Rayleigh-Bénard Convection

Fluid heated from below: conduction gives way to convection rolls as Ra exceeds critical value (~1708).

Nusselt number (heat transfer efficiency): Nu = 1.00 Ra onset ≈ 1708

Parameters

Nu vs Time

Ra: 2000
Ra_c: 1708
Ra/Ra_c: 1.17
Nu: 1.00
Ra = gαΔTL³/(νκ). Below Ra_c≈1708: conduction only (Nu=1). Above: convection rolls form (Nu>1). At higher Ra: time-dependent, then turbulent.