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Variational iteration method to solve moving boundary problem with temperature dependent physical properties

Singh Jitendra (DST‐CIMS Department of Applied Mathematics, Institute of Technology, Banaras Hindu University Varanasi, India)
Gupta Kumar Praveen (Department of Applied Mathematics, Institute of Technology, Banaras Hindu University Varanasi, India)
Rai Nath Kabindra (Department of Applied Mathematics, Institute of Technology, Banaras Hindu University Varanasi, India)

In this paper, variational iteration method is used to solve a moving boundary problem arising during melting or freezing of a semi infinite egion when physical properties (thermal conductivity and specific heat) of the two regions are temperature dependent. The Result is compared with result obtained by exact method (when thermal conductivity and specific heat in two regions are temperature independent) and semi analytical method (When thermal conductivity and specific heat are temperature dependent) and are in good agreement. We obtain the solution in the form of continuous functions. The method performs extremely well in terms of efficiency and simplicity and effective for solving the moving boundary problem.

Keywords: Moving boundary problem, phase change process, temperature distribution, thermal conductivity and specific heat, freezing, Stefan number, Variational iteration method