Abstract: Based on constructal theory，the “volume-point” heat conduction constructal optimization with triangular element at micro and nanoscales is carried out by taking minimum dimensionless maximum thermal resistance as optimization objective and releasing the constraint that the new-order assembly should be assembled by the optimized last-order assembly.The optimal construct of the “volume-point” heat conduction model under the effect of size effect is obtained.The results show that the optimal constructs with size effect and without size effect are obviously different.The heat transfer performance of the new-order assembly obtained by last-order assembly optimization constructal design method is not always the optimal one；compared with the global optimization constructal design method with the last-order assembly optimization constructal design method，the temperature limitation of the triangular assembly can be effectively reduced by using the global optimization constructal design method，and its heat transfer performance can be obviously improved.

Key words: constructal theory, triangular element, micro and nanoscales, global optimization constructal design, generalized thermodynamic optimization

摘要： 基于构形理论，以量纲1最大热阻最小为优化目标，通过释放“下一级构形体由上一级最优构形体组成”的约束，在微、纳米尺度下对基于三角形单元体的“体点”导热问题进行构形优化，得到尺寸效应影响下的量纲1最大热阻最小的“体点”导热问题最优构形。结果表明：存在尺寸效应影响时的构造体最优构形与无尺寸效应影响时的构造体最优构形有明显区别。通过上一级最优构形设计方法得到的下一级构造体导热性能并不是最优的；整体最优构形设计方法与上一级最优构形设计方法相比，三角形构造体的极限温度得到有效降低，其导热性能得到明显提高。

关键词: 构形理论, 三角形单元体, 微、纳米尺度, 整体最优构形设计, 广义热力学优化