MHD effects on heat transfer over stretching sheet embedded in porous medium with variable viscosity, viscous dissipation and heat source/sink

In this analysis, MHD boundary layer flow and heat transfer of a fluid with variable viscosity through a porous medium towards a stretching sheet by taking in to the effects of viscous dissipation in presence of heat source/sink is considered. The symmetry groups admitted by the corresponding boundary value problem are obtained by using Lie’s scaling group of transformations. These transformations are used to convert the partial differential equations of the governing equations into self-similar non-linear ordinary differential equations. Numerical solutions of these equations are obtained by Runge-Kutta fourth order with shooting method. Numerical results obtained for different parameters such as viscosity variation parameter A, permeability parameter k1, heat source/sink parameter λλ, magnetic field parameter M, Prandtl number Pr, and Eckert number Ec   are drawn graphically and effects of different flow parameters on velocity and temperature profiles are discussed. The skin-friction coefficient -f″(0)-f″(0) and heat transfer coefficient −θ′(0) are presented in tables.