## Analytical solutions and efficiency of the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient.(English)Zbl 1221.74083

Summary: 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 $$\hbar$$, which adjusts and controls the convergence region of the solution series in a simple way. By choosing the auxiliary parameter $$\hbar$$ in a suitable way, we can obtain reasonable solution for large values of $$M$$ and $$\beta$$.

### MSC:

 74S30 Other numerical methods in solid mechanics (MSC2010) 74F05 Thermal effects in solid mechanics
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