Reconstructing the Heat Transfer Coefficient in the Inverse Fractional Stefan Problem

Abstract

This paper presents an algorithm for solving the inverse fractional Stefan problem. The considered inverse problem consists of determining the heat transfer coefficient at one of the boundaries of the considered region. The additional information necessary for solving the inverse problem is the set of temperature values in selected points of the region. The fractional derivative with respect to time used in the considered Stefan problem is of the Caputo type. The direct problem was solved by using the alternating phase truncation method adapted to the model with the fractional derivative. To solve the inverse problem, the ant colony algorithm was used. This paper contains an example illustrating the accuracy and stability of the presented algorithm.

Keywords

• fractional Stefan problem
• inverse problem
• heat conduction
• alternating phase truncation method
• ant colony algorithm