In this paper, the thermal convection field and its resonance phenomena in a square cavity with sinusoidal heat-flux vibration were numerically investigated. As the angular velocity ω is changed, the thermal convection field at Pr = 0.71, Ra = 10 6 is found to be classified into 5 regions. In particular, the field has the local maximum relative amplitude of midplane Nusselt's number at ω c = 350, which corresponds to the angular velocity of internal gravity wave ω r estimated by a theoretical equation proposed by Thorpe. This shows that the local enhancement is induced by internal gravity wave resonance. Such correspondence is observed for Ra ≥ 10 5 , Ra ≥ 10 6 for Pr = 0.71, 7.1, respectively. For these ranges of Ra we propose a correlation equation, a function of Pr and Gr only, to estimate the resonant angular velocity.
In this paper the thermal convection field and its resonance phenomena in a rectangular cavity with heat-flux vibration are numerically examined and the results are compared with those of a square cavity. As in the case of α = 1, the critical angular velocity at which the relative amplitude of the midplane Nusselt number α m has a local maximum agrees very well with the resonance angular velocity of the internal gravity wave ω r , estimated by the theoretical equation proposed by Thorpe, even when the aspect ratio is α = 5 and the Prandtl number is Pr = 0.71 for a range of the Rayleigh number Ra. However, α m has two local maxima for a larger Ra, which is peculiar to the case of larger α. The time variation of sub-components of the fluctuating component of the midplane Nusselt number shows that the phase at the maximum value of α m agrees well with that of the sub-component of velocity for the first resonance angular velocity ω r . For the other angular velocity ω r2 , the phase of α m agrees with that of the sub-component of temperature. Moreover, we found that the boundary angular velocity ω 0 between the first two of the five ω regions, which classify the thermal convection fields against ω, can be expressed by a function of α, Ra, and Pr and that α m is independent of α and Ra for a relatively wide range of ω/ω 0 .
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