Theoretical modeling and optimization of fin-based enhancement of heat transfer into a phase change material

Abstract

Phase change heat transfer is used commonly for enhanced thermal management and energy storage in several engineering applications. The rate of heat transfer from a heat source into a phase change material (PCM) is limited by thermal properties and geometry, due to which, the use of metal fins protruding into the PCM has been investigated. This paper derives and solves the governing energy conservation equations to determine the transient temperature distribution in the PCM due to the presence of a Cartesian fin. A perturbation method based solution for the Stefan problem with time-dependent temperature boundary condition is used to derive an equation for the fin temperature distribution. Results show that for a given total time available for heat transfer into the fin, the presence of a fin results in two competing effects – enhanced heat transfer into the PCM through the fin and reduced heat transfer into the PCM due to lower area of direct contact between PCM and heat source. This results in a non-monotonic dependence of total heat flow into the PCM on the fin size, and shows that a fin larger than a certain optimal size may actually impede overall heat flow into the PCM. For a given total time, the optimal fin size is shown to be a function of the fin thermal conductivity. The impact of thermal properties of PCM and fin on the rate of heat transfer is also examined. The theoretical work in this paper extends the well-known governing equation for a fin in a single-phase medium to a fin in a phase change material, which is a much more complicated, transient problem. In addition to extending the theoretical understanding of extended surfaces and phase change, this work also provides practical guidelines for the optimized design of phase change based energy storage and thermal management systems.