A numerical solution for natural convection in cylindrical annuli using finite element method
Abstract
A numerical solution, using the finite element method, is developed for steady, twodimensional 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 NewtonRaphson 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.
 Publication:

International Symposium on Finite Element Methods in Flow Problems
 Pub Date:
 1976
 Bibcode:
 1976femf.symp..637T
 Keywords:

 Concentric Cylinders;
 Finite Element Method;
 Free Convection;
 Galerkin Method;
 Laminar Flow;
 NewtonRaphson Method;
 Rayleigh Number;
 Steady Flow;
 Stream Functions (Fluids);
 Two Dimensional Flow;
 Fluid Mechanics and Heat Transfer