An inverse analysis of two-phase Stefan problems using imaginary heat sources

TLDR: In this article, a new methodology for the inverse analysis of time-dependent two-phase Stefan problems is presented, where imaginary heat sources are arranged in an imaginary domain and the phase-change interface is identified as the isothermal surface at the melting temperature by controlling the imaginary heat source intensities.

Abstract: This paper presents a new methodology for the inverse analysis of time-dependent two-phase Stefan problems. The problem considered here is that of determining the time dependence of a phase-change interface at several observed temperatures. In our method, imaginary heat sources are arranged in an imaginary domain and then the phase-change interface is identified as the isothermal surface at the melting temperature by controlling the imaginary heat source intensities. Using delta-function imaginary heat sources and their corresponding Green functions, which are pre-calculated numerically, it is shown that the phase-change interface is determined non-iteratively at each time step. We offer numerical examples to demonstrate the capability of the proposed method. © 1998 Scripta Technica, Heat Trans Jpn Res, 27(3): 179–191, 1998