Stability of a thermal boundary layer in the presence of vibration in weightlessness environment

Several weightless experiment with supercritical fluids have shown that thermal boundary layers can be destabilized when submitted to a harmonic vibration. A study of the phenomenon is given here in a regular fluid during a sudden change of wall temperature in the presence of harmonic tangential vibrations and under weightlessness. A semi-infinite space is filled with a fluid and bounded by a flat wall oscillating in its plane. For this configuration, a state with the fluid velocity parallel to the wall is possible but this fluid motion does not influence the heat transfer. Then the propagation of thermal waves can be described by classical relations. The stability of this state is studied under the assumption of a “frozen” temperature profile. The vibration frequency is assumed to be high such that the viscous boundary layer thickness is small in comparison with the thermal boundary layer thickness. The calculations show that the instability develops when the thickness of the thermal boundary layer attains a critical value. The wavelength of the most dangerous perturbations is found to be about twice the critical thermal boundary layer thickness.