Analytical solutions and efficiency of the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient

In this paper, the homotopy analysis method (HAM) is used to evaluate the analytical approximate solutions and efficiency of the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient. The fin efficiency of the nonlinear fin problem with temperature-dependent thermal conductivity is obtained as a function of thermo-geometric fin parameter. It is shown that the thermal conductivity parameter has a strong influence over the fin efficiency. The analytic solution of the problem is obtained by using the HAM. The HAM contains the auxiliary parameter ℏℏ, which adjusts and controls the convergence region of the solution series in a simple way. By choosing the auxiliary parameter ℏℏ in a suitable way, we can obtain reasonable solution for large values of M   and ββ.