Boundary integral formulation and mushy zone model for phase change problem

In the present paper, a simple mushy zone model and the boundary integral technique are applied to solve a phase change moving boundary problem. Owing to the use of the mushy zone model, some mathematical considerations are taken when applying the integral equation at the extreme points of the domain. A numerical algorithm is developed to track the moving boundaries that appear throughout the process. Good accuracy is obtained using the developed algorithm and the results give good agreement with previous solutions.