Analytical model for solidification and melting in a finite PCM in steady periodic regime

Abstract

An analytical solution of the phase change problem, known as the Stefan or Moving Boundary Problem, in a PCM layer (phase change materials) subject to boundary conditions that are variable in time, is presented, in steady periodic regime. The two-phase Stefan Problem is resolved considering periodic boundary conditions of temperature or of heat flux, or even mixed conditions.This phenomenon is present in air-conditioned buildings, the walls of which use PCM layers to reduce thermal loads and energy requirements to be compensated by the plant.The resolution method used is one in which phasors allow the transformation of partial differential equations, describing conduction in the solid and liquid phase, into ordinary differential equations; furthermore the phasors allow transformation of the thermal balance equation at the bi-phase interface into algebraic equations. The Moving Boundary Problem is then reduced to a system of algebraic equations, the solution of which provides the position in time of the bi-phase interface and the thermal field of the layer. The solution obtained provides for different thermodynamic configurations that the layer can assume and makes the position of the bi-phase interface and the thermal field depend on the Fourier number and on the Stefan number calculated in the solid phase and in the liquid phase.In the case of two boundary conditions represented by a single sinusoidal oscillation, a general analysis, addressed in different thermodynamic configurations obtained by varying the Fourier and Stefan number, shows the calculation procedure of the steady and of the oscillating component of the position of the bi-phase interface, of the temperature field and of the heat flux field.In addition, we considered the particular case of a PCM layer with an oscillating temperature boundary condition on one face and a constant temperature on the other face.The analytical procedure was also used for an analysis dedicated to the thermal behaviour of Glauber’s salt subject to independent multi harmonic boundary conditions. This salt hydrate is one of the most studied, having a high latent fusion heat and a melting temperature that is suited for use in the walls of buildings.