Heat transfer analysis of a fin with temperature-dependent thermal conductivity and heat transfer coefficient

In this paper Least Square Method (LSM), Collocation Method (CM) and new approach which called Akbari-Ganji’s Method (AGM) are applied to solve the nonlinear heat transfer equation of fin with power-law temperature-dependent both thermal conductivity and heat transfer coefficient. The major concern is to achieve an accurate answer which has efficient approximation in accordance to Ruge-Kutta numerical method. Results are presented for the dimensionless temperature distribution and fin efficiency for different values of the problem parameters which for the purpose of comparison, obtained equation were calculated with mentioned methods. It was found the proposed solution is very accurate, efficient, and convenient for the discussed problem, furthermore convergence problems for solving nonlinear equations by using AGM appear small so the results demonstrate that the AGM could be applied through other methods in nonlinear problems with high nonlinearity.