Exact and approximate solutions of a phase change problem with moving phase change material and variable thermal coefficients

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This article explores a phase change problem in a one-dimensional infinite domain x≥0 including the time-dependent speed of a phase change material. In this problem, the Dirichlet type of boundary condition is considered, and the thermal conductivity and specific heat are assumed as linear functions of temperature. In case of α=β, the exact similarity solution to the problem is established, and its existence and uniqueness are also deliberated. For all α and β, we also present an approximate approach based on spectral shifted Legendre collocation method to solve the problem. The approximate results thus obtained are likened with our exact solution for different parameters and it is shown through tables. From this study, it can be seen that the approximate results are adequately accurate. The impact of different parameters appearing in the considered model on temperature profile and tracking of moving phase-front is also studied.