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: This effort deals with a numerical and analytical study of multicellular flow instability due to natural convection between narrow horizontal isothermal cylindrical annuli. Buoyancy-induced steady or unsteady flow fields between the annuli are determined using the Boussinesq approximated two-dimensional Navier-Stokes equations and the viscous-dissipation neglected thermal-energy equation. The vorticity stream function formulation of the Navier Stokes equations is adopted. Both thermal and hydrodynamic instabilities are explored. An asymptotic expansion theory is applied to the Navier-Stokes equations in the double-limit of Rayleigh number approaching infinity and gap width approaching zero. Thermal instability of air near the top portions of narrow annuli is considered for various size small gap widths. For these narrow gaps, the Rayleigh numbers corresponding to the onset of steady multicellular flow are predicted. Numerical solutions of the 2-D Navier Stokes equations also yield hysteresis behavior for the two-to-six and two-to-four cellular states, with respect to diameter ratios of 1.100 and 1.200. In contrast, an unsteady hydrodynamic multicellular instability is experienced near the vertical sections of narrow annuli when the Pr approaches 0 boundary layer equations are solved numerically. (Theses).

The numerical and analytical study of bifurcation and multicellular flow instability due to natural convection between narrow horizontal isothermal cylindrical annuli at high Rayleigh numbers