微、纳米尺度下基于构形理论的树状圆盘整体导热性能优化

Global Heat Conduction Performance Optimization for Branched-Pattern Disc Based on Constructal Theory at Micro and Nanoscales

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 constructal theory, the constructal optimization of a branched-pattern disc at micro and nanoscales is carried out by taking minimum entransy dissipation rate as optimization objective, and the optimal construct of the branched-pattern disc with optimal global heat conduction performance is obtained. The result shows that the optimal construct of the branched-pattern disc when the size effect takes effect is obviously different from that when the size effect does not take effect. There exists an optimal elemental fraction of the high conductivity material which leads to the minimum dimensionless average temperature difference of the branched-pattern disc. For the structure forms nn, nb and bb of the branched-pattern disc, the critical dimensionless radiuses are 1.16, 1.45 and 1.75, respectively. When the radius of the branched-pattern disc is large than the critical radius, branched-pattern design of the high conductivity material in the disc should be adopted, otherwise the radial-pattern design should be adopted. The optimal construct based on minimum entransy dissipation rate can reduce the average heat transfer temperature difference of the disc, and improves its global heat transfer performance.