Thermodynamic Optimization of Flow Architecture: Dendritic Structures and Optimal Sizes of Components

This paper reports two new advances on constructal design, or the generation of flow architecture in the pursuit of global thermodynamic performance subject to constraints. This is thermodynamic optimization with an emphasis on its product: flow geometry, as a mechanism for the achievement of performance under constraints. The first part of the paper relies on this principle in the design of dendritic (tree-shaped) networks that distribute a stream optimally from one source to a disc-shaped area for which the source is the center. One global objective is (i) the minimization of source-area flow resistance, which, when the overall flow rate is fixed, is the same as the minimization of the destruction of exergy. The alternative (ii) is to design the flow architecture such that the flow path followed by each stream is the shortest. Optimal dendritic flow architectures are reported based on both methods. It is shown that the performance of designs (ii) is nearly the same as that of the optimal designs (i). Examples of dendritic patterns of high-conductivity blades used for cooling a disc-shaped body show that the overall thermal resistance of the construct decreases as the size and complexity of the flow architecture increase. The same principle of maximizing global performance can be used to select the optimal sizes of flow components in all complex energy flow systems (e.g., vehicles, animals). The size of a heat transfer surface and the diameter of a tube with fluid are given as examples.