Magnetohydrodynamic Free Convection Flow with Thermal Radiation and Chemical Reaction Effects in the Presence of Variable Suction

The aim of the present study is to investigate the effect of flow parameters on the free convection and mass transfer of an unsteady magnetohydrodynamic flow of an electrically conducting, viscous and incompressible fluid past an infinite vertical porous plate in the presence of variable suction. The thermal radiation and chemical reaction effects are assumed to exist within the channel. Non dimensional partial differential equations of governing equations of flow are solved numerically using Crank Nicolson finite difference method. The skin friction, heat and mass transfer rates as well as the effects of various parameters on velocity, temperature and concentration profiles are analyzed. The signifiant results from this study are that an increase in the values of radiation parameter and chemical reaction parameter causes a reduction in the velocity, temperature and concentration.


Introduction
The range of free convective flow that occur in nature and in engineering practice is very large and has been extensively considered by many researchers due to its applications in chemically processed industries such as, drying, evaporation at the surface of a water body and food processing.Convection in porous media has applications in geothermal energy recovery, oil extraction, thermal energy storage and flow through filtering devices.Radiative convective flows are encountered in countless industrial and environment processes such as heating and cooling chambers and astrophysical flows.Acharya et al. [1] analyzed free convection and mass transfer flow through a porous medium bounded by vertical infinite surface with constant suction and heat flux.Chamkha [2] studied unsteady MHD convective heat and mass transfer past a semi-infinite vertical moving plate with heat absorption.Cosiderable research work has been published on the study of radiative convective flows in a variety of geometrical configurations with numerical and mathematical models.Chandrakala and Antony [3] discussed radiation effects on MHD flow past an impulsively started infinite vertical plate with variable temperature.Duwairi and Damesh [4] presented a study on heat transfer from radiative vertical porous surfaces.Unsteady free convection flow past a vertical porous plate was investigated by Helmy [5].Hossain and Takhar [6] reported radiation effect on mixed convection along a vertical plate with uniform surface temperature.
In recent years, progress has been considerably made in the study of heat and mass transfer with chemical reaction due to its applications in many branches of science and engineering.Kandasamy et al. [7] analyzed simultaneously the effects of chemical reaction, heat and mass transfer along a wedge with heat source and concentration in the presence of suction or injection.Kawala and Odda [8] obtained numerical results for the effect of chemical reaction on unsteady natural convection boundary layer flow over a semi-infinite vertical cylinder.Recently, a detailed numerical study was reported by Kishore et al. [9] on the effects of chemical reaction, radiation and magnetic field on the unsteady free convection flow, heat and mass transfer characteristics in a viscous, incompressible and electrically conducting fluid past an exponentially accelerated vertical plate.Mahdy [10] performed an analysis to investigate the effects of chemical reaction and heat generation or absorption on double diffusive convection from vertical truncated cone in a porous media with variable viscosity.Mohammed et al. [11] investigated the effect of similarity solution for MHD flow through vertical porous plate with suction.Patil and Chamkha [12] discussed heat and mass transfer from mixed convection flow of polar fluid along a plate in porous media with chemical reaction.In another article, Rajeshwari et al. [13] presented the effect of chemical reaction on the forced and free convection boundary layer that flows in a semi-infinite expanse of an electrically conducting viscous incompressible fluid past a vertical porous plate.
Rajput and Kumar [14] presented the effect of radiation on MHD flow past an impulsively started vertical plate with variable heat and mass transfer.Raptis and Perdikis [15] described radiation and free convection flow past a moving plate.Saleh et al. [16] examined convective heat and mass transfer characteristics of an incompressible MHD visco-elastic fluid flow immersed Magnetohydrodynamic Free Convection Flow with Thermal Radiation and Chemical Reaction Effects in the Presence of Variable Suction in a porous medium over a stretching sheet with chemical reaction and thermal stratification.Sarada and Shankar [17] presented a study of chemical reaction effect on an unsteady MHD convective flow past an infinite vertical moving plate embedded in a porous medium with heat source.
Sattar [18] took an account on the effect of free and forced convection boundary layer flow through a porous medium with large suction.Soundalgekar and Takher [19] discussed the effect of radiation on the natural convection flow of a gas past a semi-infinite plate using the Coghy-Vincentine-Gilles equilibrium model.Rahman [20] discussed the combined effects of internal heat generation and higher order chemical reaction on the non-Darcian forced convective flow of a viscous incompressible fluid with variable viscosity and thermal conductivity over a stretching surface embedded in a porous medium.
The objective of this paper is to study the effects of thermal radiation and chemical reaction on an unsteady MHD free convection heat and mass transfer flow past an infinite vertical plate in presence of variable suction.In this study, the effects of different flow parameters encountered in the equations are also studied.The problem is solved numerically using the implicit finite difference method of Crank Nicolson type, which is more economical from the computational point of view.

Mathematical analysis
An unsteady MHD free convection heat and mass transfer flow of an electrically conducting, viscous incompressible and radiating fluid over a porous vertical infinite plate with chemical reaction and thermal conductivity is considered.In the Cartesian coordinate, the ' x -axis is assumed to be along the infinite plate in the direction of the flow and the y ' -axis is taken normal to it.A magnetic field 0 B of uniform strength is applied transversely to the direction of the flow as shown in Fig. 1.Initially, the plate and the fluid are at the same temperature T f in a stationary condition with concentration level C f at all points.For t ' > 0 , the temperature and concentration at the plate y ' 0 is raised to T ' w and C ' w respectively and that of It is assumed that the induced magnetic field is negligible in comparison with the applied one which corresponds to a very small magnetic Reynolds number.The flow has significant thermal radiation, chemical reaction and suction effects.

Figure 1 .v
Figure 1.Physical configuration of the problem.

Fig. 2
Fig. 2 and 3 depicts the fluid velocity distribution profiles with variation of porosity parameter ( k ) and magnetic parameter ( M ).On increasing k , it is analyzed that the fluid velocity distribution in this figure increases.It can be seen in Fig. 3 that increasing the magnetic parameter ( M ) causes a fall in the velocity of the fluid.The effect of transverse magnetic field on an electrically conducting fluid slows down the motion of the fluid.Fig. 5, 6, 7 and 8 plot the variation of the fluid velocity, temperature and concentration distributions for various values of suction parameter ( J ) and chemical reaction parameter ( r K ).

Figure 4 .
Figure 4. Variation of velocity with (

Figure 5 .
Figure 5. Variation of temperature with (

Figure 6 .
Figure 6.Variation of concentration with (

Figure 10 .
Figure 10.Variation of temperature with R .

Figure 11 .
Figure 11.Variation of temperature with Pr .

Figure 15 . 4 *E 0 V
Figure 15.Variation of Sherwood number with ( & Pr r K