The Lie group method is applied to present an analysis of the magneto hydro-dynamics (MHD) steady laminar flow
and the heat transfer from a warm laminar liquid flow to a melting moving surface in the presence of thermal radiation.
By using the Lie group method, we have presented the transformation groups for the problem with a part from the scaling
group. The application of this method reduces the partial differential equations (PDEs) with their boundary conditions
governing the flow and heat transfer to a system of nonlinear ordinary differential equations (ODEs) with appropriate
boundary conditions. The resulting nonlinear system of ODEs is solved numerically using an implicit finite difference
method (FDM). The local skin-friction coefficients and the local Nusselt numbers for different physical parameters are
presented in a table.