Weakly non-linear analysis of Rayleigh–Benard convection with time periodic heating

The stability of a horizontal layer of fluid heated from below as well as from above is examined. The temperature gradient between the walls of the fluid layer consists of a steady part and a time-dependent part, which is oscillatory. The amplitude of temperature modulation is δ. By considering the weakly non-linear analysis, it is shown that the modulation produces a range of stable hexagons near the critical Rayleigh number. Some comparisons have been made with the other theoretical results.