Natural convective flows between a cold ceiling panel and a heated body in a cavity are particularly complex. There are two possible asymptotic flows, involving either an upward hot plume (Type I) or downward cold jet (Type II). The flow type depends crucially on both Ra and To. The structure of the solution space is described. The type II flows have lower heat transfer rates for the same Ra. This causes discontinuities in the Nu (with increasing Ra) and can have important implications for the cooling designs, particularly for micro-electronics.
For low and moderate Ra the plume is stable and asymptotically steady. For higher Ra the plume is neutrally stable and the Type I flow can be either steady or unsteady depending on T0. Any net heating or cooling of the flow exerts a stabilising influence. The degree of stabilisation increases with To−Tα. As the system approaches thermal equilibrium the amount of stabilisation declines. For T0 < 0.34, the stabilisation is sufficient to damp the plume completely to steadiness. For higher To the plume motion is diminished, but then re-accelerates and remains unsteady.
The structure of these unsteady type I flows is analysed, particularly the plume shedding cycle. Initially the plume motion is periodic. At around Ra = 6.6 × 106 there is a bifurcation and the plume motion acquires an additional long period fluctuation. At around Ra = 107 another bifurcation causes the flow to become pseudo-chaotic. Importantly the highly active plume motion and shedding reduces the thermal efficiency of the heat transfer. This causes structural changes in the flow and leads to lower Nu for the unsteady flows.