A numerical solution of a non-classical Stefan problem with space-dependent thermal conductivity, variable latent heat and Robin boundary condition

Abstract

In this article, we have considered a non-classical Stefan problem that involves the space-dependent thermal conductivity, variable latent heat and Robin boundary condition at the fixed boundary. The solution of the problem is obtained by using the operational matrix method based on Genocchi polynomials and the collocation scheme. To show the accuracy, we have compared the results obtained by the Genocchi operational matrix method and a finite difference scheme with the exact solution for a particular case of the considered Stefan problem. It is found that the proposed Genocchi operational matrix method is more accurate than the finite difference scheme. Moreover, it is shown that the proposed algorithm rapidly converges as the degree of Genocchi polynomials increases. We have also analyzed the effects of the parameters α and δ on the temperature distribution and the evolution of moving phase front in the case of the considered non-classical Stefan problem. It is observed that the phase change processes become fast as the parameters α or/and δ increase. © 2022, Akadémiai Kiadó, Budapest, Hungary.