A note on the wall singularity of a solid-liquid interface caused by a difference between the thermal conductivities of the solid and the liquid phases

H.K. Kuiken

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Abstract

In crystal-growth systems of the Bridgman-Stockbarger type, the solid-liquid interface touches a conducting wall which is the inner wall of the crucible. When the thermal conductivities of the solid and the liquid phases are different, which they usually are, the gradient of the axial thermal profile changes abruptly at the s - 1 interface. Since the thermal profile in the adjacent crucible cannot experience such a jump, the s - 1 interface must accommodate for this difference in thermal behavior at the wall. Using a fairly simple model example, we show that the s - 1 interface becomes singular there. The singularity is a weak logarithmic one.
Original languageEnglish
Pages (from-to)921-924
Number of pages4
JournalSIAM Journal on Applied Mathematics
Volume48
Issue number4
DOIs
Publication statusPublished - 1988

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