Transition to turbulent heat transfer in heated vertical channel - Scaling analysis

A thermally driven flow in a vertical channel with heated walls is studied through a scaling analysis and results are compared with the experimental data reported in [1]. As the geometry is symmetrical with respect to the vertical axis, the half-channel is considered. The domain is split into seven zones in which the flow behaviour results from a balance between several phenomena. This zonal analysis exhibits the main phenomena that drive the flow in each zone. The study leads to an expression of the wall temperature profile below and above the transition. An expression is given for the driving pressure that is found to increase along the channel. The increase rate is much more important above the transition due to the fluid heating in the center of the channel. Finally, The maximum Reynolds stress is expressed in terms of the mean velocity values and is found to fit well with the experimental data.