Numerical simulation of a non-classical moving boundary problem with control function and generalized latent heat as a function of moving interface

Abstract

Abstract In this paper, the work is concerned with the study of moving boundary based on non-classical heat equation that includes a time dependent heat flux and convection. The latent heat is represented as a function of the moving interface. Mathematical model accounts for a control function varying with heat flux. We have obtained the explicit solution of the given mathematical model in the presence of convection and a control function. The Legendre wavelet Galerkin approach (LWGA) is used to solve the mathematical problem. In a particular case, our numerical results were compared with previous results and found to be in excellent agreement. Moreover, the current numerical technique is more efficient and accurate in comparison to the previous available method. An extensive analysis of the problem parameters is presented. It is found that the control function offers a significant contribution during the melting or freezing of a PCM. A greater value of the heat flux accelerates the rate of propagation of interface. Convection heat transfer increases the speed of the interface. Results obtained from the current study are expected to improve the fundamental understanding of heat transfer and aid in sublimation and desorption like physical phenomena.