Constructal multi-scale pin–fins

In this paper we use constructal theory to determine the configuration of two rows of pin–fins so that the total heat transfer rate is maximized. The heat transfer across the fins is by laminar forced convection bathed by a free-stream that is uniform and isothermal. The optimization is subjected to fixed total volume of fin materials. The dimensions of the optimized configuration are the result of balancing conduction along the fins with convection transversal to the fin. The resulting flow structure has multiple scales that are distributed non-uniformly through the flow structure. Numerical results on the effect of Reynolds number and the thermal conductivity ratio on the optimal configuration are reported. The results predicted based on scale analysis are in good agreement with the numerical results. The results also show that the flow structure performs best when the fin diameters and heights are non-uniform.