Scaling of buoyancy-driven flows on a horizontal plate subject to a ramp heating of a finite time

Abstract

Buoyancy-driven flows on a horizontal plate subject to a ramp heating of finite time are studied in this paper. The dynamics of the thermal boundary layer and the subsequent starting plume on the heated horizontal plate are revealed and the scaling laws for different scenarios and regimes are obtained using a scaling analysis, which are further verified against results of direct numerical simulations (DNS) at the Rayleigh number of 5 × 102 ~ 5 × 104, the Prandtl number of 7 and the non-dimensional time of ramp heating from 0.072 to 0.143. A distinct sequential development of the thermal boundary layer, thermal bulges and starting plume is observed in the DNS and characterised by the scaling laws. The thicknesses of the thermal boundary layer and plume are found to decrease as the Rayleigh number increases because the convection intensifies. In addition, the scaling analysis suggests that the development of the starting plume may undergo five scenarios, each of which has a series of different regimes, depending on the Rayleigh number, the Prandtl number and the time of ramp heating. In a typical scenario, the starting plume may ascend under an unsteady viscosity conduction regime, a quasi-steady viscosity conduction regime or a steady viscosity conduction regime.