Designed porous media: maximal heat transfer density at decreasing length scales

This paper addresses the fundamental problem of maximizing the heat transfer rate density in a fixed volume in the limit of decreasing length scales. In this limit boundary layers disappear, optimized channels are no longer slender, and existing results for optimal spacings break down. Three configurations are optimized analytically based on the intersection of asymptotes method: volumes filled with parallel-plates channels, volumes filled with uniformly distributed spheres, and volumes filled with parallel plates and porous structure in each parallel-plates channel. The small-spacings asymptote is for slow Poiseuille and, respectively, Darcy flow. The large-spacings asymptote is based on heat transfer that approaches pure conduction around bodies immersed in a stationary medium. The geometric results are the optimal flow channel size, the optimal porosity of the assembly, and the maximized heat transfer rate density. The latter increases sharply as dimensions become smaller. This trend, and the method of optimizing flow architecture to achieve maximal heat transfer density, are essential in the continuing miniaturization of heat transfer devices.