Abstract
Mixed convection in a horizontal rectangular duct has the same critical Rayleigh number as natural convection in a rectangular cavity for the onset of convection. The linear stability analysis predicts either an odd or an even number of convective rolls to appear depending on the aspect ratio of the cross section. However, it has been shown both experimentally and numerically that an even number of convective rolls appears under supercritical conditions for fully developed mixed convection. The paper first presents an analytical solution for the buoyancy-induced mainstream velocity, w b , at the onset of buoyancy-induced motion in a forced convective flow. Then, a comparison in the initial growth rate of w b is made between the case of an odd and an even number of rolls; which shows the selection of an even number of rolls over an odd number in mixed convection except for low aspect ratio ducts.
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