Influence of geometric similarity in shell-and-tube heat exchangers on thermal performance of nanoparticles-fins combination in melting and solidification improvement of phase change materials

This study systematically examines the effects of shell-and-tube geometry on PCM melting and solidification rates across four configurations: similar (circular shell-circular tube, square shell-square tube) and dissimilar (circular shell-square tube, square shell-circular tube) cross-sections. To isolate the impacts of geometry, baseline cases without enhancement techniques are analyzed first. Subsequently, Al₂O₃ nanoparticles and longitudinal internal-external fins (both at 1% and 2% volume fractions) are systematically evaluated individually across various shell-tube configurations. Finally, the combined effects of the PCM/HTF container geometry, fins, and nanoparticles are assessed, enabling comprehensive quantification of individual and interactive enhancement mechanisms on phase change performance. The results demonstrate that fins alone provide superior enhancement compared to nanoparticles alone or their combination during both melting and solidification across all proposed shell-and-tube systems. Fin efficiency is highly sensitive to heat exchanger geometry in both processes. Conversely, nanoparticles exhibit no geometry dependence during melting and only minimal dependence during solidification. Across all shell-and-tube configurations, fins achieve 28.7–47.9% reduction in melting time and 20.1–47.3% reduction in solidification time. Nanoparticles yield approximately 15.1% improvement in melting rate and 2.7–7.8% in solidification rate. Overall, both enhancement methods prove more effective during the melting process in all cases. The results demonstrate that without nanoparticles or fins, the square shell-square tube configuration achieves superior melting (20.2% faster) and solidification (19.5% faster) performance compared to the circular-circular baseline, leveraging inherent geometric advantages like corner-enhanced natural convection and greater contact area. For industrial applications where enhancement techniques are unnecessary, this architecture is recommended as it delivers free baseline performance gains through simple modification alone, circumventing challenges associated with fins. However, when substantial passive enhancements become inevitable, deploying longitudinal internal-external fins in the circular shell-circular tube configuration provides optimal thermal storage performance in a complete phase-change cycle.