Unsteady Natural Convection in a Horizontal Cylinder With Internal Heat Generation

The unsteady natural convection of a fluid within a horizontal cylinder with internal heat generation is considered. The unsteady Navier-Stokes equations in the Boussinesq approximation are computed numerically for Rayleigh numbers in the range from 10⁶ to 10¹⁰ to determine the fluid flow and heat transfer characteristics. For Rayleigh numbers below a critical value, Ra_R ≈ 10⁸, the unsteady solutions approach a steady-state solution that is symmetric about the vertical center line. Above the critical Rayleigh number, however, the flow becomes highly unsteady and evolves toward a quasi-periodic asymmetric oscillation.