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The concept of relative inverse thermal admittance applied to the convective fin-wall assembly optimization of longitudinal rectangular fins under 2-D heat conduction is presented in this work. Since heat transfer at the fin tip is taken into account, it is not always possible to optimize the above cited geometry. This is relevant in optimization processes and because of this has been displayed in several graphs. Here, different values for convective conditions at the fin and wall surfaces are used and the influence of the hw/hf ratio in optimum geometry is determined. The fin effectiveness is used as the fundamental parameter to prove that the fin is fulfilling the objective of increasing heat dissipation. Once the optimum thickness has been obtained, the Biot number is easily calculated and the fin effectiveness for an isolated fin and the fin-wall assembly can be determined graphically. The optimization process is carried out through a set of universal graphs in which the range of parameters covers most of the practical cases a designer will find. The concept of relative inverse thermal admittance is applied in a general form and emerges as an easy used tool for optimizing fin-wall assemblies.
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