How to Reduce the Design of Disc-Shaped Heat Exchangers to a Zero-Degrees-of-Freedom Task

The continuous quest for improving the performance of heat exchangers, together with ever more stringent volume and weight constraints, especially in enclosed applications like internal combustion engines and electronic devices, has stimulated the search for compact, high-performance units. One of the shapes that has emerged from a vast body of research is the disc-shaped heat exchanger, in which the fluid to be heated/cooled flows through radial—often bifurcated—channels carved inside a metallic disc. The disc in turn exchanges thermal energy with the hot/cold source (the environment or another body). Several studies have been devoted to the identification of an “optimal shape” of the channels: most of them are based on the extremization of some global property of the device, like its monetary or resource cost, its efficiency, the outlet temperature of one of the fluids, the total irreversibility of the process, etc. The present paper demonstrates that-for all engineering purposes there is only one correct design procedure for such a heat exchanger, and that if a few basic rules of engineering common sense are adopted, this procedure depends solely on the technical specifications (type of operation, thermal load, materials, surface quality): the design in fact reduces to a zero-degree of freedom problem. The procedure is described in detail, and it is shown that a proper application of the constraints completely identifies the shape, size and similarity indices of both the disc and the internal channels. The goal of this study is to demonstrate that-in this, as in many similar cases-a straightforward application of prime principles and of diligent engineering rules, may generate “optimal” designs: these principles guarantee a sort of “embedded optimality”.