A numerical solution for natural convection in cylindrical annuli using finite element method

A numerical solution, using the finite element method, is developed for steady, two-dimensional natural convection between two horizontal concentric cylinders. The solution is in terms of the main variables - velocities, pressure and temperature. The necessary stream function and heat transfer coefficients are then calculated from the known velocity and temperature fields. The convergence of the solution was tested by using two numerical schemes - direct iteration and the Newton-Raphson method with the same convergence criterion. Computations were carried out for different gap/inner radius ratio for a range of Rayleigh numbers. The Rayleigh number at which secondary flows appear is predicted by numerical solutions thereby yielding a good indication of the Rayleigh number at which transition to an unsteady flow occurs. Comparisons with some experimental, analytical and finite difference solutions are included.