Longitudinal rectangular fins with asymmetrical boundary conditions and different temperatures at each base were been studied and optimized using relative inverse thermal admittance as performance coefficient. A Neutral Line was defined and determined for different temperature ratios at the bases. Using the network method for the numerical simulation, the optimization problem was solved in a classical way: starting with the fin volume, heat transfer coefficient and thermal conductivity, the optimal geometry or aspect ratio (length/thickness ratio) for dissipating maximum heat from the fin surface was determined. The results are illustrated through tables and universal graphics made with optimal points, which, are independent from the temperature ratio at the bases. Besides the optimal thickness the graphics also provide, the fin effectiveness and the transversal Biot number. Finally, the location of the Neutral Line is represented for the optimal geometry and temperature ratios. To illustrate the optimization process practical examples are shown.

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