Exact solution for cooling of electronics using constructal theory

Abstract

This article deals with the constructal-theory based solution for conductive cooling of electronics. The problem falls in the category of a more general “area to point” flow problem. Heat generated in a fixed area is to be discharged to a heat sink located on the border of the heat generating area through relatively high conductive link(s). This will maintain a limited temperature difference between the hot spot inside the heat generating area and the heat sink. Constructal-theory based solution in this article is supported by and matched with an analytical and exact heat transfer analysis of the physical problem. The solution procedure starts with heat transfer analysis and geometric optimization of the smallest heat generating area. The assembly of optimized smallest areas in a fixed but larger heat generating area by introducing a high conductive link and geometric optimization of the area leads to achieve the goal of conductive cooling of a larger area. Sequence of assembly of optimized areas in a relatively larger area and geometric optimization of this area is continued until the required area size to be cooled is obtained. The process of assembly and optimization steps leads to the formation of a tree-network of high conductive links inside the heat generating area. Along with geometric optimization of a heat generating area in each step, the tree-network of high conductive links is optimized with respect to high conductive material allocation in the heat generating area as well.