Stability of mixed convection flow

Hydrodynamic and thermal stability of a confined stratified flow is analyzed by means of linearized perturbation theory. A numerical procedure, which has generality with respect to boundary conditions, Reynolds number, Prandtl number, mean velocity, and temperature profiles, is described to solve the Orr-Sommerfeld problem altered by buoyancy. Two test cases-the study of transition of plane Poisseulle flow affected by stable and unstable stratification and the stability of flow generated by a wall heater with and without superimposed flow-have been solved, demonstrating the power and generality of the technique. A wide range of mixed convection problems has also been covered in this paper, and interesting Prandtl number effects have been observed. In the case of stratified Poisseulle flow, increasing Prandtl number significantly reduces the influence of buoyancy. Moreover, for stability of flow over a wall heater, higher values of Prandtl number strongly amplify the effect of prescribed flow.