A Multi-Level Graded Thermal Spreader Under an Equal-Mass Constraint

A Numerical Study on Thickness Redistribution Near the Heat Source for Peak-Temperature Reduction and Degradation Resistance

Abstract

This paper presents a numerical concept for a multi-level graded thermal spreader that redistributes thickness under an equal-mass constraint, so that thermally effective mass is concentrated near the heat source and gradually reduced toward the periphery. The final validated dataset consists of six benchmark cases defined by three base thicknesses (1.0, 0.5, and 0.4 mm) and two representative conductivities (k = 400 and k = 235 W/m·K), while the final tuning parameters are fixed at levels = 3, beta = 0.55, shrink = 1.0, t_boost = 8.0, radial_gamma = 1.0, directional_gamma = 0.25, gamma_hot = 0.2, and r0 = 0.01. Positive improvement was obtained in all six cases. The relative benefit increases as the base thickness decreases, and the lower-conductivity material shows a larger relative gain than the copper-like material. A controlled support comparison further shows that a cross-root shape alone provides only a partial improvement, whereas the larger performance gain arises from graded redistribution applied over the same shape. Within the scope of a two-dimensional equal-mass numerical model, the results provide numerical evidence for the concept and indicate potential relevance for thickness-constrained thermal applications.