Convective trees of fluid channels for volumetric cooling

Abstract This paper describes the geometric optimization of the internal structure of a volume that generates heat at every point and is cooled by a single stream. According to the constructal method, the optimization of the cooling design is organized in a sequence of steps that begins with the smallest volume element and continues with larger assemblies (constructs) of previously optimized building blocks. Optimized at each level of assembly are the external shape of the construct and the relative thickness of each duct for fluid flow. It is shown that in the end the fluid channels form a tree network that cools every point of the given volume. Length scales smaller than the thickness of the elemental volume are reached by conduction through the solid heat-generating material. Two fluid channel geometries are optimized: parallel-plate channels and round tubes.