Complex stationary convection with third-kind boundary conditions at the boundaries of a fluid layer

Abstract

In this paper presents analytical solutions of the Oberbeck-Boussinesq system describing layered Benard-Marangoni convection flows in an incompressible viscous fluid. On the free surface a third-kind boundary condition is used, namely Newton's heat transfer law. B'enard H. Etude exp'erimentale des courants de convection dans une nappe liquide. R'egime permanent: tourbillons cellulaires. J. Phys. Theor. Appl., 1900, vol. 9, no. 1, pp. 513-524. 4.Getling A.V. Formation of the spatial structures of Rayleigh-Benard convection. Uspekhi Fizicheskikh Nauk, 1991, vol. 161, no. 9, pp. 1-80. (In Russian Birikh R.V. Thermocappillary convection on a horizontal fluid layer.