Investigation of transient heat transfer in multi-scale PCM composites using a semi-analytical model

Abstract

Abstract This paper presents a semi-analytical model to describe the transient heat transfer in phase change material (PCM)-based composites. One such example is micro-encapsulated paraffin in gypsum plaster walls for building applications. Without the availability of an analytical solution for the problem at hand, and given the computational intensity of full-scale numerical solution of the problem, there is a need for alternate approaches that can be used in the design of PCM walls. The key assumption underlying the proposed model is that the spherical paraffin particles are small enough relative to the thickness of the wall, and therefore at each time instant each particle is surrounded by a spatially uniform, albeit time-dependent matrix temperature. This evolving matrix temperature is used as a boundary condition in order to solve for the analytical temperature distribution at the particle-scale, from which the heat flow into the particle can be determined. This procedure avoids spatial discretization of the micro-scale and results in a macro-scale model in which the paraffin particles appear as sinks/sources at each nodal point. The heat equation is then solved using the Method of Lines, which reduces a parabolic partial differential equation into a set of ordinary differential equations. The proposed model is used to simulate the constant flux wall conditions often seen in thermal characterization experiments of PCM walls and structures. Simulation results elucidate the impact of the particle radius and interfacial resistance on the transition at the end of the thermal management phase. Simulations of cyclic environmental temperatures more relevant to building applications show that PCM volume loadings as low as 5% can reduce the energy demands of an HVAC system by 15 to 20%. Moreover, the model is also shown to provide excellent agreement with the work of Savija and Schlangen, who simulated the transient thermal response of hardening concrete using the commercial finite element package FEMMASSE.