A.K. da Silva

MAXIMAL HEAT TRANSFER DENSITY IN VERTICAL MORPHING CHANNELS WITH NATURAL CONVECTION

In this article we show numerically that the entire flow geometry of a vertical diverging or converging channel with laminar natural convection can be optimized for maximal heat transfer rate density (total heat transfer rate per unit of flow system volume). The geometry is free to change in three ways: (1) the spacing between the walls, (2) the distribution of heating along the walls, and (3) the angle between the two walls. Numerical simulations cover the Rayleigh number range 105 ≤ RaH ≤ 107, where H is the channel height. Nonuniform wall heating is modeled as an isothermal patch of varying height H 0 (≤H) on each wall, which is placed either at the bottom (entrance) end of the channel, or at the top (exit) end. The results confirm that the use of upper unheated sections enhances the chimney effect and the heat transfer. The new aspect is that the heat transfer rate density decreases because the unheated sections increase the total volume. It is shown that for maximal heat transfer rate density it is better to place the H 0 sections at the channel entrance. It is also shown that the optimal angle between the two walls is approximately zero when Ra H is large, i.e., for maximal heat transfer rate density the walls should be parallel or nearly parallel. Finally, the optimized spacing (1) developed in the presence of (2) and (3) as additional degrees of freedom is of the same order of magnitude as the optimal spacing reported earlier for parallel isothermal walls, i.e., in the absence of features (2) and (3). The robustness of the optimized flow architecture is discussed. Additional degrees of freedom and global objectives that may be incorporated in this constructal approach are the curvature of the facing walls and the mechanical strength and stiffness of the confining walls.

The Formal Evolutionary Development of Low Entropy Dendritic Thermal Systems

The present work explores the formal evolutionary development of complex thermal physical systems using a bio-inspired evolutionary method. The bio-inspired method consists of Lindenmayer systems (L-systems) with its turtle interpretation for the modeling of the complex dendritic structures, the finite element method for the analysis of the structure and an evolutionary algorithm to evolve the topology of the dendritic structure. With this method, we investigate the optimal topology of a highly conductive dendritic structure for draining excessive thermal energy from a fixed area subject to uniform heat generation. The results show that the evolutionary approach can yield complex, dendritic topologies that are highly performing and robust. Moreover, our results demonstrate that a better performance in heat removal implies an increased complexity of the draining system; and that there is an optimal level of complexity beyond which the performance of the system is not substantially improved. Finally, we discuss the robustness of hierarchical, dendritic complex topologies for heat transfer systems.