Sidewall and thermal boundary condition effects on the evolution of longitudinal rolls in Rayleigh-Bénard-Poiseuille convection

Experimental and numerical studies of steady longitudinal convection rolls that develop in a Poiseuille air flow in a rectangular channel heated from below and cooled from the top are conducted in the range 3500 ≤ Ra ≤ 6000 and 20 ≤ Re ≤ 200. The effect of the lateral vertical walls on the onset and development of the convection cells is investigated by changing the transverse aspect ratio of the channel from 4.7 to 18.4. The influence of the entrance temperature and of adiabatic or conductive thermal boundary conditions at the side and top walls of the channel is also investigated. The scenario of the roll formation is described in details. It results in a symmetric pattern in the form of steady longitudinal rolls with an even number of rolls that depends not only on the aspect ratio but possibly on the inlet temperature of the flow. It is shown that the fully developed pattern is determined by the two rolls nearby each vertical side wall that are triggered just at the entrance of the channel due to the presence of velocity boundary layers adjacent to the walls. It is also shown that the heat conduction in the top horizontal wall of the experimental channel must be taken into account in the numerical simulations so that the experimental wavenumber can be properly depicted.