The work deals with the problem of natural convection of a viscous incompressible fluid that completely fills a horizontal annular channel. The inner cylinder is fixed in the center of the area and can rotate around its axis. A constant temperature difference is maintained at the outer boundary. The motion of fluid in the area will cause the motion of the inner cylinder. It is assumed that the rotation of the inner cylinder around its axis occurs without friction.The problem is considered in the two-dimensional formulation. The Navier-Stokes equations in the Boussinesq approximation are used as a mathematical model. The equations are written in a cylindrical coordinate system. The equation of motion of the inner cylinder is derived from the law of conservation of angular momentum. The problem was solved jointly for the liquid and the inner cylinder.A mathematical model is proposed for describing natural convection in an annular channel with a movable border. Comparison of the results of the computational experiment with the analytical solution and results of other authors is carried out. The influence of the method of approximating the equation of motion of the inner cylinder on the result is estimated. It was established that the method of approximation does not affect the result obtained. Preliminary calculations were carried out to determine the optimal mesh density for this problem.
