Numerical investigation of laminar Rayleigh–Bénard convection of power-law fluids in square cross-sectional cylindrical annular enclosures

Abstract

Steady-state laminar Rayleigh–Bénard convection (i.e. differentially heated horizontal walls heated from below) of power-law fluids in square cross-sectional cylindrical annular enclosures has been numerically investigated under the assumption of axisymmetry. The numerical simulations have been conducted for a range of different values of nominal Rayleigh number Ra, nominal Prandtl number Pr, power-law index n, and internal radius to enclosure height ratio ri/L (i.e. 103≤Ra≤105; 10≤Pr≤104; 0.6≤n≤1.8; 0≤ri/L≤24) for both constant wall temperature (CWT) and constant wall heat flux (CWHF) boundary conditions for differentially heated horizontal walls. It has been found that convective transport is stronger for CWT boundary condition than for CWHF boundary condition for large (small) values of Ra (n) for a given set of values of n (Ra), Pr, and ri/L, but an opposite trend is observed for small (large) values of Ra (n). The mean Nusselt number Nu−cy does not show a monotonic increase with increasing (decreasing) Ra (n) especially for small values of ri/L for a given value of Pr due to changes in flow patterns (i.e. number of convection cells). However, the mean Nusselt number Nu−cy and flow patterns for large values of ri/L approach those for square enclosures (ri/L→∞) for both CWT and CWHF boundary conditions. Additionally, the critical Rayleigh number Racrit for the onset of convection has been found to be mostly insensitive to the value of ri/L for both CWT and CWHF boundary conditions.