Constructal multi-scale cylinders with natural convection

This paper shows that in a space filled with assemblies of cylinders cooled by natural convection the heat transfer density can be increased progressively by the use of cylinders of several sizes, and the optimal placement of each cylinder in the assembly. 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 one and two cylinder sizes, which correspond to structures with one and two degrees of freedom. The heat transfer rate density increases as the optimized structure becomes more complex. The optimized cylinder diameters are relatively robust, i.e., insensitive to changes in complexity and flow regime (Rayleigh number). The optimized spacings decrease monotonically as the Rayleigh number increases. The structure performance can be improved by endowing the cylinder assemblies with more degrees of freedom.