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 apart 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 the implicit finite difference method(FDM).The local skin-friction coefficients and the local Nusselt numbers for different physical parameters are presented in a table. 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 apart 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 the implicit finite difference method (FDM). The local skin-friction coefficients and the local Nusselt numbers for different physical parameters are presented in a table.