Thermal field and heat storage in a cyclic phase change process caused by several moving melting and solidification interfaces in the layer

Abstract

This work determines the effective thermal fields in a non-sinusoidal periodic regime, which form in a layer of phase change material (PCM) within which multiple solidification and melting bi-phase interfaces are present.The physical model used describes heat conduction in the solid phase and the liquid phase and the phase change at the melting temperature with the equation of thermal balance at the bi-phase interface. The resolution of the physical model, obtained by means of the finite difference numerical model, leads to equations for calculation of the temperature in the nodes in the solid phase and in the liquid phase, and the liquid fraction in the nodes in phase change at the melting temperature. The numerical model and the resolution algorithm were obtained by extending those proposed by Halford et al. (2009). In addition, the numerical model and the resolution algorithm proposed in this paper foresee: (i) the presence of one or more bi-phase interfaces in the layer; (ii) a non-uniform spatial discretization of the sub-volumes of the layer in order to obtain a more accurate representation of heat flux discontinuity in the sub-volumes involved in the phase change; (iii) the variability in space and time of the thermal resistances and the areal heat capacities as a function of the position of the bi-phase interfaces; (iv) the use of temperature and of the liquid fraction values in a node at two previous time instants to determine the thermodynamic state at the successive time instant; (v) different thermo-physical properties in the solid phase and in the liquid phase. The numerical model is validated by means of a comparison with an exact analytical solution, which resolves the Stefan problem in a finite layer in a steady periodic regime.The calculation procedure is employed for the study of the thermal behaviour of PCM layers, with different melting temperatures and thermo-physical properties, with boundary conditions typical of those operating on the external walls of air-conditioned buildings. This procedure allows for the determination, at different time instants of the period P = 24 h, of the position of the bi-phase interfaces present in the layer, the field of temperature and heat flux and the instantaneous energy released and stored by each interface. The numerical results reveal interesting phenomena that, for such boundary conditions and in such detail, have never been reported previously in the literature.