Approximate solution for the temperature field of 1-D soil freezing process in a semi-infinite region

Unfrozen liquid water always exists in the humid soil system below freezing point, and the amount of the unfrozen water decreases continuously with the temperature decreasing. This phenomenon is a special characteristic for the freezing of the humid soil system. The temperature field of 1-D soil freezing process in a semi-infinite region has been studied. The problem is a Stefan-like problem. After the continuous phase change process of soil water is divided into a finite number of substeps, the Stefan problem of a multi-phase material is obtained. A similarity solution is found and determined. In order to get the right solution of the nonlinear equations, a variable substitution technique is introduced. The approximate solution is verified by the numerical results of the continuous phase change model of soil freezing process. Finally, for practical purpose, the advancing factor of the freezing front and the mean squared error of the temperature caused by the measurement errors are defined. Computational examples concerning the effect of different parameters on the advancing factor of the freezing front and the effect of the measurement errors on the accuracy of the solution are presented and discussed.