ISSN: 2250-3005 - ijcer

International Journal Of Computational Engineering Research (ijceronline.com) Vol. 2 Issue. 8In the present work, thermal radiation effects on heat transfer of second grade fluid over a stretching sheet throughporous medium with temperature dependent viscosity and thermal conductivity is investigated. The governing equations aretransformed by using similarity transformation and the resultant dimensionless equations are solved numerically using theRunge-Kutta fourth order method with shooting technique. The effects of various governing parameters on the velocity,temperature, skin-friction coefficient and Nusselt number are shown in figures and tables and analyzed in detail. Numericalresults are presented for velocity and temperature profiles for different parameters of the problem.2. Mathematical FormulationWe consider the two-dimensional laminar boundary layer flow of viscous, incompressible, electrically conductingand radiating second grade fluid with temperature dependent viscosity and thermal conductivity past a semi -infinitestretching sheet coinciding with the plane y 0 embedded in a uniform porous medium. A uniform magnetic field ofstrength B is applied in the direction perpendicular to the plate. The transverse applied magnetic field and magnetic0Reynolds number are assumed to be very small, so that the induced magnetic field is negligible. Keeping the origin fixed,two equal and opposite forces are applied along the x - axis, so that the sheet is stretched with a velocity proportional to thedistance from the fixed origin. Under the above assumptions, the basic boundary layer equations governing the flow and heattransfer of second grade fluid due to the stretching sheet are given by the following equations:The equation of continuity:uv 0x y(1)Momentum conservation:3 3 2 2 u u u u u u v u u 2 u v k0u v B2 3 2 0u u x y y y xy y y xy x y K(2)Thermal energy conservation: T T T u qru u uCpu v k k0 u v x y y y r y y y y x yAlong with the boundary conditions,u Uw cx,v 0,T Tw2 at y 0u 0, v 0, T T as y (3)(4)Where u and v are the flow velocity components along x- and y - directions respectively, B is the applied magnetic0field, and k are the constant viscosity and constant thermal conductivity of the free stream of the fluidrespectively. T is the temperature of the flu id. and k are the coefficient of variable viscosity and variable thermalconductivity respectively of the fluid which are considered to vary as a function of temperature.Cp is the specific heat atconstant pressure and k0 is the coefficient of visco-elastricity. is the electrical conductivity. c is the constant stretchingrate. T and are the free stream temperature and density. K is the permeability of the porous medium.radiation heat flux.Flowing Lai and Kulacki [17] We assumeqr is theIssn 2250-3005(online) December| 2012 Page 60