Sufficient conditions for existence of free convection flow in vertical  narrow channels

It is proved that the existence of free convection flow (FCF) in a vertical slit with asymmetric heating is sufficient to satisfy the condition:0 < n< n_ex, where n_ex — the polytropic index in the FCF, n_ex - polytropic index corresponding to the equilibrium state of the gas column. In particular, if the equilibrium state corresponds to the condition of no supply of heat, then: 0 < n< k, k— ratio of specific heats. For the existence of the gap in the maximum mass flow rate it is necessary that: n=gL/RT₀, where L— the height of the slit, T₀ - temperature at ground level. Polytropic index n is related to the intensity of heat transfer from hot wall to the flow: with increasing intensity of heat transfer n →+0.