Instabilities during convection–diffusion of binary mixtures in a non-isothermal flow: A linear stability analysis

Abstract

This paper reports a fully developed thermo–solutal mixed convection flow of the binary mixture of some important chemical species and its linear stability characteristics in a vertical channel. The flow is jointly driven by an external pressure gradient as well as simultaneous buoyancy effects of thermal and chemical species diffusion. A spectral collocation method is adopted to solve the governing equations numerically. The numerical calculation is performed for a wide range of the governing flow parameters. The main emphasis is given to examine the effect of the buoyancy ratio, which is defined as N, on basic flow characteristics and the instability mechanism for chemical species diffusion of interest in the air (Pr = 0.7) over a Schmidt number (Sc) range 0.2–2.01. A comprehensive investigation shows that when N≥−1, the heat and mass transfer rates increase monotonically on increasing the thermal buoyant force, whereas for N<−1 they are in a sinusoidal form. The velocity profiles contain the point of inflection for N>−1; however, both the point of inflection and flow separation are present when N<−1. The stability of the flow decreases on increasing the value of Sc, when the buoyant force from species diffusion acts in the same direction as the thermal buoyant force. The flow is also unstable under mild heating conditions for a relatively large magnitude of N. The disturbance kinetic energy analysis at the linear stability critical point shows that more contribution of the shear term in the production of disturbance kinetic energy effectively stabilizes the flow.