Phase Change Material-Based Cooling Systems Subject to Periodic Heating: Lumped Analysis and Experimental Verification

Phase change material (PCM) based thermal man-agement systems have seen significant attention in the literature to dampen thermal oscillations in applications with transient heat loads. Developing reliable engineering design rules for these systems has proven difficult due to the complexity of the moving boundary and phase change process. However, it is simpler to analyze PCM-based systems where the internal thermal gradients are significantly smaller than external thermal gradients, i.e., “lumped” systems with low Biot numbers
$(\mathbf{Bi < 0.1)}$
, as is the case in many electronic cooling applications. As more PCMs are developed with higher thermal conductivities, a specific set of “lumped” PCM design guidelines would become very valuable. In this work, we present an experimental setup to study the behaviour of such a system under periodic heat loads. A relatively thin layer of a metallic PCM is placed between a heater on one face and a heat sink on the other to represent a lumped PCM system. Thermocouples are embedded in both the heat source and sink to study the temperature and temperature gradients in the PCM. Field's metal (32.5-Bi, 51-In, 16.5-Sn), a eutectic alloy is chosen as the working PCM due to its high thermal conductivity (19.2 W/m-K). The external thermal resistance is varied (2.4-4.2 K/W) to study systems of Biot numbers from 0.07 to 0.13 and determine the limits of the lumped system approximation. A series of simple expressions are derived to predict the melting behaviour and establish the theoretically ideal operating point of lumped PCM cooling systems, and these expressions are validated with our experimental measurements.