Free thermal stationary convection of incompressible fluid in a closed loop

The natural thermal stationary convection of a one-component fluid in a closed long loop is investigated theoretically. A solution of the two-dimensional boundary value problem is proposed. The gravitational convection equations have analytically reduced to non-linear equations, which contains a set of parameters included in the temperature and velocity fields functions. Calculation of the parameters values has carried out used a computer algebra package. Rayleigh and Nusselt numbers interrelation has computed in the case of long contour. Comparison of the presented simulation with a one-dimensional model has also been made.