Natural convection in cylindrical containers

A numerical method has been developed using alternating direction implicit and Fourier series to solve the finite difference approximations to the equations governing natural convection in a cylinder. The accuracy of the numerical method is investigated by comparing the results with experimental results and an analytical solution. It is shown that the method accurately predicts the flow and temperature distributions within the cavity. Two-dimensional natural convection solutions in a horizontal cylinder have been obtained for Rayleigh numbers up to 10 to the 6th power and Prandtl numbers in the range 0.2 to 10 to the 5th power. There is little difference in the motion of the fluid and heat transfer for Prandtl numbers in the range 7.0 and 10 to the 5th power except in the locations of the secondary rolls. The effect on the flow and heat transfer is also studied when heating is applied from different directions.