Homotopy perturbation method for temperature distribution, fin efficiency and fin effectiveness of convective straight fins with temperature-dependent thermal conductivity

Homotopy perturbation method is a novel approach that provides an approximate analytical solution to differential equations in the form of an infinite power series. In our previous work, homotopy perturbation method has been used to evaluate thermal performance of straight fins with constant thermal conductivity. A dimensionless analytical expression has been developed for fin effectiveness. In this study, homotopy perturbation method has been applied to convective straight fins considering thermal conductivity of the fin material is a function of the fin temperature. Former expression for fin effectiveness has been rearranged. The fin efficiency and the fin effectiveness have been obtained as a function of thermo-geometric fin parameter. The results have revealed that homotopy perturbation method is a very effective and practical approach for a rapid assessment of physical systems even if the energy balance equations include terms with strong nonlinearities. The resulting correlation equations can assist thermal design engineers for designing of straight fins with both constant and temperature-dependent thermal conductivity.