The mathematical model of a two-phase Lamé-Clapeyron-Stefan problem for a semi-infinite material with a density jump is considered. The purpose of this paper is to study the analytical solutions of the models and show the performance of several parameters.
To describe the heat conduction, the Caputo type time fractional heat conduction equation is used and a convective term is included since the changes in density give rise to motion of the liquid phase. The similarity variables are used to simplify the models.
The analytical solutions describing the changes of temperature in both liquid and solid phases are obtained. For the solid phase, the solution is given in the Wright function form. While for the liquid phase, since the appearance of the advection term, an approximate solution in series form is given. Based on the solutions, the performance of the parameters is discussed in detail.
From the point of view of mathematics, the moving boundary problems are nonlinear, so barely any analytical solutions for these problems can be obtained. Furthermore, there are many applications in which a material undergoes phase change, such as in melting, freezing, casting and cryosurgery.
The work is supported by the Natural Science Foundation of China (No. 11002049), the Shandong Province Young and Middle-aged Research Awards Fund (No. BS2012SW002) and the Doctor Foundations of University of Jinan (No. XBS1209).
Li, X. (2014), "Analytical solutions to a fractional generalized two phase Lame-Clapeyron-Stefan problem", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 24 No. 6, pp. 1251-1259. https://doi.org/10.1108/HFF-03-2013-0102Download as .RIS
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