Thermoeconomic design and analysis of constant cross-sectional area fins

A closed-form model for the second-law-based thermoeconomic optimization of constant cross-sectional area fins, is discussed with an example problem. In this approach, different monetary values are attached to the irreversible losses caused by the finite temperature difference heat transfer (T₀Ṡ_ΔT) and pressure drop (T₀Ṡ_ΔP) in the fin application. In addition, a simplified closed-form solution is presented for the case when the capital cost of the fin is negligible and only operational costs are considered. To illustrate the usefulness of the present analytical approach, the simplified cost optimized results are compared with the numerical results obtained from Poulikakos and Bejan's analysis, who have assumed same monetary values for T₀Ṡ_ΔT and T₀Ṡ_ΔP. Furthermore, the influence of important fin thermal, physical, geometrical and cost parameters on the optimum Reynolds numbers Re_Dopt and Re_Lopt are presented in algebraic forms, and also graphical results are shown for the case of pin and plate fin, as examples.