Layered Marangoni convection with the Navier slip condition

A new exact solution to the problem of Marangoni layered convection is obtained. This describes a steady-state flow viscous incompressible fluid at varying gradients temperature and pressure. The velocity components depend only on transverse coordinate; pressure fields are three-dimensional. effect observed upper free surface layer. On lower solid layer, three different cases defining boundary conditions considered: no-slip condition, perfect slip condition Navier condition. obtained determined by interaction flows: caused drop (the Poiseuille flow), heating/cooling gravity force thermogravitational tension thermocapillary flow). solutions in case each types specified analyzed detail. It has been proved that, when certain ratios value parameters fulfilled, may acquire stagnation points, this being indicative presence counterflow areas layer under consideration. In particular, up two points longitudinal cause stratification field more than regions. can describe flows thin films through variation geometric anisotropy factor.