Transient Natural Convective Conjugate Cooling Mechanism in Vertical Fins

摘要

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.