Thermal Performance and Geometric Optimization of Fractal T-Shaped Highly-Conductive Material for Cooling of a Rectangular Chip

Abstract

To improve the thermal performance of inserted highly-conductive material (HCM) for the cooling of a chip, the present work numerically investigates the effects of various geometric and structural parameters of a fractal T-shaped branched HCM on the maximum temperature of the chip. These parameters include the length ratios of branches at two consecutive branching levels α, the width ratio of branches at two consecutive branching levels β, the maximum branching level m, the length of the branch at the initial level L0, the thickness of the HCM H, and the total volume of the HCM V. The results indicate that the maximum temperature of the chip first drops and then rises with the increase of β, which means the existence of the optimal geometric structure of the branched HCM for the cooling of the chip. In addition, the maximum temperature of the chip decreases with the increase of m and V, decreases with the decrease of H, while first drops and then rises with the increase of α and L0. Further, the present work investigates the effects of the thermal conductivity ratio of HCM and chip γ on the optimal width ratio βm of the branched HCM with a different length ratio α, maximum branching level m, length of the branch at the initial level L0, thickness H, total volume V, and thermal conductivity of the rectangular chip Kc. It was found that βm increases with the increase of γ and V, and decreases with the increase of α, L0, and H. The present finding is beneficial to the improvement of the thermal performance of the inserted HCM via geometric optimization.