Convection in Hele-Shaw cell with parametric excitation

The linear stability of a thin vertical fluid layer heated from below is considered. Here the gravitational field consists of two parts: a constant part and a time-dependent part varying periodically. The time-dependent part has been expressed in Fourier series. The effect of gravity modulation on the fluid layer is examined. Using an asymptotic analysis the convective threshold has been determined. Some comparisons are made with the known results.