Convective and Absolute Instabilities Induced by Viscous Dissipation in the Thermocapillary Convection With Through-Flow

Abstract

The mixed convection in a thin liquid film flow over a horizontal plate is investigated under finite Prandtl numbers. The gas–liquid interface is considered free, nondeformable and subject to surface tension gradients and convection, while gravity is assumed negligible. Therefore, thermocapillary instead of buoyancy effects appears due to the unstable temperature stratification induced by the internal heating generated by viscous dissipation. A linear and modal stability analysis of this model is then performed to identify its convective/absolute nature. This is achieved by solving the resulting differential eigenvalue problem with a shooting method. Longitudinal rolls are the most unstable at the onset of instability for most parametric conditions. Otherwise, transverse rolls are the first to become convectively unstable. Finally, longitudinal rolls are absolutely stable. A transition to absolute instability occurs through transverse rolls, but only within a limited region in parametric space.