Transient natural convective conjugate cooling mechanism in vertical fins

Abstract

An analysis is presented of the time-periodic conjugate free convective heat transfer from a long vertical, thermally thin fin heated from above to the surrounding fluid. The temperature at the top of the fin oscillates with a given frequency about a mean value that, is higher than the temperature of the ambient fluid. The solution for very long fins depends on four nondimensional parameters: the Prandtl number of the fluid

the relative amplitude of the thermal oscillation

the Fourier number, which is the ratio of the period of the thermal oscillation to the conduction time in the fin over a length determined by the steady solution;, and the ratio of this latter time to the residence time of the fluid in the boundary layer. Numerical and asymptotic results are given covering a wide region of the parametric space. A linearized version of the governing equations is worked out and shown to give oscillatory Nusselt numbers in excellent accordance with the results from the full nonlinear equations.