An investigation of transient mixed convection heat transfer of cold water in a tall vertical annulus with a heated rotating inner cylinder

Abstract

The transient buoyant rotating convective flow and heat transfer in a tall vertical annulus containing cold water near the density inversion have been investigated via a finite difference procedure. Simulations are carried out by solving axisymmetric Navier-Stokes equations adhering to the Boussinesq approximation coupled to the energy equation for an aspect ratio A = 8 and radius ratio RR = 2, two density inversion parameters θ m = 0.4 and 0.5, three Reynolds numbers Re = 50, 100, and 150, and varying Rayleigh number (up to 10 6). Numerical results demonstrate that the transient mixed convective flow and heat transfer may evolve into sustained oscillation over a certain range of Rayleigh number at given θ m and Re; outside such unstable Ra-range, the transient evolution converges to steady-state solution. The transition into oscillatory convection arises at higher Rayleigh number with higher Reynolds number. Within the unstable convection regimes, simple as well as complex periodic oscillation, and chaotic oscillations have been detected. Moreover, the unstable Ra-ranges under fixed Re for θ m = 0.5 are found to be wider than those for θ m = 0.4 , clearly reflecting the effects of the density inversion on the transient buoyant rotating convective flow and heat transfer in the tall vertical annulus.