A double decomposition method for solving the periodic base temperature in convective longitudinal fins

In this paper, the double decomposition method is used not only in analyzing the oscillating base temperature processes occurring in a convective rectangular fin with variable thermal conductivity, but also in determining the temperature distribution within the fin. It is a useful and practical method, which can be used to solve the nonlinear transient energy equations which are associated with variable thermal conductivity. The periodic condition assumes the oscillating base temperature around a mean value; the obtained double decomposition analytic solution is in the form of an infinite power series. Thus, results including the fin tip temperature, the fin base oscillating temperature, and the fin’s temperature distribution can all be calculated directly without the need of iteration. Results also indicate that the series has high accuracy by comparing with those generated by the complex combination method.