A new algorithm for moving boundary problems subject to periodic boundary conditions

Purpose - The paper aims to introduce a new algorithm based on the boundary integral method developed to solve moving boundary phase change problem subject to all possible cases of cyclic boundary temperature. Design/methodology/approach - In the present paper, the phase change problem with periodic boundary temperature, which may be above or below the phase change temperature, is analyzed. The analysis is based on applying the boundary integral method in a new numerical algorithm. There are two main topics of the analysis herein. The first one is to study the direct effect of the cyclic boundary temperature on the movement of the moving boundary for various Stefan numbers. The second one is check that the proposed method covers all possible cases of cyclic boundary temperature with respect to the phase change temperature. Findings - When using the proposed method, it is found an easy mathematical manipulation and the results can be improved when fine time step size used. Originality/value - The proposed method is a very new method, which can be applied to any case of moving boundary phase change problem subject to any case of cyclic boundary temperature. Also the proposed method takes into consideration different parameters that affect directly on the evolution of the moving boundary such as Stefan number, etc.