Numerical investigation of aspect ratio influences on Rayleigh-Bénard convection of power-law fluids in vertical cylindrical annuli

Abstract

The influences of aspect ratio on laminar Rayleigh-Bénard convection of power-law fluids in cylindrical annular enclosures have been numerically investigated for Neumann and Dirichlet boundary conditions for the differentially heated horizontal walls. The axisymmetric simulations have been carried out for a range of different Rayleigh number (i.e. Ra=103-105), aspect ratio (i.e. AR=H/L where H is the enclosure height and L is the difference between outer and inner radii) (i.e. AR=0.25-4), power-law index (i.e. n=0.6-1.8) and normalised inner radius (i.e. ri/L=0-16 where ri is internal cylinder radius) for a nominal representative Prandtl number (i.e. Pr=103). It has been found that thermal convection weakens with an increase in AR and conductive thermal transport becomes dominant for AR>3 irrespective of the values of Ra, n and ri/L for both boundary conditions. The mean Nusselt number Nu‾cy exhibits a complex non-monotonic behaviour with the variations of above parameters due to the changes in flow pattern (e.g. number of cells) for shear-thinning fluids (i.e. n<1). However, this tendency is much weaker for shear-thickening fluids (i.e. n>1) for both boundary conditions. Moreover, the critical Rayleigh number Racrit for the onset of convection of power-law fluids is found to be largely independent of ri/L for both Neumann and Dirichlet boundary conditions.