The structures of attractors reconstructed with time-evolution data of average heat transfer on thermal convection field in a vibrating square enclosure

Abstract

In this paper the time-dependent characteristics of surface-averaged Nusselt number in a square enclosure with hot and cold side walls exposed to vertical vibrations were numerically examined. In the computation, the Prandtl number, the Rayleigh number, and the vibration Grashof number were held constant at 0.71, 104, and 106, respectively. The angular frequency of vibration was changed in the range between 10 and 7680. The results showed that the change in the characteristics of the surface-averaged Nusselt number proposed by Fu and Shieh corresponded to the change in the shape of reconstructed attractor and that these regions could also be characterized by the three indices defined in phase space: average location of trajectory, the largest Lyapunov exponent, and the correlation dimension. Moreover, the time scale with which the autocorrelated coefficient of the surface-averaged Nusselt number becomes 1/e was found to be a very important parameter for the time- and surface-averaged Nusselt number. © 2000 Scripta Technica, Heat Trans Asian Res, 30(1): 11–21, 2001