STABILITY OF MIXED CONVECTION IN A DIFFERENTIALLY HEATED VERTICAL CHANNEL

In this study, the linear stability of mixed convection in a different ially heated vertical channel is investigated for various Prandtl numb ers. The results indicate that this fully developed heated flow can be come unstable cinder appropriate conditions. It is Sound that both the Prandtl number and Reynolds number hold very important effects on the critical Grashof number, wave number, wave speed, and instability mec hanism for higher Prandtl numbers. For low Prandtl numbers, the effect s from the Prandtl number and Reynolds number are relatively small. Th e most significant finding is that the local minimum wave numbers can be as high as eight for Pr = 1000, which is substantially higher than those found before for other heated flows. The existence of multiple l ocal minimum wave numbers is responsible for the sudden jumps of the c ritical wave number and wave speed and the sudden shift of instability type for higher Prandtl numbers. The energy budget analysis shows tha t the thermal-shear and shear instabilities dominate at both low and h igh Reynolds numbers for Pr = 0.7 and 7. Irt is the thermal-buoyant in stability for Re < 1365 and shear instability for Re greater than or e qual to 1365 for Pr = 100. The thermal-buoyant and mixed instabilities are the possible instability types for Pr = 1000. In general, for mix ed convection channel flows, the instability characteristics of differ entially heated flows are found to be substantially different from tho se of uniformly heated flows.