Constructal multi-scale cylinders in cross-flow

This paper reports a new concept for maximizing heat transfer density in assemblies of cylinders in cross-flow: the use of cylinders of several sizes, and the optimal placement of each cylinder in the assembly. The heat transfer is by laminar forced convection with specified overall pressure difference. The resulting flow structure has multiple scales that are distributed nonuniformly through the available volume. Smaller cylinders are placed closer to the entrance to the assembly, in the wedge-shaped flow regions occupied by fluid that has not yet been used for heat transfer. The paper reports the optimized flow architectures and performance for structures with 1, 2 and 3 cylinder sizes, which correspond to structures with 1, 2 and 4 degrees of freedom. The heat transfer rate density increases (with diminishing returns) as the optimized structure becomes more complex. The optimized cylinder diameters are relatively robust, i.e., insensitive to changes in complexity and flow regime (pressure difference). The optimized spacings decrease monotonically as the driving pressure difference increases. The multi-scale flow architectures optimized in this paper have features and qualities similar to tree-shaped (dendritic) designs, where the length scales are numerous, hierarchically organized, and nonuniformly distributed through the available space.