ANALYTICAL SOLUTION AND NEUTRAL CURVES OF THE STATIONARY LINEAR RAYLEIGH PROBLEM WITH RIGID OR MIXED BOUNDARY CONDITIONS IN CYLINDRICAL GEOMETRY

On the basis of the Navier-Stokes equations in the Boussinesq approximation in the linear approximation the classical problem of Rayleigh, dedicated to the study of stable stationary solutions to the horizontal plane layer of a viscous, incompressible fluid heated from below in the case of execution on the upper and lower boundaries of the layer of solid boundary conditions is considered. The analytical solutions describing the perturbed velocity and temperature of the fluid in a cylindrical convection cell with solid boundary conditions are obtained. The obtained analytical solution to build similar solutions of the problem with mixed boundary conditions is used. The analytical expressions for the neutral curves in the case of solid and mixed boundary conditions based on the obtained solutions are built. A comparison of the analytically constructed neutral curves with numerical simulations obtained by other authors is carried out. The derived analytical expressions for the neutral curves of solid and mixed boundary conditions with sufficient accuracy correspond to the numerical calculations is shown