Stability analysis of Rayleigh-Bénard convection in a cylinder with internal heat generation.

The flow instabilities of Rayleigh-Bénard convection in a cylinder with effect of uniform internal heat source are investigated numerically. The instabilities of the static state and of axisymmetric flows are investigated by linear stability analysis. The convection threshold depends on the strength of internal heat source q and the aspect ratio of the cylinder Γ.

Rayleigh-Bénard convection in a vertical annular container near the convection threshold.

The instabilities and transitions of flow in an annular container with a heated bottom, a cooled top, and insulated sidewalls are studied numerically. The instabilities of the static diffusive state and of axisymmetric flows are investigated by linear stability analysis. The onset of convection is independent of the Prandtl number but determined by the geometry of the annulus, i.

Multiplicity of steady states in cylindrical Rayleigh-Bénard convection.

Three-dimensional steady Rayleigh-Bénard convection in a vertical cylinder is investigated by numerical simulation and bifurcation analysis. The complex pattern formation beyond the onset of the convection is presented by a bifurcation diagram. The coexistence of multiple stable states is observed near the threshold of the first bifurcation and two group symmetries are summarized for the corresponding primary branches.