The shearing steady convective motion of a viscous incompressible fluid in an infinite horizontal layer is studied in this paper. The flow of the fluid is due to the thermocapillary effect, heat exchange according to the Newton-Rikhman law, and a thermal source at the boundaries of the fluid layer. The effect of the thermocapillary effect is due to the inclusion of tangential capillary forces on the upper (free) boundary. Heat transfer according to the Newton-Richman law is carried out at the upper boundary. The horizontal temperature gradients are given at the lower boundary. The pressure is set at the upper limit. For the Oberbeck-Boussinesq system, a new exact solution has been found. The boundary problem describing the complex convection of Marangoni is overdetermined. The system of Oberbeck-Boussinesq equations consists of five equations for determining two velocities, pressure and temperature. For the Oberbeck-Boussinesq system, a new exact solution has been found. The velocity field depends only on the vertical (transverse) coordinate. The pressure and temperature fields are linear forms with respect to horizontal (longitudinal) coordinates. The coefficients of linear forms depend on the vertical coordinate. This exact solution identically satisfies the equation of incompressibility. This allows us to solve the initial boundary value problem. To determine the unknown functions that determine the velocity field, the temperature field and the pressure field, a system of ordinary differential equations is obtained. This system of differential equations is integrated. An exact polynomial solution of this system is obtained. The procedure for reducing the exact solution to the dimensionless form is described in the paper. Two characteristic scales for coordinates have been introduced, which allows to describe large-scale flows of a viscous incompressible fluid (fluid flow in a thin layer). The velocity field in this paper is studied in detail. To study the polynomial exact solution for velocities, the Routh-Hurwitz theorem is used. It is shown at what number of similarities in the fluid there is a counterflow in the case of large-scale fluid motion. Thus, there are stagnant points in the liquid layer. The existence of stagnant points leads to the vanishing of the kinetic energy. The kinetic energy can take one zero value or be zero at two points. The nonmonotonic distribution of the kinetic energy over the layer thickness is due to the consideration of several factors that cause convective fluid motion. Examples of localized viscous incompressible fluid flows are given. Such examples demonstrate the possibility of a local description of spiral fluid flows. In addition, for classical liquids, the thickness of the layer is determined, at which the tangential stresses at the lower boundary are zero. For anomalous fluids in which the surface tension coefficient is negative, shear stresses cannot take zero values.