Abstract
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”.
Highlights
Published: 8 February 2022The general structure of a disc-shaped heat exchanger (DSHE) element is shown inOne of the first problems designers must solve is the identification of the—rarely unique—set of lengths Lj and diameters dj of the channels
This is the well-known dilemma of the heat exchanger designer: smaller tubes lead to higher pumping work but a higher heat transfer coefficient
This is the well-known dilemma of the heat exchanger designer: smaller tubes lead design procedure leads to an under-specified problem, to higher pumping work but a higher heat transfer coefficient
Summary
The channels may have different cross-sections, hydraulic diameters and lengths. For the sake of simplicity, in this paper the internal channels are assumed to have a circular section and to perform the function of cooling the disc material. One of the first problems designers must solve is the identification of the—rarely unique—set of lengths Lj and diameters dj of the channels. Another design issue is how to determine whether a larger number of branchings (i.e., a “more dendritic” structure) leads to a performance improvement, and how to quantify the correlation between the number of branches and the DSHE performance.
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