Lie similarity analysis of MHD flow past a stretching surface embedded in porous medium along with imposed heat source/sink and variable viscosity

The present examination is centered around the transfer of heat for the flow of a boundary layer free convective incompressible fluid, past a stretching porous surface, assuming viscosity dependent on temperature linearly along with heat source and sink with imposed magnetic field. Lie group similarity transformation is used to obtain the symmetric graphs of the given problem. Solutions for velocity and heat profile are encountered numerically with fourth-order Runga-Kutta shooting technique and graphically presented and explained the impact on velocity profile and temperature profile of several physical parameters as temperature-dependent parameter of viscosity A, k1 as parameter of permeability, Prandtl number, λas parameter of heat generation and absorption and M as parameter of magnetic field. We observed that the thermal boundary layer thickness can be reduced by increasing viscosity parameter A and heat sink parameterλ. As we give increment in k1 we find a decrement in the horizontal velocity profile, which leads to the enhanced deceleration of the flow and, hence, the velocity decreases.