Constructal multi-scale structure for maximal heat transfer density in natural convection

In this paper we investigate a new design concept for generating multi-scale structures in natural convection with the objective of maximizing the heat transfer density, or the heat transfer rate per unit of volume. The flow volume is filled with vertical equidistant heated blades of decreasing lengths. The spacings between the blades are optimized for maximal heat transfer density. Smaller blades are installed in the center plane between two adjacent longer blades, in the entrance region where the boundary layers are thin and the fluid is unheated. Based on the same principle, new generations of even smaller blades are added stepwise to the multi-scale structure. Constructal theory is applied to each new generation of blades, and this method leads to the optimal spacings between blades and the optimal lengths scales. As the number of length scales increase, the flow rate and the volume-averaged heat transfer density increase. It is also shown that there is a smallest (cutoff) length scale below which the boundary layers are no longer distinct, and where the sequence of generating optimal length scales ends. The maximized heat transfer density increases as the optimized complexity of the flow structure increases.