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, 10 4 , and 10 6 , 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 surfaceaveraged 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.

Internal gravity wave resonance of thermal convection fields in a square cavity with heat‐flux vibration

“…There have been many studies on the response of natural convection field in a closed cavity to a vibrational condition [1,[3][4][5][6][7][8][9][10][11]. The resonance phenomena induced by the condition are related to the enhancement of heat transfer [1] or laminar flow mixing in a reactive tank [3] and, therefore, they are very important in practical applications.…”

“…The resonance phenomena induced by the condition are related to the enhancement of heat transfer [1] or laminar flow mixing in a reactive tank [3] and, therefore, they are very important in practical applications. Fu and Shieh [1] and Ishida and Kimoto [3,4] investigated the thermal convection field in a square cavity with a forced vertical vibration numerically , and they showed that the thermal convection field can be classified into 5 regions as the frequency of vibration is changed, and that the average heat transfer rate is remarkably increased when the cavity is vibrated with a specified frequency (resonant frequency). This is caused by the agreement between the period of the thermal convection circulation, determined by the velocity in the Stokes layer, and that of the forced vibration [1].…”

Enhancement of forced convection heat transfer in a three-dimensional laminar channel flow with insertion of a moving block

“…In order to lead the velocity of the next time step U n+1 to be equal to the desired value V s on the immersed boundary, the source term F B of Eq. (20) can be expressed as follows [38]:…”

“…At present well-known methods of the enlargement of heat dissipation surface [3][4][5][6][7][8][9][10][11], the disturbance of flow field [12][13][14][15][16][17][18][19] and the vibration of heat surface [20][21][22][23][24][25][26] are most usually adopted to enhance the forced convection heat transfer rate of the channel flow and the results of the above methods are remarkable and available. However, the increment of the heat transfer rate of the above methods seems to have limitation because a thermal boundary layer which is disadvantageous to heat transfer mechanisms still forms on the heat surface.…”