CONSTRUCTAL TREE NETWORKS FOR HEAT-TRANSFER

This paper addresses the fundamental problem of how to connect a heat generating volume to a point heat sink by using a finite amount of hig h-conductivity material that can be distributed through the volume. Th e problem is one of optimizing the access (or minimizing the thermal r esistance) between a finite-size volume and one point. The solution is constructed by covering the volume with a sequence of building blocks , which proceeds toward larger sizes (assemblies), hence, the ''constr uctal'' name for this approach. Optimized numerically at each stage ar e geometric features such as the overall shape of the building block, its number of constituents, and the internal distribution of high-cond uctivity inserts. It is shown that in the optimal design, the high-con ductivity material has a distribution with the shape of a tree. Every aspect of the tree architecture is deterministic: the shapes of the la rgest assembly and all its constituents, the number of branches at eac h level of assembly, the relative position of building blocks in each assembly, and the relative thicknesses of successive branches. The fin er, innermost details of the tree architecture (e.g., the branching an gle) have a negligible effect on the overall thermal resistance. The m ain conclusion is that the structure, working mechanism, and minimal r esistance of the tree network can be obtained deterministically, and t hat the constrained optimization of access routes accounts for the mac roscopic structure in nature. (C) 1997 American Institute of Physics.