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An numerical study has been conducted for the phase-changed Stefan problem in the freezing process of shaft support in earth with liquid nitrogen or liquid carbon dioxide vaporizing means. The method of equivalent specific heat was adopted during the discretization of the non-linear equation of conduction. With the developed code the performances of single cooling tube and multiple cooling tubes have been investigated. In addition, an optimized result to the arranging pattern of the cooling tubes for an actual project is presented.
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