Group method analysis of melting effect on MHD mixed convection flow from radiate vertical plate embedded in a saturated porous media

The linear transformation group approach is developed to simulate problem of hydromagnetic heat transfer by mixed convection along vertical plate in a liquid saturated porous medium in the presence of melting and thermal radiation effects for opposing external flow. The application of a one-parameter transformation group reduces the number of independent variables by one so that the governing partial differential equations with the boundary conditions reduce to an ordinary differential equations with appropriate corresponding conditions. The Runge-Kutta shooting method is used to solve the determining equations of the set of nonlinear ordinary differential equations. are presented in the form of the temperature and flow fields in the melting region within the boundary layer for different parameters entering into the analysis. Also the effects of the pertinent parameters on the rate of the heat transfer in terms of the local Nusselt number at the solid–liquid interface are also discussed.