Linear Heating of the Upper Boundary of a Fluid Layer in the Case of Stationary Nonisothermal Couette Flow

摘要

A new exact solution of the two-dimensional Oberbeck-Boussinesq equations has been found in this paper. The solution is found in the case of the nonuniform distribution of velocities and a linear heat source at the upper boundary of an infinite layer of a viscous incompressible fluid. Analysis of polynomial solutions describing the natural fluid convection is presented. The existence of points at which hydrodynamic fields vanish inside the fluid layer is demonstrated.