Tree flows through hierarchical slits and orifices

This is a fundamental theoretical and numerical study of the evolution of tree-shaped flow on one side of the heat transfer surface of a ‘dendritic’ heat exchanger. The flow is shaped by step changes in the dimensions of the available openings. The architecture evolves toward providing easier access to the stream. Two extremes of this flow architecture are treated theoretically, orifices in parallel and equidistant partitions, and slender two-dimensional channels (slits) in sequential blocks of channels. The orifice and channel sizes change stepwise in the downstream direction. Theoretically, the recommended step down ratio for orifice diameters is 0.707, and for the slit size is 0.595. The theoretical step down ratio for the lengths of parallel channels is 0.648. Numerical simulations conducted in a wide parametric domain illustrate the evolution of the flow configuration toward greater access. Remarkable is that the numerical results for the step down ratio in slit sizes covers the very narrow range 0.72–0.75. This study contributes fundamentals that can serve as reliable reference in future designs of dendritic heat exchangers spearheaded by constructal theory.