ABSTRACT

Inspired by the natural bifurcating structures, tree-like microchannels have been applied for microelectronics cooling. In order to understand the thermal-hydraulic performance of a flat-plat tree-like microchannel, successive branching ratios of tree-like structure are optimized based on minimization of flow resistance. It is shown that the optimal successive diameter ratio of symmetrical and dichotomous structures under volume constraint follows Murray’s law, while the optimal successive length ratio under the constraint of fixed channel area follows the power law 2^−2/3. A mathematical model of convection in disc-shaped heat sink composed of a tree-like microchannel with self-affine rough surface is developed by the fractal geometry and finite element method. The flat-plate tree-like micro-channel with optimal successive diameter and length ratio shows enhanced thermal-hydraulic performance. The Nusselt number of the flat-plat tree-like micro-channel increases with the inlet Reynolds number and the self-affine fractal dimension of the rough wall. The present optimization method and mathematical model for the flat-plate tree-like microchannel shed light on the design of flat-plate micro-channel heat sinks and flow channel in fuel cell among other potential cooling applications.

摘要

受天然分叉结构的启发，树状微通道已应用于微电子冷却。为了了解平板树状微通道的热工水力性能，树状结构的连续分支比在流阻最小化的基础上进行了优化。结果表明，对称结构和二分结构在体积约束下的最佳连续直径比遵循默里定律，而固定通道面积约束下的最佳连续长度比服从幂律2 ^−2/3. 通过分形几何和有限元方法建立了由具有自仿射粗糙表面的树状微通道组成的盘形散热器中的对流数学模型。具有最佳连续直径和长度比的平板树状微通道显示出增强的热工水力性能。平板树状微通道的努塞尔数随着入口雷诺数和粗糙壁的自仿射分形维数的增加而增加。目前的平板树状微通道优化方法和数学模型为燃料电池中平板微通道散热器和流道的设计以及其他潜在的冷却应用提供了思路。