Heat transfer in thermally modulated two-dimensional Rayleigh Bénard convection

The evolution of instability of a fluid-layer between two horizontal rigid planes subjected to sinusoidally varying temperatures of the horizontal boundaries is investigated for supercritical Rayleigh numbers. The nonlinear equations governing the system are solved numerically using the characteristic based split finite element scheme in a two dimensional rectangular-box of aspect-ratio 10, which is a good approximation to the horizontally unbounded fluid-layer. Under the supercritical conditions, the nonlinear instability in the modulated fluid-layer is found to evolve in the form of a time-periodic flow-pattern, which oscillates harmonically or sub-harmonically, depending upon the modulation parameters. The heat transfer through the fluid layer is described in terms of a time averaged Nusselt number, which is found to be significantly affected by the modulation parameters.