The conundrum of employability of 2D simplifications in phase change numerical problems: A case of finite sized PCM heat sink

This study investigated the conundrum of 2D simplification employability in transient thermal management problems by comparing 2D and 3D numerical simulations of finite-size finned Phase Change Material (PCM) heat sinks. Gallium has been employed as the PCM in the heat sinks owing to its superior thermal response as opposed to conventional paraffinic PCMs. We analyzed two designs; a taller/narrower (Case 2A) and a shorter/wider (Case 1A); both with identical PCM volume, fin material, and heated base dimensions, subjected to a constant 10 W/cm² heat flux. Initial 2D simulations indicated superior heat dissipation for the shorter/wider design. Consistent with this, 3D results corroborated the shorter/wider finned PCM heat sink's superior performance, exhibiting peak base temperatures 10 to 25 K lower than the taller/narrower configuration (Fig. 4a). This advantage is attributed to the strategic PCM allocation in the shorter/wider design, positioning a larger latent heat storage capacity closer to the heat source. Crucially, 3D effects, notably the onset and nature of chaotic mixing, were found to be highly dependent on the applied base boundary conditions. In Case 1A, an unheated base portion created a stabilizing cool region, promoting prolonged near-two-dimensional flow despite emerging 3D effects. Conversely, Case 2A, with its entirely heated base, lacked this stabilization, leading to earlier and more pronounced three-dimensionality and highly chaotic mixing. Quantitatively, these enhanced 3D effects in Case 2A resulted in peak sink base temperatures up to about 10 °C lower than its 2D counterpart (Case 2), alongside faster melting. Despite these significant quantitative deviations, 2D simulations demonstrated qualitative consistency with 3D findings regarding the relative performance ranking of the two designs and the overall PCM melting behavior. These results confirm that while 3D simulations offer a more complete capture of the underlying physics, 2D models remain invaluable for preliminary design purposes, serving as a computationally efficient approach for initial comparative assessments and concept screening before detailed 3D modeling or experimental validation for final design optimization.