THERMAL RADIATION EFFECT ON MHD NATURAL CONVECTION BOUNDARY LAYER FLOW OVER A PLATE WITH SUCTION (INJECTION) AND VARIABLE VISCOSITY RADIATION EFFECT ON MHD NATURAL CONVECTION BOUNDARY LAYER FLOW OVER A PLATE WITH SUCTION (INJECTION) AND VARIABLE VISCOSITY.”

The effect of thermal radiation on steady natural convection boundary layer flow over a plate with variable viscosity and magnetic field has been studied in this paper. The effect of suction and injection is also considered in the investigation. The system of partial differential equations governing the nonsimilar flow has been solved numerically using implicit finite difference scheme along with a quasilinearization technique. The thermal radiation has significant effect on heat transfer coefficient and thermal transport in presence of viscosity variation parameter and magnetic field in case of suction and injection.


Introduction
Convective boundary-layer flows are often controlled by injecting or withdrawing fluid through a porous bounding heated surface. This can lead to enhanced heating or cooling of the system and can help to delay the transition from laminar to turbulent flow. Several researchers studied the effect of suction and injection for different situations on different geometries [1][2][3][4]. To calculate precisely the flow and heat transfer rates, it is necessary to take account of variation of viscosity. Also, the study of the flow of a viscous fluid with temperature dependent properties is of great importance in industries. Eswara and Bommaiah [5], Jayakumar.et.al [6] and Lai and Kulacki [7] considered variable viscosity and investigated its effect in various problems. In recent times, the effect of variable viscosity on free convection flow over a plate with an applied magnetic field and suction (injection) is studied by Jayakumar.et.al. [8]. The idea of the proposed  work is to consider the effect of thermal radiation on MHD free convection boundary layer flow over a plate with variable viscosity and suction (injection).

Analysis
Consider a semi-infinite porous plate at a uniform temperature T w0 which is played vertical in a quiescent fluid of infinite extent maintained at constant temperature T  . The plate is fixed in a vertical position with leading edge horizontal. The physical co-ordinates (x,y) are chosen such that x is measured from the leading edge in the stream wise direction and y is measured normal to the surface of the plate. The co-ordinate system and flow configuration are shown in Fig.1. Further, the fluid added (injection) or removed (suction) is the same as that involved in flow. A magnetic field B 0 is applied in y-direction normal to the body surface and it is assumed that magnetic Reynolds number is small. The Hall current and displacement current effects have been neglected.
The initial and boundary conditions are Here, the radiative heat flux r q under Roseland approximation, has the form Expanding 4 T in a Taylor series about  T and neglecting higher orders yields: Substituting (5) and (6) into (3) gives, Introducing the following transformations (5) and (10), we see that the continuity Eq.(5) is identically satisfied and Eqns. (5) and (10) reduces, respectively, to It is remarked here that the upper sign in Eqns. (9) and (10) is taken throughout for suction and the lower sign for blowing (injection).
The transformed boundary conditions are F = 0; G = 1 at  = 0 F = 0; G = 0 as   for   0 (15) The local skin friction parameter and heat transfer parameter can be expressed as Here, u and v are velocity components in x and y direction; F is dimensionless velocity; T and G are dimensional and dimensionless temperatures, respectively; , are transformed co-ordinates;  and f are the dimension and dimensionless stream functions respectively; Pr is the Prandtl number; ,  are respectively kinetic viscosity and thermal diffusivity; w 0 and  denote conditions at the edge of the boundary layer on the wall and in the free stream respectively and prime   ' denotes derivatives with respect to .
The dimensionless temperature G and viscosity ratio / are redefined as follows: It may be remarked here that, if Ge is large (i.e.,Ge) the effect of variable viscosity can be neglected. On the other hand, for a smaller value of Ge, either the fluid viscosity changes markedly with temperature or operating temperature difference is high. In either case, the variable viscosity effect is expected to become very significant. Also, it may be noted here that, liquid viscosity varies differently with temperature than that of gas and therefore, it is important to note that Ge<0 for liquids and Ge>0 for gases when the temperature difference T is positive.
It is worth mentioning here that when N R = 0.0 Eqns.(12) and (13) reduces to which are exactly same as those of Jayakumr et al. [8].

Results and Discussion
The set of partial differential Eqns. (9) and (10) along with the boundary conditions (12) has been solved numerically employing an implicit finite difference scheme with a quasilinearization technique which is presented great detail in [9].   (Ge = 3.0) is presented for different values of stream wise coordinate () in the Fig.3.It is clearly noted from the graphs that the heat transfer decreases and the thermal boundary layer thickness increases with the increase of thermal radiation parameter. In fact the percentage of decrease of heat transfer parameter is 54.81% and the percentage of increase in G is 21.55% at  = 1.0 from N R = 0.0 to N R = 2.0. It is remarked here that the skin friction parameter ( w ) and velocity field (F) is little affected by the thermal radiation parameter (N R ) as it is present only in the energy equation.

Conclusions
The influence of thermal radiation on steady laminar incompressible MHD free convection boundary layer flow over a plate with viscosity variation parameter along with suction and injection have been obtained. It is found from the results that, the heat transfer decreases whereas the thickness of thermal boundary layer increases with the increase of thermal radiation parameter in case of both suction and injection.