Proposing an optimal tree-like design of highly conductive material configuration with unequal branches for maximum cooling a heat generating piece

Abstract

Due to the concerns regarding the space and cost of high thermal conductivity materials, researching for a better design of high thermal conductivity pathways embedded into a heat generating piece is important. Constructal design theory is applied and a numerical optimization procedure is carried out to find a new geometric pattern of tree-like highly conductive material pathways with unequal branches. The optimization purpose is the minimization of the peak temperature in the heat generating piece, by varying the lengths of the branches and the initial distance from the middle plane. The constraint is the fixed volume fraction occupied by the high thermal conductivity insert. Heat conduction equations are solved by a finite element method (FEM). The numerical code develops in MATLAB software and use unstructured triangular elements for meshing. Because of the multiple optimization variables existed in this work, the “Pattern Search” algorithm is used. The results indicate that the performance of the tree-like configuration with unequal branches is better than the one with equal branches for the same number of branches, the same volume fraction of the highly conductive material and the same conductive ratio. It is also shown that the new proposed configurations of highly thermal conductive pathways, significantly surpass the latest configurations presented in the literature. Depending on the volume fraction of highly conductive material and thermal conductivity ratio, the performance of the proposed configurations is observed to be 2–61% better than the performance of the best result existed in previous works.