Geometric optimization for the maximum heat transfer density rate from cylinders rotating in natural convection

Abstract

In this study we investigates the thermal behavior of an assembly of consecutive cylinders in a 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 an optimization algorithm was used to find the optimal structure for flow configurations with two or more degrees of freedom. The geometric structure of the consecutive cylinders was optimized for each flow regime (Rayleigh number) and cylinder rotation speed for one and 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 the optimized spacing decreases and the heat transfer density rate increases as the Rayleigh number increases, for the optimized structure. It was also found that the optimized spacing decreases and the maximum heat transfer density rate increases, as the cylinder rotation speed was increased for the single scale configuration at each Rayleigh number. Results further showed that there was an increase in the heat transfer density rate of the rotating cylinders over stationary cylinders for a single scale configuration. For a multi scale 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 serve to suppress the heat transfer density rate. It was, however, found that the optimized spacing decreases as the cylinder rotation speed was increased at each Rayleigh number. Results further showed that the maximum heat transfer density rate for a multi scale configuration (with stationary cylinders) was higher than a single scale configuration (with rotating cylinders) with an exception at very low Rayleigh numbers.