Lie group analysis of effects of radiation and chemical reaction on heat and mass transfer by unsteady slip flow from a non-isothermal stretching sheet immersed in a porous medium

Lie group method is investigated for solving problem of heat and mass transfer in an unsteady, laminar, boundary-layer flow of a viscous and incompressible fluid along a horizontal stretching surface embedded in porous medium in the presence of thermal radiation, chemical reaction and slip effects. The infinitesimal generators accepted by the equations are calculated and the extension of the Lie algebra for the problem is also presented. The restrictions imposed by the boundary conditions on the generators are calculated. The investigation of the three-independent-variable partial differential equations is converted into a two-independent-variable system by using one subgroup of the general group. The resulting equations are solved numerically by an efficient implicit, iterative, finite-difference method. Numerical results for the steady-state velocity, temperature and concentration profiles as well as the time histories of the skin-friction coefficient, Nusselt number and the Sherwood number are presented graphically and discussed.