Optimal Internal Structure of Volumes Cooled by Single-Phase Forced and Natural Convection

Abstract

This article is a principle-based review of a growing body of fundamental research that documents the opportunity for optimizing geometrically the cooling of spaces (e.g., electronics packages) that generate heat volumetrically. The chief result of geometric optimization is the identification of an optimal internal structure—optimal spacings between components (e.g., plates and fins), optimal sizes and aspect ratios for cooling channels, and optimal frequencies for pulsating flows. The origin of these optimal geometric features—the construction of the system—lies in the global effort to use every infinitesimal volume to the maximum, i.e., to pack the volume not only with the most heat generating components, but also with the ‘most’ coolant, in such a way that every fluid packet is engaged effectively in cooling. The optimal aspect ratio for ducts with forced and natural convection corresponds to the special geometry and flow conditions where boundary layers meet just as the coolant exits the channel. This “constructal” design principle is illustrated by several classes of examples: laminar forced and natural convection, and various internal arrangements (parallel plates, staggered plates, cylinders in cross flow, square pins with impinging flow). General trends (scaling laws) of optimal geometric form are revealed by the optimal-structure results, this, in spite of the diversity of the optimized configurations.