Al-Qadisiyah Journal for Engineering Sciences

3D-Numerical simulation of free convection inside a cubical cavity filled with non-Newtonian-Bingham fluid

Document Type : Research Paper

Authors

Mohammed Keddar 1
Belkacem Draoui 1
Brahim Mebarki 1
Marc Medale 2
Kada Benhanifia 1

1 Laboratory of Arid Zones Energetic - (ENERGARID), Faculty of Technology, University of Tahri Mohamed Bechar, BP 417 (08000), Bechar, Algeria

2 Université Aix-Marseille, Polytech Marseille, Dépt Mécanique Energétique Laboratoire IUSTI, UMR 7343 CNRS-Université Aix-Marseille Technopole de Chateau-Gombert, 5 rue Enrico Fermi 13453 MARSEILLE, Cedex 13, France

10.30772/qjes.2024.150673.1271
Abstract
This work focuses on a numerical study of the natural convection of a non-Newtonian viscoplastic fluid within a cubic enclosure. The viscoplastic behavior is described by the Bingham model. The considered three-dimensional convective flow is confined within a cavity, subjected to a horizontal temperature gradient, where the vertical walls have two imposed temperatures while the rest of the walls are adiabatic. The Navier-Stokes equations, along with the mass and energy conservation equations, are numerically solved. Fluid flow and heat transfer characteristics are systematically studied over a wide range of Rayleigh numbers Ra (103 - 106) and Bingham number Bn (0 - 20). Finally, comparisons were made with previous results obtained in two dimensions in order to analyze the existence of a three-dimensional effect on the flow of the Bingham fluid. The results show that the Nusselt number decreases with the increase of the Bingham number, and for the large values ​​of the latter the heat transfer is done by conduction. It is also noteworthy that the critical Bn of the 2D model is higher than that of the 3D model, which confirms the existence of the three-dimensional effect. This is attributed to the presence of a wall along the Z axis which hinders and limits the flow of fluid within the enclosure.

Keywords

Natural convection
Non-Newtonian fluid
Bingham fluid
3D Numerical simulation
Cubical Cavity
  • E. C. Bingham, An investigation of the laws of plastic flow, no. 278. US Government Printing Office, 1917.
  • W. H. Herschel and R. Bulkley, “Calibration of the Buret consistometer,” Ind Eng Chem, vol. 19, no. 1, pp. 134–139, 1927.
  • M. Aneja, A. Chandra, and S. Sharma, “Natural convection in a partially heated porous cavity to Casson fluid,” International Communications in Heat and Mass Transfer, vol. 114, p. 104555, 2020.
  • K. Benhanifia et al., “Investigation of mixing viscoplastic fluid with a modified anchor impeller inside a cylindrical stirred vessel using Casson–Papanastasiou model,” Sci Rep, vol. 12, no. 1, pp. 1–19, 2022.
  • V. De Graef, F. Depypere, M. Minnaert, and K. Dewettinck, “Chocolate yield stress as measured by oscillatory rheology,” Food Research International, vol. 44, no. 9, pp. 2660–2665, 2011.
  • M. A. Rao and M. A. Rao, “Flow and functional models for rheological properties of fluid foods,” Rheology of fluid, semisolid, and solid foods: Principles and applications, pp. 27–61, 2014.
  • F. Ali, N. A. Sheikh, I. Khan, and M. Saqib, “Magnetic field effect on blood flow of Casson fluid in axisymmetric cylindrical tube: A fractional model,” J Magn Magn Mater, vol. 423, pp. 327–336, 2017.
  • M. W. S. Khan and N. Ali, “Theoretical analysis of thermal entrance problem for blood flow: an extension of classical Graetz problem for Casson fluid model using generalized orthogonality relations,” International Communications in Heat and Mass Transfer, vol. 109, p. 104314, 2019.
  • M. S. Sadeghi, T. Tayebi, A. S. Dogonchi, M. K. Nayak, and M. Waqas, “Analysis of thermal behavior of magnetic buoyancy-driven flow in ferrofluid–filled wavy enclosure furnished with two circular cylinders,” International Communications in Heat and Mass Transfer, vol. 120, p. 104951, 2021.
  • M. A. Ghurban, K. Al-Farhany, and K. Benhanifia, “Effects of Fin on mixed convection heat transfer in a vented square cavity: A numerical study,” 2023.
  • A. M. Barik and K. Al-Farhany, “Numerical investigation of the effect of baffle inclination angle on nanofluid natural convection heat transfer in a square enclosure,” Al-Qadisiyah Journal for engineering sciences, vol. 12, no. 2, pp. 61–71, 2019.
  • Q.-H. Deng and J.-J. Chang, “Natural convection in a rectangular enclosure with sinusoidal temperature distributions on both side walls,” Numeri Heat Transf A Appl, vol. 54, no. 5, pp. 507–524, 2008.
  • A. Bejan, “Convection heat transfer, Wiley,” New York, 1984.
  • G. de Vahl Davis, “Natural convection of air in a square cavity: a bench mark numerical solution,” Int J Numer Methods Fluids, vol. 3, no. 3, pp. 249–264, 1983.
  • A. Vikhansky, “On the onset of natural convection of Bingham liquid in rectangular enclosures,” J Nonnewton Fluid Mech, vol. 165, no. 23–24, pp. 1713–1716, 2010.
  • A. Boutra, Y. K. Benkahla, D. E. Ameziani, and N. Labsi, “Etude numérique du transfert de chaleur pour un fluide de Bingham dans une cavité carrée en mode de convection naturelle instationnaire,” in CFM 2011-20ème Congrès Français de Mécanique, AFM, Maison de la Mécanique, 39/41 rue Louis Blanc-92400 Courbevoie, 2011.
  • I. Karimfazli and I. A. Frigaard, “Natural convection flows of a Bingham fluid in a long vertical channel,” J Nonnewton Fluid Mech, vol. 201, pp. 39–55, 2013.
  • M. Sairamu, N. Nirmalkar, and R. P. Chhabra, “Natural convection from a circular cylinder in confined Bingham plastic fluids,” Int J Heat Mass Transf, vol. 60, pp. 567–581, 2013.
  • G. H. R. Kefayati, “Lattice Boltzmann method for natural convection of a Bingham fluid in a porous cavity,” Physica A: Statistical Mechanics and Its Applications, vol. 521, pp. 146–172, 2019.
  • G. H. R. Kefayati, “Double-diffusive natural convection and entropy generation of Bingham fluid in an inclined cavity,” Int J Heat Mass Transf, vol. 116, pp. 762–812, 2018.
  • F. Danane, A. Boudiaf, O. Mahfoud, S.-E. Ouyahia, N. Labsi, and Y. K. Benkahla, “Effect of backward facing step shape on 3D mixed convection of Bingham fluid,” International journal of thermal sciences, vol. 147, p. 106116, 2020.
  • P. R. M. Santos, A. Lugarini, S. L. M. Junqueira, and A. T. Franco, “Natural convection of a viscoplastic fluid in an enclosure filled with solid obstacles,” International Journal of Thermal Sciences, vol. 166, p. 106991, 2021.
  • O. Turan, R. J. Poole, and N. Chakraborty, “Aspect ratio effects in laminar natural convection of Bingham fluids in rectangular enclosures with differentially heated side walls,” J Nonnewton Fluid Mech, vol. 166, no. 3–4, pp. 208–230, 2011.
  • O. Turan, N. Chakraborty, and R. J. Poole, “Laminar natural convection of Bingham fluids in a square enclosure with differentially heated side walls,” J Nonnewton Fluid Mech, vol. 165, no. 15–16, pp. 901–913, 2010.
  • M. A. Hassan, M. Pathak, M. K. Khan, and N. H. Khan, “Natural convection of viscoplastic fluids in an enclosure with partially heated bottom wall,” International Journal of Thermal Sciences, vol. 158, p. 106527, 2020.
  • H. Abderrahmane, D. Salah-Eddine, and N. Ait-Messaoudene, “Natural convection for a Herschel-Bulkely fluid inside a differentially heated square cavity,” International Journal of Mechanics and Energy (IJME), vol. 6, no. 1, pp. 7–15, 2018.
  • R. R. Huilgol and G. H. R. Kefayati, “Natural convection problem in a Bingham fluid using the operator-splitting method,” J Nonnewton Fluid Mech, vol. 220, pp. 22–32, 2015.
  • S. Bijjam and A. K. Dhiman, “CFD analysis of two-dimensional non-Newtonian power-law flow across a circular cylinder confined in a channel,” Chem Eng Commun, vol. 199, no. 6, pp. 767–785, 2012.
  • B. Mebarki et al., “A CFD examination of free convective flow of a non-Newtonian viscoplastic fluid using ANSYS Fluent,” Arabian Journal of Chemistry, vol. 16, no. 12, p. 105309, 2023.
  • Mohammed, K., Belkacem, D., Brahim, M., & Marc, M. (2023). Rayleigh Benard convection of Bingham fluid in a square enclosure with sinusoidal temperatures. Proceedings of the 9th World Congress on Mechanical, Chemical, and Material Engineering, 1–8. https://doi.org/10.11159/htff23.14
  • Mohammed, K., Belkacem, D., Brahim, M., & Marc, M. (2023). Natural Rayleigh   Benard Convection of Bingham Fluid in Enclosure Cavity with Sinusoidal Profiles. International Conference on Fluid Flow, Heat and Mass Transfer, 127. https://doi.org/10.11159/ehst23.127
Al-Qadisiyah Journal for Engineering Sciences
Volume 17, Issue 3
Summer 2024
Pages 273-281

  • Receive Date 15 March 2024
  • Revise Date 14 May 2024
  • Accept Date 10 September 2024

Submit Manuscript

Guide for Authors

Article Processing Charges (APC)

Reviewers

Call for Reviewers

Contact Us