Numerical investigation of laminar Rayleigh-Bénard convection of Bingham fluids in square cross-sectioned cylindrical enclosures

Numerical simulations have been conducted under the assumption of axisymmetry to analyse steady-state laminar natural convection of yield stress fluids obeying Bingham model in square cross-sectioned cylindrical annular enclosures heated from below (i.e. Rayleigh-Bénard configuration). The simulations have been carried out for a representative value of nominal Prandtl number (i.e. Pr = 500) for different internal cylinder radius (0≤ri/L≤16 where ri and L are the inner radius and the cylinder height respectively) for a nominal Rayleigh number range 103≤Ra≤105. Both constant wall temperature and constant wall heat flux boundary conditions have been imposed for differentially heated horizontal walls to analyse the effects of wall boundary condition. Although the buoyancy-driven transport strengthens with increasing Ra  , the mean Nusselt number Nu¯cy does not show a monotonic increase with increasing Ra for small values of ri/L   because of the change in flow pattern (i.e. number of convection rolls/cells). By contrast, Nu¯cy monotonically increases with increasing Ra, and only one cell flow pattern is obtained for large values of ri/L  . Furthermore, Nu¯cy has been found to increase with increasing ri/L but asymptotically approaches the corresponding value obtained for square enclosures (ri→∞) for both CWT and CWHF boundary conditions for large values of ri/L  . It has also been found that both the flow pattern and the mean Nusselt number Nu¯cy are dependent on the initial conditions for Bingham fluid cases since hysteresis is evident for small values of ri/L   for both CWT and CWHF boundary conditions. It has been found that convection could be sustained up to a higher value of Bingham number due to stronger convection arising from higher temperature difference between horizontal walls in the case of CWT boundary condition than in the corresponding CWHF configuration. Finally, the numerical findings have been used to propose a correlation for Nu¯cy in the range of 2≤ri/L≤16 (0.25≤ri/L≤16) and 103≤Ra≤105 for the CWT (CWHF) boundary condition.