Abstract
A one-dimensional semi-analytical model is developed for the finite domain of air- phase change material (PCM) systems to analyze the formation of void during the solidification shrinkage. A pure material, paraffin and a salt mixture of sodium nitrate and potassium nitrate are considered as PCMs. Heat diffusion equations of three phases, namely air, solid and liquid are solved using prescribed boundary and interface conditions, while shrinkage is calculated by conserving the mass of PCM. The solute redistribution in the salt mixture is modeled by using Scheil law. The developed analytical solutions are extended to evaluate the effect of the presence of shrinkage void on the fraction of energy extracted from the air-PCM systems. Further, a simplified heat diffusion model based on the volume averaging technique is used to compare the one-dimensional analytical model and is found both in good agreement. A new relation is proposed for thermal conductivity of solid and liquid phases of NaNO3-KNO3 as a function of solute concentration with and without porosity, which can be used to assess heat transfer characteristics of PCMs during thermal cycling. The simplified analytical approach can be used to design and select the PCMs and their combinations for a given engineering application.
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