Abstract:
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 a ¼ b, the exact similarity solution to the problem is established, and its existence
and uniqueness are also deliberated. For all a and b, 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.
2018 The Authors. Production and hosting by Elsevier B.V. on behalf of King Saud University. This is an
open access article under the CC BY-NC-ND license
