Constructal multi-scale structures for maximal heat transfer density

Abstract

This paper reviews recent constructal-theory advances: the optimal distribution of discrete heat sources cooled by laminar natural convection. Three scenarios are investigated: (i) many small heat sources mounted on a vertical wall, (i) a few small finite-size heat sources mounted on the side wall of a two-dimensional enclosure, and (iii) one heated area on the wall of a vertical diverging or converging channel with chimney flow. In (i) and (ii), the optimally distributed heat sources are not equidistant. In (iii), the geometry changes by varying the space between the walls, the distribution of heating along the walls, and the angle between the two walls. Numerical simulations in the Rayleigh number range 10 5≤Ra H≤10 7 show that for maximal heat transfer rate density it is better to install heated sections at the channel entrance. The optimal angle between the two walls is approximately zero when Ra H is large. The robustness of flow architectures with optimized distribution of heat sources is discussed.