Theoretical understanding of phase change heat transfer problems is of much interest for multiple engineering applications. Exact solutions for phase change heat transfer problems are often not available, and approximate analytical methods are needed to be used. This paper presents a solution for a one-dimensional (1D) 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 toward design of phase change based thermal management for a variety of engineering applications, such as cooling of Li-ion batteries.
Solution of the Phase Change Stefan Problem With Time-Dependent Heat Flux Using Perturbation Method
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Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received April 20, 2018; final manuscript received October 22, 2018; published online December 13, 2018. Assoc. Editor: George S. Dulikravich.
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Parhizi, M., and Jain, A. (December 13, 2018). "Solution of the Phase Change Stefan Problem With Time-Dependent Heat Flux Using Perturbation Method." ASME. J. Heat Transfer. February 2019; 141(2): 024503. https://doi.org/10.1115/1.4041956
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