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基于构形理论,以(火积)耗散率最小为优化目标,对环形高导热通道的三维圆柱形单元体和微、纳米尺度下矩形、三角形单元体“体-点”导热问题进行构形优化,得到无量纲当量热阻最小的“体-点”导热问题最优构形.结果表明:无量纲当量热阻最小和无量纲最大热阻最小目标下三维圆柱形构造体最优构形是不同的,这与对应的二维矩形构造体两种目标下最优构形比较结论不同.在微、纳米尺度下,存在尺寸效应影响时与无尺寸效应影响时的基于矩形和三角形单元体的构造体最优构形有明显区别;由于第二级构造体高导热材料通道中的热流不再服从线性分布,(火积)耗散率最小的和最大温差最小的第二级构造体最优构形是不同的.基于(火积)耗散率定义的当量热阻反映了构造体的平均散热性能,在三维条件和微、纳米尺度下研究(火积)耗散率最小的“体-点”导热构形问题进一步拓展了(火积)耗散极值原理的应用范围.
Based on the theory of configuration and the minimization of the (fire product) dissipation ratio, the three-dimensional cylindrical cell with circular highly conductive channels and the thermal conductivity of rectangular and triangular cells at the micro-and nano-scale are studied. The optimum configuration of the “body-point” thermal conductivity with the smallest dimensionless equivalent thermal resistance is obtained. The results show that the best three-dimensional cylindrical structure with the smallest dimensionless equivalent thermal resistance and the smallest dimension with the largest dimensionless thermal resistance The optimal configuration is different from that of the corresponding two-dimensional rectangular configuration, which is different from the optimal configuration under two kinds of targets.At the micro and nano-scale, Because of the linear distribution of the heat flow in the channel of the high thermal conductivity material of the second-stage structure, the second-stage structure with the smallest (fire product) dissipation rate and the smallest maximum temperature difference has obvious difference. The optimal configuration of the body is different. The equivalent thermal resistance, as defined by the (Eff) dissipation rate, reflects the average heat dissipation of the structure. The three-dimensional conditions and micro- and nano- “Body - point ” thermal structure asked Further expand the (fire product) dissipation of the scope of application of the maximum principle.