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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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