The stability of natural convection in a vertical slot, in which the wall temperature is time-periodically modulated, is investigated by a perturbation technique.
The Floquet exponents (i.e. the complex growth rates of the disturbances to the oscillatory flow) are computed in powers of the oscillatory to steady temperature amplitude ratio. It is found that the oscillatory flow is more stable than the steady flow for values of Grashof number and disturbance wave number in the vicinity of critical values for the steady flow, when frequency of imposed oscillation is larger than about $\omega^{＊}=3$. For $\omega^{＊}\leq 2$, the unsteady flow is less stable than steady. At very high values of imposed oscillation frequency, the oscillating effect to the stabilization is very slight. The results hold for small values of the amplitude of temperature modulation.
