The SIMPLE algorithm is used to solve the MHD equations and the solutions of MHD equations are presented for the whole free-burning arc, excluding the electrodes. The SIMPLE algorithm has been revised in order to solve MHD equations and the flow chart is showed. A self-consistent numerical solution of the MHD equations yields the temperature and velocity distributions. And different types of radiation term are examined on the numerical results and it is found that the radiation term redults in a small decrease on the temperature of the arc.