ON PATTERN SELECTION IN MIXED CONVECTION IN RECTANGULAR DUCTS

Mixed convection in a horizontal rectangular duct has the same critica l Rayleigh number as natural convection in a rectangular cavity for th e onset of convection. The linear stability analysis predicts either a n 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 ex perimentally and numerically that an even number of convective rolls a ppears under supercritical conditions for fully developed mixed convec tion. The paper first presents an analytical solution for the buoyancy -induced mainstream velocity, w(b), at the onset of buoyancy-induced m otion in a forced convective flow. Then, a comparison in the initial g rowth rate of w(b) is made between the case of an odd and an even numb er 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.