Nonlinear MHD boundary layer flow of a liquid metal with heat transfer over a porous stretching surface with nonlinear radiation effects

Nonlinear hydromagnetic two dimensional steady, laminar, boundary layer flow of a viscous, incompressible, electrically conducting and radiating liquid metal, with nonlinear radiation past a porous plate stretching with power-law velocity is analysed in the presence of a variable magnetic field. The liquid metal is assumed to be a gray, emitting, absorbing but non-scattering medium. Governing nonlinear partial differential equations are transformed to nonlinear ordinary differential equations by utilizing suitable similarity transformation. The resulting nonlinear ordinary differential equations are solved numerically using Fourth-Order Runge-Kutta shooting method along with the Nachtsheim-Swigert iteration for satisfaction of asymptotic boundary conditions. The numerical results for velocity and temperature distribution are obtained for different values of porosity parameter, velocity exponent parameter, magnetic interaction parameter, surface temperature parameter, radiation parameter and Prandtl number and are shown graphically. Numerically values of skin friction coefficient and nondimensional rate of heat transfer are also derived.