Parametric study and approximation of the exact analytical solution of the Stefan problem in a finite PCM layer in a steady periodic regime

Since an analytical expression in an explicit form of the position of the bi-phase interface in the layer is not available, an approximate analytical solution was obtained, which makes the bi-phase interface position depends on the product between the Fourier number and the Stefan number calculated in the two phases. The limits of validity of such a solution were determined evaluating the relative error, which is committed in the determination of the amplitude and of the argument of the oscillating component of the bi-phase interface position. Finally, the fields of variation of the thermal parameters that ensure a relative error value lower than 3% and the corresponding values of the maximum errors of the amplitude or the argument are determined. In PCM layer thermal analysis it is useful to have an expression in an explicit form of the oscillating component of the bi-phase interface position to obtain the mathematical expression of the temperature and heat flux field as a function of only dimensionless thermal parameters and boundary loadings.