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基于构形理论,以(火积)耗散率最小为优化目标,在微、纳米尺度下对树状圆盘导热问题进行构形优化,得到整体导热性能最优的树状圆盘最优构形.结果表明:在微、纳米尺度下,尺寸效应影响下的树状圆盘构造体最优构形与无尺寸效应影响时的树状圆盘构造体最优构形有明显区别.存在高导热材料最佳单元体占比使得树状圆盘无量纲平均传热温差取得最小值.对于3种结构形式(nn、nb和bb)的树状圆盘,其无量纲临界半径分别为1.16、1.45和1.75.当树状圆盘半径大于临界半径时,圆盘高导热材料需采用树状布置,反之则采用辐射状布置.基于(火积)耗散率最小的树状圆盘导热构形优化能够降低圆盘构造体的平均传热温差,提高其整体传热性能.
Based on the theory of configuration, the optimization of the heat dissipation of the dendritic disk is taken as the optimization objective, and the optimization of the thermal conductivity of the dendritic disk under the micro and nano-scale is optimized. The optimal structure of the dendritic disk with the best overall thermal conductivity The results show that under the micro and nanoscale, the optimal configuration of the dendritic disc structure under the influence of size effect is obviously different from the optimal configuration of the dendritic disc structure under the effect of no size effect. The optimal unit volume ratio of the thermal conductive material makes the dimensionless mean heat transfer temperature difference of the dendritic disc obtain the minimum value.The dimensionless critical radius of the dendritic disc with three structures (nn, nb and bb) is 1.16, 1.45 and 1.75. When the radius of the dendrites is larger than the critical radius, the dendrites should be arranged in the shape of a tree, while the dendrites should be arranged in a radial manner. Optimization reduces the average heat transfer temperature difference of the disk structure and improves its overall heat transfer performance.