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.