Influences of Boundary Condition on Laminar Natural Convection of Bingham Fluids in Square Cross-Sectioned Cylindrical Annular Enclosures with Differentially Heated Vertical Walls

Numerical simulations have been carried out to analyze steady-state laminar natural convection of yield stress fluids obeying Bingham model in square cross-sectioned cylindrical annular enclosures with differentially heated vertical walls for both constant wall temperature and constant wall heat flux boundary conditions for active walls. The simulations have been performed under the assumption of axisymmetry for a nominal Rayleigh number range of 10³ to 10⁶ and nominal Prandtl number range of 10 to 10³ for different ratio of internal cylinder radius to cylinder height range of 0.125 to 16. The mean Nusselt number on the inner periphery for the constant wall heat flux configuration has been found to be smaller than that in the case of constant wall temperature configuration for a given set of values of nominal Rayleigh and Prandtl numbers for both Newtonian and Bingham fluid cases. The mean Nusselt number normalized by the corresponding value obtained for pure conductive transport increases with increasing internal radius before approaching the corresponding mean Nusselt number for square enclosures regardless of the boundary conditions. Detailed physical explanations have been provided for the effects of the aforementioned parameters on the mean Nusselt number on the inner periphery. Finally, the new Nusselt number correlations have been proposed for laminar natural convection of both Newtonian and Bingham fluids in square cross-sectioned cylindrical annular enclosures for both constant wall temperature and constant wall heat flux boundary conditions.