N. V. Burmasheva, E. Yu. Prosviryakov

EXACT SOLUTIONS FOR NATURAL CONVECTION OF LAYERED FLOWS OF A VISCOUS INCOMPRESSIBLE FLUID WITH SPECIFIED TANGENTIAL FORCES AND THE LINEAR DISTRIBUTION OF TEMPERATURE ON THE LAYER BOUNDARIES

A new exact solution of the Oberbeck-Boussinesq equations for the convective flow of a viscous incompressible fluid is considered. Layered flows of a viscous incompressible fluid are investigated within the class of the Sidorov-Lin exact solutions, which generalizes the family of the Ostroumov-Birikh solutions. The use of an exact solution allows an overdetermined system of fluid motion equations to be solved. The fluid is heated by setting a heat source at both boundaries. The dimension of the studied boundary value problem cannot be lowered by the transformation of the rotation. The obtained exact solution describes the counterflow in the fluid. Thermocline and a boundary layer occur near one of the boundary layers in the fluid flow.

Acknowledgment: This work was supported by the Foundation for Assistance to Small Innovative Enterprises in Science and Technology (the UMNIK program); the agreement no. 12281 GU/2017.

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