Stage-dependent performance and design criteria of functionally graded TPMS–PCM composites: Joint effects of gradient function and steepness

Enhancing heat transfer in phase change energy storage using functionally graded Triply Periodic Minimal Surface skeletons is a key technology. However, existing research has largely focused on linear gradients, lacking a combined evaluation of the gradient function and steepness (characterized by the minimum bottom porosity, ε min ). This study employs a numerical model to systematically compare the effects of different combinations of gradient functions (uniform, linear, quadratic, and exponential) and ε min on heat transfer performance under an identical average porosity of 0.75. The results reveal that the graded strategy exhibits significant stage-wise advantages and a “performance reversal” phenomenon. Relative to the uniform structure with natural convection, an exponential gradient with a low ε min (e.g., 0.55) shortens the initial melting time by 17.5%, whereas a quadratic gradient with a medium ε min (e.g., 0.6) achieves a 6.5% reduction in total melting time. Mechanistic analysis reveals that this reversal stems from the dynamic migration of the heat transfer bottleneck: the limiting factor shifts from “near-wall heat injection” during the initial stage to “remote solid-phase melting” in the later stage. Furthermore, a lower ε min leads to a faster melting rate but also results in a larger system temperature difference. Finally, the study formulates application-oriented selection criteria based on gradient function and ε min : for rapid response, a combination of exponential/linear gradients with a low ε min is preferred; to achieve the shortest total melting time, a quadratic gradient with a medium ε min should be selected; and for maximizing temperature uniformity, the uniform structure is the optimal choice.