A new look in heat balance integral method to a two-dimensional Stefan problem with convection

In the current work, we developed a new approximation function for temperature profile with the help of Legendre wavelet in heat-balance integral method (HBIM) to solve a two-dimensional moving boundary problem with moving phase change material (PCM). It is assumed that PCM moves with induced velocity u along x and y direction. In heat transfer mechanism conduction and convection driven by fluid flow in liquid region is considered. To validate the current approximate method, we compared our numerical results with a previous work and found in strong acceptance. In particular, to show the accuracy of the present approximate method, we compared our numerical results against exact solution by converting present problem into a one-dimensional standard melting problem and found in good acceptance. The effect of Peclet number on temperature profile and moving melting front are analyzed in detail. Furthermore, it is shown that with a moving phase change material (PCM) the liquid/solid interface get accelerated and hence, the melting process becomes fast. This study may be applicable in thermal management and energy storage system.