There are physical relations between the velocities of the isotherms for two heat conduction problems having the same initial and boundary conditions, but one of them has phase change while the other one has not. The main idea of this study is to find these relations mathematically, which stand on a physical base, depending on the physical properties of the phases and the common parameters of these two different problems. If such kind of relations are known, then it will be possible to find the position of solid-liquid interface by using the analytical solutions and the relation itself, not solving the phase change problem. This idea is applied to heat conduction problem in semi infinite media and one dimensional phase change problem is solved for three different kind of boundary conditions via the Enthalpy Method. The results are correlated with the analytical solutions of the problem having same geometry and conditions but without phase change and obtained some relations having correlation coefficients changing between 0.91 and 0.98. This result shows that the regression analysis made is statistically meaningful.