Numerical analysis for phase change problems with the mushy zone

A hybrid numerical method is developed to solve one-dimensional phase change problems with the mushy zone. This hybrid numerical method involves the control volume formulation for the space domain and the Laplace transform technique for the time domain. In the present study, nonlinear terms are linearized by using the Taylor series approximation. The growth of the mushy zone is unknown a priori and is predicted by using the least squares concept. To show the efficiency of the present numerical method, various comparative examples are illustrated. It can be seen that excellent agreement is observed between present numerical results and those of early works.