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Technical Brief

Solution of the phase change Stefan problem with time-dependent heat flux using perturbation method

[+] Author and Article Information
Mohammad Parhizi

Mechanical and Aerospace Engineering Department, University of Texas at Arlington, Arlington, TX, USA
mohammad.parhizi@mavs.uta.edu

Ankur Jain

Mechanical and Aerospace Engineering Department, University of Texas at Arlington, Arlington, TX, USA
jaina@uta.edu

1Corresponding author.

ASME doi:10.1115/1.4041956 History: Received April 20, 2018; Revised October 22, 2018

Abstract

Theoretical understanding of phase change heat transfer problems is of much interest for multiple engineering applications. Exact solutions for most phase change heat transfer problems are not available, and approximate analytical methods are needed to be used. This paper presents a solution for one-dimensional phase change problem with time-dependent heat flux boundary condition using the perturbation method. Two different expressions for propagation of the phase change front are derived. For the special case of constant heat flux, the present solution is shown to offer key advantages over past papers. Specifically, the present solution results in greater accuracy and does not diverge at large times unlike past results. The theoretical result is used for understanding the nature of phase change propagation for linear and periodic heat flux boundary conditions. In addition to improving the theoretical understanding of phase change heat transfer problems, these results may contribute towards design of phase change based thermal management for a variety of engineering applications, such as cooling of Li-ion batteries.

Copyright (c) 2018 by ASME
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