A three-dimensional shape design problem to determine the filler geometry for optimal system thermal conductivity

摘要

A three-dimensional shape design problem is considered in this work, based on the desired thermal conductivity ratio and filler volume, to determine the optimal shape of filler between two conductive bodies in a three-dimensional composite material. The Levenberg-Marquardt method (LMM), commercial software CFD-ACE + and B-spline surface generation technique are adopted in the present shape design algorithm. The design analysis is examined using the numerical experiments and different filler volume and thermal conductivity are considered in the numerical test cases to justify the validity of this study. The estimated results obtained with optimal filler are then compared with those using original filler shapes and it is found that (i) the optimal filler shapes are found as a family of "hourglass" shape with a smooth nozzle-diffuser shape in the central parts of filler and (ii) the radiuses of the top and bottom surfaces of filler play the most significant role on the effective thermal conductivity. Besides, by fixing the filler thermal conductivity, the effective thermal conductivities using optimal fillers can be increased from 15.3% to 47.6% depending on different filler volumes and by fixing the filler volume, the effective thermal conductivities using optimal fillers can be increased from 5.5% to 57.4% depending on different filler conductivities. (C) 2015 Elsevier Masson SAS. All rights reserved.