Exact solutions to problems of conductive heat transfer with solidification are rare due to the nonlinearity of the equations. The heat balance integral technique is used to obtain an approximate solution to the freezing of a semi-infinite region with a linear, initial temperature distribution. The results indicate that the constant temperature Neumann solution is acceptable for soil systems with a geothermal gradient unless extremely long freezing times are considered. The heat balance integral will yield good solutions, with simple numerical work, even for non-constant initial temperatures.

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