An approximate solution to the Neumann problem has been obtained by using the heat balance integral method. The accuracy of the solution is shown to be very good for all practical soil system cases. The thermal properties of soil systems are also expressed in terms of only the liquid volumetric fraction and combine with the approximate solution to give a rapid, accurate solution for freeze / thaw problems without using graphs, tables, or transcendental equations. A simple relation is also given for the analogous problem in cylindrical coordinates, but its range of validity is somewhat limited.

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