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BOUNDARY CONDITION EFFECTS ON NATURAL CONVECTION OF BINGHAM FLUIDS IN A SQUARE ENCLOSURE WITH DIFFERENTIALLY HEATED HORIZONTAL WALLS

Volume 4, Issue 1, 2012, pp. 77-97
DOI: 10.1615/ComputThermalScien.2012004759
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ABSTRACT

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.

CITED BY
  1. Turan Osman, Lai Jiawei, Poole Robert J., Chakraborty Nilanjan, Laminar natural convection of power-law fluids in a square enclosure submitted from below to a uniform heat flux density, Journal of Non-Newtonian Fluid Mechanics, 199, 2013. Crossref

  2. Sairamu M., Nirmalkar N., Chhabra R.P., Natural convection from a circular cylinder in confined Bingham plastic fluids, International Journal of Heat and Mass Transfer, 60, 2013. Crossref

  3. Yigit Sahin, Poole Robert J., Chakraborty Nilanjan, Effects of aspect ratio on natural convection of Bingham fluids in rectangular enclosures with differentially heated horizontal walls heated from below, International Journal of Heat and Mass Transfer, 80, 2015. Crossref

  4. Hassan M.A., Pathak Manabendra, Khan Mohd. Kaleem, Rayleigh–Benard convection in Herschel–Bulkley fluid, Journal of Non-Newtonian Fluid Mechanics, 226, 2015. Crossref

  5. Baranwal Ashok K., Chhabra Raj P., Effect of Fluid Yield Stress on Natural Convection From Horizontal Cylinders in a Square Enclosure, Heat Transfer Engineering, 38, 6, 2017. Crossref

  6. Yigit Sahin, Chakraborty Nilanjan, Laminar Natural Convection of Bingham Fluids in Square Cross-Sectioned Cylindrical Annular Cavity with Differentially Heated Vertical Walls Subjected to Constant Heat Fluxes, Heat Transfer Engineering, 38, 13, 2017. Crossref

  7. Yigit Sahin, Chen Siqi, Quinn Paul, Chakraborty Nilanjan, Numerical investigation of laminar Rayleigh-Bénard convection of Bingham fluids in square cross-sectioned cylindrical enclosures, International Journal of Thermal Sciences, 110, 2016. Crossref

  8. Yigit Sahin, Foxon Tom, Chakraborty Nilanjan, Influences of Boundary Condition on Laminar Natural Convection of Bingham Fluids in Square Cross-Sectioned Cylindrical Annular Enclosures with Differentially Heated Vertical Walls, Heat Transfer Engineering, 39, 4, 2018. Crossref

  9. Turan O., Yigit S., Chakraborty N., Critical condition for Rayleigh-Bénard convection of Bingham fluids in rectangular enclosures, International Communications in Heat and Mass Transfer, 86, 2017. Crossref

  10. Yigit Sahin, Chakraborty Nilanjan, Influences of aspect ratio and wall boundary condition on laminar Rayleigh–Bénard convection of Bingham fluids in rectangular enclosures, International Journal of Numerical Methods for Heat & Fluid Flow, 27, 2, 2017. Crossref

  11. Jagnade Sujit, Mishra Lubhani, Baranwal Ashok K., Chhabra Raj P., Laminar Free Convection in Power-law Fluids in a Right Angle Triangular Duct with Heated Base, Heat Transfer Engineering, 40, 19, 2019. Crossref

  12. Yİğİt Şahin, Poole Robert J., Chakraborty Nilanjan, Laminar Natural Convection of Bingham Fluids in Inclined Differentially Heated Square Enclosures Subjected to Uniform Wall Temperatures, Journal of Heat Transfer, 137, 5, 2015. Crossref

  13. Mishra Lubhani, Chhabra R. P., Combined Effects of Fluid Yield Stress and Geometrical Arrangement on Natural Convection in a Square Duct From Two Differentially Heated Horizontal Cylinders, Journal of Thermal Science and Engineering Applications, 12, 1, 2020. Crossref

  14. Yigit Sahin, Hasslberger Josef, Chakraborty Nilanjan, Klein Markus, Effects of Rayleigh-Bénard convection on spectra of viscoplastic fluids, International Journal of Heat and Mass Transfer, 147, 2020. Crossref

  15. Mulamootil Jacob Koshy, Rath Subhasisa, Dash Sukanta Kumar, Relative importance of temperature-dependent properties in non-Newtonian natural convection around curved surfaces, International Communications in Heat and Mass Transfer, 124, 2021. Crossref

  16. Turan Osman, Fotso-Choupe Frank, Lai Jiawei, Poole Robert J., Chakraborty Nilanjan, Boundary Condition Effects on Laminar Natural Convection of Power-Law Fluids in a Square Enclosure Heated from below with Differentially Heated Horizontal Walls, Industrial & Engineering Chemistry Research, 53, 1, 2014. Crossref

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