On vibration-convective flows in a Hele-Shaw cell

The influence of high-frequency horizontal vibrations on convective flow conditions in a Hele-Shaw cell located in a homogeneous gravitational field and heated from below has been studied theoretically and experimentally. The linear problem of stability of mechanical quasi-equilibrium in the case of model boundary conditions has been solved analytically. The supercritical conditions of vibrational convection have been investigated numerically by the finite-difference method. It has been shown that at small values of the thermal and vibration Rayleigh numbers in a fluid a state close to quasi-equilibrium is realized. The critical values of the thermal and vibration Rayleigh numbers at which a change of different stationary and nonstationary convective regimes takes place have been determined. A stability map of vibration-convective flows has been generated. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 4, pp. 712–720, July–August, 2008.