an impulsively started infinite vertical plate with variable temperature and uniform mass diffusion in the presence of transverse applied magnetic field through porous medium have been studied. The -axis is taken along the plate in vertical upward direction and -axis is taken normal to it in the direction of applied transverse magnetic field. Initially, it is assumed that the plate and surrounding fluid are at the same temperature and concentration in stationary condition for all the points in entire flow region. At time, the plate is given an impulsive motion with constant velocity. At the same time, the plate temperature is raised linearly with time t and the concentration levels near the plate are raised to. A magnetic field of uniform strength is assumed to be applied normal to the flow. For free convection flow, it is also assumed that1) The induced magnetic field is assumed to be negligible as the magnetic Reynolds number of the flow is taken to be very small.

2) The viscous dissipation is neglected in the energy equation.

3) The effects of variation in density with temperature and species concentration are considered only on the body force term, in accordance with usual Boussinesq approximation.

4) The fluid considered here is gray, absorbing/emitting radiation but a non-scattering medium.

5) Since the flow of the fluid is assumed to be in the direction of axis, so the physical quantities are functions of the space co-ordinate and only.

Then by usual Boussinesq’s approximation, the flow is governed by the following equations.

with the following initial and boundary conditions

where The local radiant for the case of an optically thin gray gas is expressed by

It is assumed that the temperature differences within the flow are sufficiently small and that may be expressed as a linear function of the temperature. This is obtained by expanding in a Taylor series about and neglecting the higher order terms, thus we get

From Equations (5) and (6), Equation (2) reduces to

On introducing the following non-dimensional quantities

We get the following governing equations which are dimensionless

The initial and boundary conditions in dimensionless form are as follows:

The appeared physical parameters are defined in the nomenclature. The dimensionless governing equations from (9) to (11), subject to the boundary conditions (12) are solved by usual Laplace transform technique and the solutions are expressed in terms of exponential and complementary error functions.

,

From temperature field, now we study Nusselt number (rate of change of heat transfer) which is given in nondimensional form as

From Equations (14) and (16), we get Nusselt number as follows:

From concentration field, now we study Sherwood number (rate of change of mass transfer) which is given in non-dimensional form as

From Equations (13) and (17), we get Sherwood number as follows:

In order to get a clear insight of the physical problem the velocity, temperature, concentration, the rate of heat transfer and the rate of mass transfer have been discussed by assigning numerical values to the parameters like radiation parameter (R), magnetic parameter (M), Schmidt parameter (Sc), Prandtl number (Pr), Dufour number (Du), thermal Grashof number (Gr), mass Grashof number (Gm) and time t from Figures 1-13 for the cases of cooling (Gr > 0, Gm >0) and heating (Gr < 0, Gm < 0) of plate. The heating and cooling takes place by setting up free convection currents due to temperature and concentration gradient.

The influence of various flow parameters on the fluid temperature are illustrated in Figures 8-10.

effects of Prandtl number Pr on the temperature field. It is observed that an increase in the Prandtl number leads to decrease in the fluid temperature. It is due to the fact that thermal conductivity of the fluid decreases with increasing Pr, resulting a decrease in thermal boundary layer thickness.

The concentration profiles for different values of Schmidt number (Sc) and time t are presented in

Absorption coefficient

External magnetic field

Species concentration

Concentration of the plate

Concentration of the fluid far away from the plate

Dimensionless concentration

Specific heat at constant pressure

Concentration susceptibility

Acceleration due to gravity

Thermal Grashof number

Mass Grashof number

Magnetic field parameter

Nusselt number

Prandtl number

Radiative heat flux in the y-direction

Coefficient of mass diffusivity

Radiative parameter

Schmidt number

Temperature of the fluid near the plate

Temperature of the plate

Temperature of the fluid far away from the plate

Time

Dimensionless time

Velocity of the fluid in the -direction

Velocity of the plate

Dimensionless velocity

Co-ordinate axis normal to the plate

Dimensionless co-ordinate axis normal to the plate

Thermal conductivity of the fluid

Thermal diffusivity

Volumetric coefficient of thermal expansion

Volumetric coefficient of expansion with concentration

μ Coefficient of viscosity

ν Kinematic viscosity

r Density of the fluid

ρ Electric conductivity

σ Dimensionless temperature

erf Error function

erfc Complementary error function

Conditions on the wall

Free stream conditions