Periodic heat transfer in fins with variable thermal parameters

Abstract

Periodic heat transfer in a convecting fin with temperature dependent thermal conductivity and coordinate dependent heat transfer coefficient, is analyzed using a perturbation analysis. The zero-order problem, which corresponds to steady-state fin behaviour, is solved by quasilinearization. A method of complex combination is used, in conjunction with a noniterative numerical scheme, to solve the first-order and the second-order problems. The nonlinear nature of the problem gives rise to a nonoscillatory component in the second-order term, which causes a net change in the mean values of temperature and heat transfer rate. The direction of change depends on the thermal conductivity parameter [alpha]. For [alpha] [mu] 0, the mean temperature is increased, while the mean heat transfer rate is decreased. For [alpha] < 0, the effect is opposite. Detailed results showing the effects of various parameters on temperature distribution, heat transfer rate and time-averaging fin efficiency are presented and discussed.