Abstract:A finite element method based on enthalpy formulation of convection-diffusion is developed for numerical solution of liquid-solid phase change problems. It avoids many difficulties which will appear when temperature formulation be used. The basic feature of the proposed method lies in its naturality and the simplicity. The test problems of freezing in a thermal cavity (planar and axisymmetrial problems) under natural convection are used to demonstrate the reliability and the efficiency of this method.