The linear stability of mixed convection in a vertical channel flow

In this study, the linear stability of mixed-convection flow in a vertical channel is investigated for both buoyancy-assisted and -opposed conditions. The disturbance momentum and energy equations were solved by the Galerkin method. In addition to the case with a zero heat flux perturbation 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 disturbances dominate, while for buoyancy-opposed flow, the Rayleigh-Taylor instability prevails for zero heat flux perturbation boundary condition, and for the zero temperature perturbation on the boundaries the two-dimensional disturbances dominate except at lower Reynolds numbers where the Rayleigh-Taylor instability dominates again. The instability characteristics of buoyancy-assisted flow are found to be strongly dependent on the Prandtl number whereas the Prandtl number is a weak parameter for buoyancy-opposed flow. Also the least-stable disturbances are nearly one-dimensional for liquids and heavy oils at high Reynolds numbers in buoyancy-assisted flows. From an energy budget analysis, we found that the thermal-buoyant instability is the dominant type for buoyancy-assisted flow. In buoyancy-opposed flow, under the zero temperature perturbation boundary condition the Rayleigh-Taylor instability dominates for low-Reynolds-number flow and then the thermal-shear instability takes over for the higher Reynolds numbers whereas the Rayleigh-Taylor instability dominates solely for the zero heat flux perturbation boundary 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 amplification rates, we offer some suggestions regarding the totally different laminar-turbulent transition patterns for buoyancy-assisted and -opposed flows.