Natural convection in nanofluid-filled quadrantal cavities under magnetic field: Application of the SUPS formulation

References

• D. Wen, G. Lin, S. Vafaei, and K. Zhang, “Review of nanofluids for heat transfer applications,” Particuology, vol. 7, no. 2, pp. 141–150, 2009. DOI: 10.1016/j.partic.2009.01.007.
   Web of Science ®Google Scholar
• D. S. Saidina, M. Z. Abdullah, and M. Hussin, “Metal oxide nanofluids in electronic cooling: a review,” J. Mater. Sci.: Mater. Electron, vol. 31, no. 6, pp. 4381–4398, 2020. DOI: 10.1007/s10854-020-03020-7.
   Web of Science ®Google Scholar
• B. Bhanvase and D. Barai, Nanofluids for Heat and Mass Transfer: Fundamentals, Sustainable Manufacturing and Applications. Cambridge, MA, USA: Academic Press, 2021, DOI: 10.1016/c2019-0-03241-4.
   Google Scholar
• A. Kambli and P. Dey, “A critical review on recent developments and applications of microchannels in the field of heat transfer and energy,” Heat Mass Transf., vol. 59, no. 9, pp. 1707–1747, 2023. DOI: 10.1007/s00231-023-03358-8.
   Web of Science ®Google Scholar
• I. Babuška, “The finite element method with Lagrangian multipliers,” Numer. Math., vol. 20, no. 3, pp. 179–192, 1973. DOI: 10.1007/BF01436561.
   Web of Science ®Google Scholar
• F. Brezzi, “On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers,” R.A.I.R.O. Analyse Numérique, vol. 8, no. R2, pp. 129–151, 1974. DOI: 10.1051/m2an/197408R201291.
   Google Scholar
• T. E. Tezduyar and T. J. R. Hughes, “Development of time-accurate finite element techniques for first-order hyperbolic systems with particular emphasis on the compressible Euler equations,” NASA Technical Report. NASA-CR-204772, NASA, 1982.
   Google Scholar
• T. E. Tezduyar and T. J. R. Hughes, “Finite element formulations for convection dominated flows with particular emphasis on the compressible Euler equations,” Proceedings of AIAA 21st Aerospace Sciences Meeting, AIAA Paper 83-0125. DOI: 10.2514/6.1983-125.
   Google Scholar
• T. J. R. Hughes and T. E. Tezduyar, “Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations,” Comput. Methods Appl. Mech. Eng., vol. 45, no. 1–3, pp. 217–284, 1984. DOI: 10.1016/0045-7825(84)90157-9.
   Web of Science ®Google Scholar
• T. J. R. Hughes and A. N. Brooks, “A multi-dimensional upwind scheme with no crosswind diffusion,” in Finite Element Methods for Convection Dominated Flows, AMD, vol. 34, T. J. R. Hughes, Ed. New York: ASME, 1979, pp. 19–35.
   Google Scholar
• A. N. Brooks and T. J. R. Hughes, “Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations,” Comput. Methods Appl. Mech. Eng., vol. 32, no. 1–3, pp. 199–259, 1982. DOI: 10.1016/0045-7825(82)90071-8.
   Web of Science ®Google Scholar
• T. E. Tezduyar, S. Mittal, and R. Shih, “Time-accurate incompressible flow computations with quadrilateral velocity-pressure elements,” Comput. Methods Appl. Mech. Eng., vol. 87, no. 2–3, pp. 363–384, 1991. DOI: 10.1016/0045-7825(91)90014-W.
   Web of Science ®Google Scholar
• T. E. Tezduyar, “Stabilized finite element formulations for incompressible flow computations,” Adv. Appl. Mech., vol. 28, pp. 1–44, 1992. DOI: 10.1016/S0065-2156(08)70153-4.
   Google Scholar
• T. J. R. Hughes, L. P. Franca, and G. M. Hulbert, “A new finite element formulation for computational fluid dynamics: VIII. the Galerkin/least-squares method for advective-diffusive equations,” Comput. Methods Appl. Mech. Eng., vol. 73, no. 2, pp. 173–189, 1989. DOI: 10.1016/0045-7825(89)90111-4.
   Web of Science ®Google Scholar
• T. E. Tezduyar and Y. Osawa, “Finite element stabilization parameters computed from element matrices and vectors,” Comput. Methods Appl. Mech. Eng., vol. 190, no. 3–4, pp. 411–430, 2000. DOI: 10.1016/S0045-7825(00)00211-5.
   Web of Science ®Google Scholar
• L. P. Franca and F. Valentin, “On an improved unusual stabilized finite element method for the advective–reactive–diffusive equation,” Comput. Methods Appl. Mech. Eng., vol. 190, no. 13–14, pp. 1785–1800, 2000. DOI: 10.1016/s0045-7825(00)00190-0.
   Web of Science ®Google Scholar
• T. Tezduyar and S. Sathe, “Stabilization parameters in SUPG and PSPG formulations,” J. Comput. Appl. Mech., vol. 4, pp. 71–88, 2003.
   Google Scholar
• T.-P. Fries and H. G. Matthies, A review of Petrov-Galerkin stabilization approaches and an extension to meshfree methods, technical report 2004-01. Institute of Scientific Computing, Technical University Braunschweig, 2004. DOI: 10.24355/DBBS.084-200511080100-466.
   Google Scholar
• V. John and P. Knobloch, “On spurious oscillations at layers diminishing (SOLD) methods for convection-diffusion equations: part I–A review,” Comput. Methods Appl. Mech. Eng., vol. 196, no. 17–20, pp. 2197–2215, 2007. DOI: 10.1016/j.cma.2006.11.013.
   Web of Science ®Google Scholar
• V. John and P. Knobloch, “On spurious oscillations at layers diminishing (SOLD) methods for convection-diffusion equations: part II–Analysis for P1 and Q1 finite elements,” Comput. Methods Appl. Mech. Eng., vol. 197, no. 21–24, pp. 1997–2014, 2008. DOI: 10.1016/j.cma.2007.12.019.
   Web of Science ®Google Scholar
• V. John and E. Schmeyer, “Finite element methods for time-dependent convection–diffusion–reaction equations with small diffusion,” Comput. Methods Appl. Mech. Eng., vol. 198, no. 3–4, pp. 475–494, 2008. DOI: 10.1016/j.cma.2008.08.016.
   Web of Science ®Google Scholar
• T. E. Tezduyar and M. Senga, “Stabilization and shock-capturing parameters in SUPG formulation of compressible flows,” Comput. Methods Appl. Mech. Eng., vol. 195, no. 13–16, pp. 1621–1632, 2006. DOI: 10.1016/j.cma.2005.05.032.
   Web of Science ®Google Scholar
• B. Ghasemi, S. M. Aminossadati, and A. Raisi, “Magnetic field effect on natural convection in a nanofluid-filled square enclosure,” Int. J. Therm. Sci., vol. 50, no. 9, pp. 1748–1756, 2011. DOI: 10.1016/j.ijthermalsci.2011.04.010.
   Web of Science ®Google Scholar
• S. V. Patankar, Numerical Heat Transfer and Fluid Flow. New York: McGraw Hill, 1980, DOI: 10.1201/9781482234213.
   Google Scholar
• H. F. Oztop, K. Al-Salem, and I. Pop, “MHD mixed convection in a lid-driven cavity with corner heater,” Int. J. Heat Mass Transf., vol. 54, no. 15–16, pp. 3494–3504, 2011. 2011.03.036. DOI: 10.1016/j.ijheatmasstransfer.
   Web of Science ®Google Scholar
• A. H. Mahmoudi, I. Pop, and M. Shahi, “Effect of magnetic field on natural convection in a triangular enclosure filled with nanofluid,” Int. J. Therm. Sci., vol. 59, pp. 126–140, 2012. DOI: 10.1016/j.ijthermalsci.2012.04.006.
   Web of Science ®Google Scholar
• M. Sheikholeslami and R. Ellahi, “Three dimensional mesoscopic simulation of magnetic field effect on natural convection of nanofluid,” Int. J. Heat Mass Transf., vol. 89, pp. 799–808, 2015. DOI: 10.1016/j.ijheatmasstransfer.2015.05.110.
   Web of Science ®Google Scholar
• M. Mamourian, K. Milani Shirvan, and I. Pop, “Sensitivity analysis for MHD effects and inclination angles on natural convection heat transfer and entropy generation of Al2O3-water nanofluid in square cavity by response surface methodology,” Int. Commun. Heat Mass Transf., vol. 79, pp. 46–57, 2016. DOI: 10.1016/j.icheatmasstransfer.2016.10.001.
   Web of Science ®Google Scholar
• K. Ghasemi and M. Siavashi, “MHD nanofluid free convection and entropy generation in porous enclosures with different conductivity ratios,” J. Mag. Magn. Mater., vol. 442, pp. 474–490, 2017. DOI: 10.1016/j.jmmm.2017.07.028.
   Web of Science ®Google Scholar
• R. Sarlak, S. Yousefzadeh, O. A. Akbari, D. Toghraie, S. Sarlak, and F. Assadi, “The investigation of simultaneous heat transfer of water/Al2O3 nanofluid in a close enclosure by applying homogeneous magnetic field,” Int. J. Mech. Sci., vol. 133, pp. 674–688, 2017. DOI: 10.1016/j.ijmecsci.2017.09.035.
   Web of Science ®Google Scholar
• M. Sheikholeslami, “Numerical simulation of magnetic nanofluid natural convection in porous media,” Phys. Lett. A, vol. 381, no. 5, pp. 494–503, 2017. DOI: 10.1016/j.physleta.2016.11.042.
   Web of Science ®Google Scholar
• B. R. Baliga and S. V. Patankar, “A new finite element formulation for convection-diffusion problems,” Numer. Heat Transf., vol. 3, no. 4, pp. 393–409, 1980. DOI: 10.1080/01495728008961767.
   Google Scholar
• M. A. Mansour, S. Siddiqa, R. S. R. Gorla, and A. M. Rashad, “Effects of heat source and sink on entropy generation and MHD natural convection of Al2O3-Cu/water hybrid nanofluid filled with square porous cavity,” Therm. Sci. Eng. Prog., vol. 6, pp. 57–71, 2018. DOI: 10.1016/j.tsep.2017.10.014.
   Google Scholar
• A. M. Rashad, A. J. Chamkha, M. A. Ismael, and T. Salah, “Magnetohydrodynamics natural convection in a triangular cavity filled with a Cu-Al2O3/water hybrid nanofluid with localized heating from below and internal heat generation,” J. Heat Transf., vol. 140, no. 7, pp. 072502, 2018. DOI: 10.1115/1.4039213.
   Web of Science ®Google Scholar
• B. P. Geridonmez and H. F. Oztop, “MHD natural convection in a cavity in the presence of cross partial magnetic fields and Al2O3-water nanofluid,” Comput. Math. Appl., vol. 80, no. 12, pp. 2796–2810, 2020. DOI: 10.1016/j.camwa.2020.10.003.
   Web of Science ®Google Scholar
• C. Revnic, T. Groşan, M. Sheremet, and I. Pop, “Numerical simulation of MHD natural convection flow in a wavy cavity filled by a hybrid Cu-Al2O3-water nanofluid with discrete heating,” Appl. Math. Mech.-Engl. Ed., vol. 41, no. 9, pp. 1345–1358, 2020. DOI: 10.1007/s10483-020-2652-8.
   Google Scholar
• M. S. Sadeghi, T. Tayebi, A. S. Dogonchi, T. Armaghani, and P. Talebizadehsardari, “Analysis of hydrothermal characteristics of magnetic Al2O3-H2O nanofluid within a novel wavy enclosure during natural convection process considering internal heat generation,” Math Meth. App. Sci., pp. 1–13, 2020. DOI: 10.1002/mma.6520.
   Web of Science ®Google Scholar
• S. K. Saha, “Magnetohydrodynamic buoyancy driven Al2O3-water nanofluid flow in a differentially heated trapezoidal enclosure with a cylindrical barrier,” Int. Commun. Heat Mass Transf., vol. 114, pp. 104593, 2020. DOI: 10.1016/j.icheatmasstransfer.2020.104593.
   Web of Science ®Google Scholar
• S. Dutta, S. Pati, and L. Baranyi, “Numerical analysis of magnetohydrodynamic natural convection in a nanofluid filled quadrantal enclosure,” Case Stud. Therm. Eng., vol. 28, pp. 101507, 2021. DOI: 10.1016/j.csite.2021.101507.
   Web of Science ®Google Scholar
• M. Nemati, H. M. Sani, R. Jahangiri, and A. J. Chamkha, “MHD natural convection in a cavity with different geometries filled with a nanofluid in the presence of heat generation/absorption using lattice Boltzmann method,” J. Therm. Anal. Calorim., vol. 147, no. 16, pp. 9067–9081, 2022. DOI: 10.1007/s10973-022-11204-y.
   Web of Science ®Google Scholar
• C. Sivaraj, S. Gowtham, M. Elango, and M. A. Sheremet, “Analysis of thermo-magnetic convection and entropy generation of Al2O3-water nanofluid in a partially heated wavy electronic cabinet,” Int. Commun. Heat Mass Transf., vol. 133, pp. 105955, 2022. DOI: 10.1016/j.icheatmasstransfer.2022.105955.
   Web of Science ®Google Scholar
• I. Haq et al., “Impact of homogeneous and heterogeneous reactions in the presence of hybrid nanofluid flow on various geometries,” Front Chem., vol. 10, pp. 1032805, 2022. DOI: 10.3389/fchem.2022.1032805.
   PubMed Web of Science ®Google Scholar
• R. Hossain, M. J. Hasan, A. K. Azad, and M. M. Rahman, “Numerical study of low Reynolds number effect on MHD mixed convection using CNT-oil nanofluid with radiation,” Res. Eng., vol. 14, pp. 100446, 2022. DOI: 10.1016/j.rineng.2022.100446.
   Google Scholar
• R. S. Varun Kumar, R. N. Kumar, S. Ben Ahmed, J. Madhu, A. Verma, and R. J. Punith Gowda, “Unsteady flow of a ternary nanofluid over a slow-rotating disk subject to uniform suction and backpropagated neural network,” Numer. Heat Transf. Part B: Fund., pp. 1–21, 2023. DOI: 10.1080/10407790.2023.2269610.
   Web of Science ®Google Scholar
• P. Srilatha, R. S. V. Kumar, R. N. Kumar, R. J. P. Gowda, A. Abdulrahman, and B. C. Prasannakumara, “Impact of solid-fluid interfacial layer and nanoparticle diameter on Maxwell nanofluid flow subjected to variable thermal conductivity and uniform magnetic field,” Heliyon, vol. 9, no. 11, pp. e21189, 2023. DOI: 10.1016/j.heliyon.2023.e21189.
   PubMed Web of Science ®Google Scholar
• A. K. Azad, M. J. Hasan, M. F. Karim, E. M. Morshed Alam, and M. M. Rahman, “Rotational effect of a cylinder on hydro-thermal characteristics in a partially heated square enclosure using CNT-water nanofluid,” Heliyon, vol. 9, no. 12, pp. e22744, 2023. DOI: 10.1016/j.heliyon.2023.e22744.
   PubMed Web of Science ®Google Scholar
• M. K. Nayak, A. S. Dogonchi, and A. Rahbari, “Free convection of Al2O3-water nanofluid inside a hexagonal-shaped enclosure with cold diamond-shaped obstacles and periodic magnetic field,” Case Stud. Therm. Eng., vol. 50, pp. 103429, 2023. DOI: 10.1016/j.csite.2023.103429.
   Web of Science ®Google Scholar
• T. Saha, T. Islam, S. Yeasmin, and N. Parveen, “Thermal influence of heated fin on MHD natural convection flow of nanofluids inside a wavy square cavity,” Int. J. Thermofl., vol. 18, pp. 100338, 2023. DOI: 10.1016/j.ijft.2023.100338.
   Google Scholar
• A. V. Roşca, N. C. Roşca, I. Pop, and M. A. Sheremet, “Natural convection and entropy generation in a trapezoidal region with hybrid nanoliquid under magnetic field,” HFF, vol. 34, no. 2, pp. 429–450, 2023. DOI: 10.1108/HFF-04-2023-0193.
   Web of Science ®Google Scholar
• M. Hasan, A. K. Azad, R. Hossain, M. M. Rahman, and M. F. Karim, “Analysis of mixed convection under radiation and magnetohydrodynamics utilizing Kerosene-CNT nanofluid in a lid-driven cavity,” Int. J. Thermofl., vol. 21, pp. 100528, 2024. DOI: 10.1016/j.ijft.2023.100528.
   Google Scholar
• S. Cengizci, H. F. Öztop, and G. Mülayim, “Stabilized finite element simulation of natural convection in square cavities filled with nanofluids under various temperature boundary conditions,” Int. Commun. Heat Mass Transf., vol. 156, pp. 107655, 2024. DOI: 10.1016/j.icheatmasstransfer.2024.107655.
   Web of Science ®Google Scholar
• H. C. Brinkman, “The viscosity of concentrated suspensions and solutions,” J. Chem. Phys., vol. 20, no. 4, pp. 571–571, 1952. DOI: 10.1063/1.1700493.
   Web of Science ®Google Scholar
• K. Khanafer, K. Vafai, and M. Lightstone, “Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids,” Int. J. Heat Mass Transf., vol. 46, no. 19, pp. 3639–3653, 2003. DOI: 10.1016/s0017-9310(03)00156-x.
   Web of Science ®Google Scholar
• J. C. Maxwell, A Treatise on Electricity and Magnetism, vol. 1. Oxford, England: Clarendon Press, 1873,
   Google Scholar
• G. A. Sheikhzadeh, A. Arefmanesh, M. H. Kheirkhah, and R. Abdollahi, “Natural convection of Cu–water nanofluid in a cavity with partially active side walls,” European J. Mech.–B/Fluids, vol. 30, no. 2, pp. 166–176, 2011. DOI: 10.1016/j.euromechflu.2010.10.003.
   Web of Science ®Google Scholar
• K. Takizawa and T. E. Tezduyar, “Multiscale space–time fluid–structure interaction techniques,” Comput. Mech., vol. 48, no. 3, pp. 247–267, 2011. DOI: 10.1007/s00466-011-0571-z.
   Web of Science ®Google Scholar
• T. E. Tezduyar, S. Mittal, S. E. Ray, and R. Shih, “Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements,” Comput. Methods Appl. Mech. Eng., vol. 95, no. 2, pp. 221–242, 1992. DOI: 10.1016/0045-7825(92)90141-6.
   Web of Science ®Google Scholar
• F. Shakib, “Finite element analysis of the compressible Euler and Navier-Stokes equations,” Ph.D. thesis, Department of Mechanical Engineering, Stanford University, 1988.
   Google Scholar
• T. E. Tezduyar, S. Ramakrishnan, and S. Sathe, “Stabilized formulations for incompressible flows with thermal coupling,” Numer. Methods Fluids, vol. 57, no. 9, pp. 1189–1209, 2008. DOI: 10.1002/fld.1743.
   Web of Science ®Google Scholar
• T. E. Tezduyar, “Computation of moving boundaries and interfaces and stabilization parameters,” Numer. Methods Fluids, vol. 43, no. 5, pp. 555–575, 2003. DOI: 10.1002/fld.505.
   Web of Science ®Google Scholar
• T. E. Tezduyar and S. Sathe, “Modeling of fluid–structure interactions with the space–time finite elements: solution techniques,” Numer. Methods Fluids, vol. 54, no. 6–8, pp. 855–900, 2007. DOI: 10.1002/fld.1430.
   Web of Science ®Google Scholar
• Y. Bazilevs, V. M. Calo, T. E. Tezduyar, and T. J. R. Hughes, “Discontinuity capturing for advection-dominated processes with application to arterial drug delivery,” Numer. Methods Fluids, vol. 54, no. 6–8, pp. 593–608, 2007. DOI: 10.1002/fld.1484.
   Web of Science ®Google Scholar
• S. Cengizci and O. Uğur, “SUPG formulation augmented with YZβ shock-capturing for computing shallow-water equations,” ZAMM – J. Appl. Math. Mech./Zeitschrift Für Angewandte Mathematik Und Mechanik, vol. 103, 2023a. DOI: 10.1002/zamm.202200232.
   Web of Science ®Google Scholar
• S. Cengizci and O. Uğur, “A stabilized FEM formulation with discontinuity-capturing for solving Burgers’-type equations at high Reynolds numbers,” Appl. Math. Comput., vol. 442, pp. 127705, 2023b. DOI: 10.1016/j.amc.2022.127705.
   Web of Science ®Google Scholar
• S. Cengizci, O. Uğur, and S. Natesan, “A stabilized finite element formulation with shock-capturing for solving advection-dominated convection–diffusion equations having time-fractional derivatives,” J. Comput. Sci., vol. 76, pp. 102214, 2024a. DOI: 10.1016/j.jocs.2024.102214.
   Web of Science ®Google Scholar
• S. Cengizci, O. Uğur, and S. Natesan, “Supg-based stabilized finite element computations of convection-dominated 3D elliptic PDEs using shock-capturing,” J. Comput. Appl. Math., vol. 451, pp. 116022, 2024b. DOI: 10.1016/j.cam.2024.116022.
   Google Scholar
• A. Logg, K.-A. Mardal, and G. Wells, “Automated solution of differential equations by the finite element method: the FEniCS book,” Lecture Notes in Computational Science and Engineering, vol. 84. Berlin Heidelberg: Springer-Verlag, 2012. DOI: 10.1007/978-3-642-23099-8.
   Google Scholar
• B. E. Abali, “Computational reality: solving nonlinear and coupled problems in continuum mechanics,” Advanced Structured Materials, vol. 55. Singapore: Springer, 2016. DOI: 10.1007/978-981-10-2444-3.
   Google Scholar
• M. Alnæs et al., “The FEniCS Project Version 1.5, Archive of numerical software 3,” 2015, pp. 9–23, DOI: 10.11588/ANS.2015.100.20553.
   Google Scholar
• C. Geuzaine and J. Remacle, “Gmsh: a 3-D finite element mesh generator with built-in pre- and post-processing facilities,” Numer. Methods Eng., vol. 79, no. 11, pp. 1309–1331, 2009. DOI: 10.1002/nme.2579.
   Web of Science ®Google Scholar