Constructal optimization for “disc-point” heat conduction at micro and nanoscales

Based on constructal theory, the construct of a “disc-point” heat conduction model at micro and nanoscales is optimized by taking maximum temperature difference minimization as optimization objective, and the optimal constructs of the radial-pattern and first order branched-pattern discs under the effect of size effect are obtained. The results show that the size effect has an obvious influence on the optimal construct of the disc. The minimum dimensionless maximum temperature difference of the first order disc for structure form nn is relative to the number of elemental tributaries, but those for structure forms nb and bb are independent of the number of elemental tributaries. There exist the critical dimensionless radiuses, which determine whether the radial-pattern design or branched-pattern design for the high conductivity channels is adopted. The critical dimensionless radiuses of the first order branched-pattern discs for the structure forms nn, nb and bb are 1.25, 1.72 and 2.18, respectively. With the increase in the product of thermal conductivity ratio and the square of elemental high conductivity material fraction, the minimum dimensionless thermal resistance of the first order disc for structure form nn decreases, but that for structure form nb is undetermined. The optimal “disc-point” construct at micro and nanoscales improves the heat transfer performance of the disc.