A Simplified Analytical Solution of a Two-Dimensional Stefan Problem with a Periodic Boundary Condition


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Abstract


A two-dimensional heat conduction problem with phase-change is solved by using a linear perturbation method. Temperature at the outer surface of the mold is approximately uniform, but contains a small sinusoidal perturbation in one space dimension. The problem is solved analytically with the assumption of infinitely large diffusivities of the solidified shell and mold materials. Results are obtained for the solid/melt interface as a function of time and for the temperature distributions in the shell and mold. The inverse problem, in which the solid/melt boundary is prescribed and the mold outer surface temperature is to be determined, is also discussed. The effect of process parameters such as the mold thickness, the thermal contact resistance between the shell and mold, and the thermal conductivity ratios between the shell and mold materials on the growth of the perturbation in the shell thickness and the outer temperature of the mold is  investigated in detail.
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Keywords


Perturbation; Phase-Change; Solidification; Stefan

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