THE LINEAR-STABILITY OF MIXED CONVECTION IN A VERTICAL CHANNEL FLOW

In this study, the linear stability of mixed-convection flow in a vert ical channel is investigated for both buoyancy-assisted and -opposed c onditions. The disturbance momentum and energy equations were solved b y the Galerkin method. In addition to the case with a zero heat flux p erturbation boundary condition, we also examined the zero temperature perturbation boundary condition. In general, the mixed-convection flow is strongly destabilized by the heat transfer and therefore the fully developed heated flow is very unstable and very difficult to maintain in nature. For buoyancy-assisted flow, the two-dimensional disturbanc es dominate, while for buoyancy-opposed flow, the Rayleigh-Taylor inst ability prevails for zero heat flux perturbation boundary condition, a nd for the zero temperature perturbation on the boundaries the two-dim ensional disturbances dominate except at lower Reynolds numbers where the Rayleigh-Taylor instability dominates again. The instability chara cteristics of buoyancy-assisted flow are found to be strongly dependen t on the Prandtl number whereas the Prandtl number is a weak parameter for buoyancy-opposed flow. Also the least-stable disturbances are nea rly one-dimensional for liquids and heavy oils at high Reynolds number s in buoyancy-assisted flows. From an energy budget analysis, we found that the thermal-buoyant instability is the dominant type for buoyanc y-assisted flow. In buoyancy-opposed flow, under the zero temperature perturbation boundary condition the Rayleigh-Taylor instability domina tes for low-Reynolds-number flow and then the thermal-shear instabilit y takes over for the higher Reynolds numbers whereas the Rayleigh-Tayl or instability dominates solely for the zero heat flux perturbation bo undary condition. It is found that the instability characteristics for some cases of channel flow in this study are significantly different from previous results for heated annulus and pipe flows. Based on the distinctly different wave speed characteristics and disturbance amplif ication rates, we offer some suggestions regarding the totally differe nt laminar-turbulent transition patterns for buoyancy-assisted and -op posed flows.