Application of a Partially Invariant Exact Solution of the Thermosolutal Convection Equations for Studying the Instability of an Evaporative Flow in a Channel Heated from Above

Abstract

The characteristics of a stationary flow of a volatile liquid driven by a co-current gas flux in a flat horizontal mini-channel upon the non-zero transverse temperature drop are studied. We use an exact solution of the thermosolutal convection equations for describing the heat and mass transfer caused by the combined action of gas pumping, buoyancy, thermocapillarity and linear heating of the channel walls in a two-layer system. The influence of heating from above on the parameters of the ground state and the stability characteristics of the basic flow is explored using an example of the ethanol–air system. We evaluate the thresholds of the linear stability and select the most dangerous modes. Heating from above results in flow stabilization. Instability appears in the form of oscillatory cellular convective patterns.

Keywords

• mathematical modeling
• exact solution
• evaporative convection
• oscillatory instability