New Finite Element Method for Multidimensional Phase Change Heat Transfer Problems

A new method, called the exact specific heat method, is introduced for finite element analysis of transient heat transfer with phase change. The method is ideally suited for metals and alloys that exhibit discontinuous specific heat functions across the phase transition temperature. The method uses an exact representation of the specific heat function and exploits its mathematical properties in obtaining the latent heat matrix. A derivation of the finite element formulation is presented. Numerical results are presented for several two-dimensional test cases and compared with analytical solutions and other finite element and finite difference numerical results. Excellent agreement was found.