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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、纳米尺度下对圆盘导热问题进行构形优化,得到尺寸效应影响下的无量纲当量热阻最小的圆盘构造体最优构形.结果表明:在微、纳米尺度下,尺寸效应影响下的圆盘构造体最优构形与无尺寸效应影响时的圆盘构造体最优构形有明显区别.存在最佳无量纲高导热材料通道长度使无量纲当量热阻取得最小值;随着扇形单元体数目的增大,最小无量纲当量热阻先减小后增大,存在最佳的扇形单元体数目使得无量纲当量热阻取得双重最小值,这与常规尺度下圆盘构造体相应的性能特性明显不同.(火积)耗散率最小的圆盘构造体(火积)耗散率比最大温差最小的构造体(火积)耗散率降低了7.31%,也即圆盘构造体的平均传热温差降低了7.31%.微、纳米尺度下基于(火积)耗散率最小的圆盘构造体最优构形能够降低圆盘构造体的平均传热温差,同时有助于提高其整体传热性能.本文工作有助于进一步拓展(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 rate, the disk thermal optimization problem is optimized at the micro and nano scale, and the disk structure with the smallest equivalent thermal resistance under the size effect is obtained The results show that there is a significant difference between the optimal configurations of disk structures under the influence of size effect and the optimal configurations of disk structures under the effect of size effect at micro and nano scale The dimensionless thermal conductivity of the non-dimensional and high thermal conductivity material minimizes the dimensionless equivalent thermal resistance. As the number of fan-shaped unit increases, the minimum dimensionless equivalent thermal resistance first decreases and then increases. The optimal number of fan-shaped units makes The non-dimensional equivalent thermal resistance achieves a double minimum, which is obviously different from the corresponding performance characteristics of the disc structure under the normal scale. (Fire product) The dissipation factor of the disc structure with the smallest dissipation rate is the smallest (Fire product) dissipation rate decreased by 7.31%, that is, the average heat transfer temperature difference of the disc structure decreased by 7.31% .At the microstructure, the disc structure based on the (Fire Product) The optimal configuration can reduce the average transmission of the disk structure Heat temperature difference, at the same time help to improve its overall heat transfer performance.This work will help further expand the (fire product) the application of the principle of dissipation extreme.