The conduction problem for cylinders embedded in a medium with variable thermal properties cannot be solved exactly if phase change occurs. New, approximate solutions have been found using the quasi-steady method. These solutions consider heat flow from the entire pipe surface, rather than from a single point, as has been assumed in the past. The temperature field, phase change location, and pipe surface heat transfer can be evaluated using graphs presented for parametric ranges of temperature, thermal properties, burial depth, and insulation thickness. The theoretical results show good agreement with complete numerical solutions. The accuracy of the method increases as the Stefan number decreases and the results are of particular value for insulated hot pipes or refrigerated gas lines.

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