Numerical study of transient flow within a horizontal cylinder heated from below and cooled from the top

The time dependent natural convection in a horizontal circular cylinder, heated from below and cooled from above, is computed using the stream function-vorticity formulation for the two-dimensional equations of motion and energy. The fluid studied has a Prandtl number of 7. The range of Rayleigh numbers (Ra) presented in this paper is 580 <= Ra <= 100,000. For the range of Ra presented, the initial motion consists of four cells. As Ra is increased, a large single cell with two weak cells is formed. At low Rayleigh numbers, steady state solutions are obtained. At higher values of Ra, the flow becomes unsteady. The temperature, streamlines, relative total Kinetic Energy (KE) and Nusselt number are presented as functions of time.