Soil freezing problem: an exact solution

We have studied soil freezing (thawing) processes which exhibit a definite zone of phasechange. By assuming that conduction is the only heat-transfer mechanism in the system, we approach phase-change problems, with thermophysical properties temperature dependent, via an enthalpic formulation. Mathematical formulation leads to a nonlinear boundary-value problem; we obtained an analytic solution to the problem for different geometric shapes by applying a group theory method. Finally, we can use the analytical solution to describe the thermal regime and the position of the free boundary in soil phase-change problems.