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Computational Thermal Sciences: An International Journal
ESCI SJR: 0.244 SNIP: 0.434 CiteScore™: 0.7

ISSN Imprimir: 1940-2503
ISSN En Línea: 1940-2554

Computational Thermal Sciences: An International Journal

DOI: 10.1615/ComputThermalScien.2012004759
pages 77-97


Osman Turan
Deptartment of Mechanical Engineering, Karadeniz Technical University, Turkey
Robert J. Poole
School of Engineering, University of Liverpool, Brownlow Hill, Liverpool, L69 3GH, UK
Nilanjan Chakraborty
School of Mechanical and Systems Engineering, Newcastle University, Newcastle-Upon-Tyne, NE17RU, United Kingdom


Natural convection of Bingham fluids in square enclosures with differentially heated horizontal walls has been numerically analyzed for both constant wall temperature (CWT) and constant wall heat flux (CWHF) boundary conditions for different values of Bingham number Bn (i.e., nondimensional yield stress) for nominal Rayleigh and Prandtl numbers ranging from 103 to 105 and from 0.1 to 100, respectively. A semi-implicit pressure-based algorithm is used to solve the steady-state governing equations in the context of the finite-volume methodology in two dimensions. It has been found that the mean Nusselt number Nu increases with increasing Rayleigh number, but Nu is found to be smaller in Bingham fluids than in Newtonian fluids (for the same nominal values of Rayleigh and Prandtl numbers) due to augmented flow resistance in Bingham fluids. Moreover, Nu monotonically decreases with increasing Bingham number irrespective of the boundary condition. Bingham fluids exhibit nonmonotonic Prandtl number Pr dependence on Nu and a detailed physical explanation has been provided for this behavior. Although variation of Nu in response to changes in Rayleigh, Prandtl, and Bingham numbers remains qualitatively similar for both CWT and CWHF boundary conditions, Nu for the CWHF boundary condition for high values of Rayleigh number is found to be smaller than the value obtained for the corresponding CWT configuration for a given set of values of Prandtl and Bingham numbers. The physical reasons for the weaker convective effects in the CWHF boundary condition than in the CWT boundary condition, especially for high values of Rayleigh number, have been explained through a detailed scaling analysis. The scaling relations are used to propose correlations for Nu for both CWT and CWHF boundary conditions and the correlations are shown to capture Nu satisfactorily for the range of Rayleigh, Prandtl, and Bingham numbers considered in this analysis.