Dendritic constructal heat exchanger with small-scale crossflows and larger-scales counterflows

This paper describes the constructal route to the conceptual design of a two-stream heat exchanger with maximal heat transfer rate per unit volume. The flow structure has multiple scales. The smallest (elemental) scale consists of parallel-plates channels the length of which matches the thermal entrance length of the small stream that flows through the channel. This feature has two advantages: it eliminates the longitudinal temperature increase (flow thermal resistance) that would occur in fully developed laminar flow, and it doubles the heat transfer coefficient associated with fully developed laminar flow. The elemental channels of hot fluid are placed in crossflow with elemental channels of cold fluid. The elemental channel pairs are assembled into sequentially larger flow structures (first construct, second construct, etc.), which have the purpose of installing (spreading) the elemental heat transfer as uniformly as possible throughout the heat exchanger volume. At length scales greater than the elemental, the streams of hot and cold fluid are arranged in counterflow. Each stream bathes the heat exchanger volume as two trees joined canopy to canopy. One tree spreads the stream throughout the volume (like a river delta), while the other tree collects the same stream (like a river basin). It is shown that the spacings of the elemental and first-construct channels can be optimized such that the overall pumping power required by the construct is minimal. The paper concludes with a discussion of the advantages of the proposed tree-like (vascularized) heat exchanger structure over the use of parallel small-scale channels with fully developed laminar flow.