Application of homotopy analysis method for fin efficiency of convective straight fins with temperature-dependent thermal conductivity

In this paper, the homotopy analysis method (HAM) has been used to evaluate the efficiency of straight fins with temperature-dependent thermal conductivity and to determine the temperature distribution within the fin. The fin efficieny of the straight fins with temperature-dependent thermal conductivity has been obtained as a function of thermo-geometric fin parameter. It has been observed that the thermal conductivity parameter has a strong influence over the fin efficiency. The series solution is developed and the reccurance relations is given. Comparison of the results with those of the homotopy perturbation method (HPM) and the Adomian decomposition method (ADM), has led us to significant consequences. The analytic solution of the problem is obtained by using the HAM. The HAM contains the auxiliary parameter ℏℏ, which provides us with a simple way to adjust and control the convergence region of solution series. By suitable choice of the auxiliary parameter ℏℏ, we can obtain reasonable solution for large values of ττ and ηη.