Thermocapillary Convection of a Vertical Swirling Liquid

Abstract

Abstract A new exact solution of the Oberbeck–Boussinesq equations has been presented which describes the steady-state Marangoni convection of a vertical swirling liquid in the shear flow of a viscous incompressible liquid. The velocity field of the nonuniform vortical liquid flow is studied in detail. It is shown that there are stagnation points in the liquid flow, the number of which can be as large as five. The existence of stagnation points leads to the formation of counterflows with very complex topology resembling cellular flow patterns. The tangential stresses in the liquid flow are not constant. They are also stratified from the zone of tensile and compressive stresses. Because of the structure of the exact solution, the vorticity components coincide to within a dissipative coefficient with the expressions for the tangential stresses, which means that there are several counterrotating vortices in the liquid. Similar studies of polynomial exact solutions for temperature and pressure determined the number of zones of stratification of the corresponding fields.