A novel approximation method for two dimensional phase transfer problem in a moving domain with heat generation parameter

Abstract This study presents a two dimensional mathematical model of heat transfer process, describing the melting process in a moving domain, which deals with the effect of temperature dependent heat generation and absorption. In many physical processes, as materials undergo phase change, they experience heat generation or heat loss as a result of various internal mechanisms including chemical transformations and Joule heating. Therefore, it is necessary to incorporate the effect of internal heat variations for ensuring the accuracy of phase transfer process. This study also addresses the consequences of time dependent boundary temperature. Another major finding of this study includes the development of a hybrid numerical technique based on the operational matrix of Vieta-Fibonacci polynomials with heat balance integral method (HBIM) to determine the solution of the considered two dimensional heat transfer process in a moving domain. Since, the exact solution of this complex problem is not yet possible. Therefore, a comparison between the obtained results and exact solution for a specific one- dimensional case is presented, which reveals that both results are nearly identical. The consequences of heat generation and heat absorption on the temperature profile and melting curve are shown graphically.