Constructal multi scale cylinders with rotation cooled by natural convection

This paper investigated the thermal behaviour of an assembly of multi scale cylinders in a staggered counter-rotating configuration cooled by natural convection with the objective of maximizing the heat transfer density rate (heat transfer rate per unit volume). A numerical model was used to solve the governing equations that describe the temperature and flow fields and a mathematical optimisation algorithm was used to find the optimal structure for flow configurations with two degrees of freedom. The multi scale structure of the cylinder assembly was optimized for each flow regime (Rayleigh number) and cylinder rotation speed for two degrees of freedom. Smaller cylinders were placed at the entrance to the assembly, in the wedge-shaped flow regions occupied by fluid that had not yet been used for heat transfer, to create additional length scales to the flow configuration. It was found that there was almost no effect of cylinder rotation on the maximum heat transfer density rate, when compared to stationary cylinders, at each Rayleigh number; with the exception of high cylinder rotation speeds, which served to suppress the heat transfer density rate. It was, however, found that the optimized spacing decreased as the cylinder rotation speed was increased at each Rayleigh number. Results further show that the maximum heat transfer density rate for a multi scale configuration (without cylinder rotation) was higher than a single scale configuration (with rotating cylinders) with an exception at very low Rayleigh numbers.