Correlation of optimal sizes of bodies with external forced convection heat transfer

This paper shows how to correlate the optimal sizes of bodies with specified external forced convection heat transfer, when the objective is to minimize 1) the total rate of entropy generation, or 2) the total cost. Specific results are reported for the cylinder in cross-flow, the sphere, and the flat plate in parallel flow. The results are presented in terms of dimensionless parameters that show that regardless of the body shape, the optimal size increases monotonically with the heat transfer duty parameter. A universal correlation is obtained by nondimensionalizing the body size as a Reynolds number based on the transversal length scale of the flow. The by replacing the body with an equivalent one in two-dimensional flow. The optimal sizes correlated in this manner can be applied to bodies of other shapes.