HEAT BALANCE INTEGRAL METHOD FOR A TIME-FRACTIONAL STEFAN PROBLEM WITH ROBIN BOUNDARY CONDITION AND TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY

Abstract

Here, we consider a time-fractional Stefan problem in one dimension corresponding to the melting process in a semi-infinite domain with a Robin boundary condition at the first fixed boundary and variable thermal conductivity. The classical approach of the heat balance integral method with quadratic and exponential temperature profiles is applied to the problem to find an approximate solution. To test the validation of the proposed approach, we compare our solution with the analytical solutions for standard (integer-order derivative) and fractional order cases when thermal conductivity is a constant. In this study, the effects of variable thermal conductivity and Biot number (Bi) on the temperature distribution and moving interface are also analyzed for the fractional-order system. © 2021 by Begell House, Inc. www.begellhouse.com.