Analytical thermal study on nonlinear fundamental heat transfer cases using a novel computational technique

In this paper a novel computational technique called Parameterized Perturbation Method (PPM) is used to obtain the solutions of nonlinear fundamental heat conduction equations. Three well known problems in the area of heat transfer are addressed to be solved. An analytical investigation is carried out for: (a) the temperature distribution in a fin with a temperature-dependent thermal conductivity, (b) the cooling of the lumped system with variable specific heat, and (c) the temperature distribution of a convective-radiative fin. The validity of the results of PPM solution was verified via comparison with numerical results obtained using a fourth order Runge-Kutta method. These comparisons revealed that PPM is a powerful approach for solving these problems. Also, the results showed that the main attributions of this method are very straightforward calculations and low computational burden compared to previous analytical and numerical approaches.