A computational study on the effect of magnetohydrodynamic mixed convection of nanofluid flow in a square split lid driven cavity with a block placed near the bottom wall is undertaken. Two different nanoparticles gold and alumina are considered for the study. The observations for the study are obtained by solving the non-dimensionalized governing equations by Finite Element Method with variational approach as accessible with the FreeFEM++ software. The results for different Prandtl numbers (Pr), Richardson number (Ri), volume fractions of nanoparticles , Reynolds number (Re), and MHD parameters (M) are displayed through graphs and figures. It has been observed that the pressure distribution significantly increases with the increment in Reynolds number but both the nanoparticles behave differently. The magnetic field enhancement (M = 0.1, 0.2, 0.5 and 0.9) decreases the velocity within the cavity. The convective heat transfer is faster in the case of Reynolds number (Re) = 100 than in the case of Reynolds number (Re) = 14 or 21. And also increasing the Richardson Number from 0.1 to 1.0, the average Nusselt number shows increment of ∼9.5% and with Ri = 1.0 to 10.0, an increment of ∼3% whereas decrement with higher Reynolds Number (Re = 21, 100) for Gold and Allumina nanoparticles respectively. The present simulations have various applications for the study of natural phenomenon like climate control, meteorological and geophysical activities and industrial applications like cooling of electronics equipment, heat exchanger.
PrandtlL.Über Flüssigkeitsbewegung bei sehr kleiner Reibung. In: Verhandlungen des III. Internationalen Mathematiker Kongresses, Heidelberg, 1904, pp.484–491. Leipzig: B. G. Teubner.
2.
BatchelorGK. On steady laminar flow with closed streamlines at large Reynolds number. J Fluid Mech1956; 1(2): 177–190.
3.
KawagutiM. Numerical solution of the Navier-Stokes equations for the flow in a two-dimensional cavity. J Phys Soc Jpn1961; 16(11): 2307–2315.
4.
BurggrafOR. Analytical and numerical studies of the structure of steady separated flows. J Fluid Mech1966; 24(1): 113–151.
5.
ZhuJHolmedalLEWangH, et al. Vortex dynamics and flow patterns in a two-dimensional oscillatory lid-driven rectangular cavity. Eur J Mech2020; 79: 255–269.
6.
JosserandCRossiM. The merging of two co-rotating vortices: a numerical study. Eur J Mech2007; 26(6): 779–794.
ÖztopHFEstelléPYanWM, et al. A brief review of natural convection in enclosures under localized heating with and without nanofluids. Int Commun Heat Mass Transf2015; 60: 37–44.
9.
ChengMHungKC. Vortex structure of steady flow in a rectangular cavity. Comput Fluids2006; 35(10): 1046–1062.
10.
ShankarPNDeshpandeMD. Fluid mechanics in the driven cavity. Annu Rev Fluid Mech2000; 32(1): 93–136.
11.
BorboraMHVasuBChamkhaAJ. A review study of numerical simulation of lid-driven cavity flow with nanofluids. J Nanofluids2023; 12(3): 589–604.
12.
KuhlmannHCRomanòF. The lid-driven cavity. In: GelfgatA (ed.) Computational modelling of bifurcations and instabilities in fluid dynamics. Cham: Springer, 2019, pp. 233–309.
13.
FerrariMAFrancoAT. Exploring the periodic behavior of the lid-driven cavity flow filled with a Bingham fluid. J Non-Newton Fluid Mech2023; 316: 105030.
14.
JoshiBSenguptaASundaramP. Exploring role of aspect ratio for compressible flow in a rectangular lid-driven cavity with a vertical temperature gradient. Phys Fluids2023; 35(6): 066135. DOI: 10.1063/5.0155851.
15.
LiSGrecovD. Numerical simulation of the 2D lid-driven cavity flow of chiral liquid crystals. Liquid Cryst2023; 50(5): 798–808.
16.
BhattiMMAnwar BégOEllahiR, et al. Electro-magnetohydrodynamics hybrid nanofluid flow with gold and magnesium oxide nanoparticles through vertical parallel plates. J Magn Magn Mater2022; 564: 170136.
17.
SelimefendigilFÖztopHFChamkhaAJ. MHD mixed convection and entropy generation of nanofluid filled lid driven cavity under the influence of inclined magnetic fields imposed to its upper and lower diagonal triangular domains. J Magn Magn Mater2016; 406: 266–281.
18.
YeasminSBillahMMMollaMZ, et al. Numerical analysis of unsteady mixed convection heat transfer characteristics of nanofluids confined within a porous lid-driven L-shaped cavity. International Journal of Thermofluids2022; 16: 100218.
19.
WahidNSArifinNMKhashi'ieNS, et al. Hybrid nanofluid stagnation point flow past a slip shrinking Riga plate. Chin J Phys2022; 78: 180–193.
20.
BatoolSRasoolGAlshammariN, et al. Numerical analysis of heat and mass transfer in micropolar nanofluids flow through lid driven cavity: finite volume approach. Case Stud Therm Eng2022; 37: 102233.
21.
IzadiSArmaghaniTGhasemiaslR, et al. A comprehensive review on mixed convection of nanofluids in various shapes of enclosures. Powder Technol2019; 343: 880–907.
22.
HossainANagPMollaMM. Mesoscopic simulation of MHD mixed convection of non-newtonian ferrofluids with a non-uniformly heated plate in an enclosure. Phys Scr2023; 98(1): 015008.
23.
AhmedSHossainAZahangir HossainM, et al. Forced convection of non-Newtonian nanofluid in a sinusoidal wavy channel with response surface analysis and sensitivity test. Results Eng2023; 19: 101360.
24.
HossainAMollaMMKamrujjamanM, et al. MHD mixed convection of non-Newtonian Bingham nanofluid in a wavy enclosure with temperature-dependent thermophysical properties: a sensitivity analysis by response surface methodology. Energies2023; 16(11): 4408.
25.
ThohuraSHossainAMollaMM. Numerical simulation of thermosolutal natural convection of power-law non-Newtonian fluids in a parallelogram with sensitivity analysis by response surface methodology. Numer Heat Transf A Appl2024; 85: 1–29. DOI: 10.1080/10407782.2023.2298679.
26.
HossainAMollaMM. MHD mixed convection of non-Newtonian power-law ferrofluid in a wavy enclosure. J Therm Anal Calorim2023; 148(21): 11871–11892.
27.
KhanMHossainAParvinA, et al. Implicit finite difference simulation of hybrid nanofluid along a vertical thin cylinder with sinusoidal wall heat flux under the effects of magnetic field. Adv Math Phys2023; 2023(1): 1–18.
28.
ChoiSUEastmanJA. 1995). Enhancing thermal conductivity of fluids with nanoparticles (No. ANL/MSD/CP-84938; CONF-951135-29). Argonne National Lab., IL (United States).
29.
LundH. Renewable energy systems: a smart energy systems approach to the choice and modeling of 100% renewable solutions. Cambridge: Academic Press, 2014.
30.
SheikholeslamiMKhaliliZScardiP, et al. Environmental and energy assessment of photovoltaic-thermal system combined with a reflector supported by nanofluid filter and a sustainable thermoelectric generator. J Clean Prod2024; 438: 140659.
31.
ZafarMHKhanNMMansoorM, et al. Towards green energy for sustainable development: Machine learning based MPPT approach for thermoelectric generator. J Clean Prod2022; 351: 131591
32.
NawaflehASTaamnehYBatainehK. Combined convection heat transfer in a lid driven cavity filled with nanofluids. Heat Transf2023; 52(1): 526–547.
33.
BibiAXuH. Numerical simulation and intelligent prediction of thermal transport of a water-based copper oxide nanofluid in a lid-driven trapezoidal cavity. Phys Fluids2023; 35(9): 093613. DOI: 10.1063/5.0169202.
34.
SheikholeslamiM. Numerical investigation for concentrated photovoltaic solar system in existence of paraffin equipped with MWCNT nanoparticles. Sustain Cities Soc2023; 99: 104901.
35.
SheikholeslamiMKhaliliZ. Solar photovoltaic-thermal system with novel design of tube containing eco-friendly nanofluid. Renew Energy2024; 222: 119862.
36.
SheikholeslamiMKhaliliZ. Environmental and energy analysis for photovoltaic-thermoelectric solar unit in existence of nanofluid cooling reporting CO2 emission reduction. J Taiwan Inst Chem Eng2024; 156: 105341.
37.
PaulANathJMDasTK. Thermally stratified Cu–Al2O3/water hybrid nanofluid flow with the impact of an inclined magnetic field, viscous dissipation and heat source/sink across a vertically stretching cylinder. ZAMM2024; 104(2): e202300084.
38.
PaulAMani NathJKanti DasT. An investigation of the MHD Cu-Al2O3/H2O hybrid-nanofluid in a porous medium across a vertically stretching cylinder incorporating thermal stratification impact. J Therm Eng2023; 9(3): 799–810. DOI: 10.18186/thermal.1300847.
39.
ShiLChewMYL. A review on sustainable design of renewable energy systems. Renew Sustain Energ Rev2012; 16(1): 192–207.
40.
SarmaNPaulA. Thermophoresis and brownian motion influenced bioconvective cylindrical shaped ag–cuo/h2o ellis hybrid nanofluid flow along a radiative stretched tube with inclined magnetic field. BioNanoScience2024; 14(2): 1266–1292.
41.
SoufianeNMustaphaAHZakariaL, et al. Numerical simulation of mixed convection cooling of electronic component within a Lid-Driven cubic cavity filled with nanofluid. ASME J Heat Mass Transf2023; 145(9): 091502. DOI: 10.1115/1.4062564.
KhanZHKhanWAHamidM, et al. Finite element analysis of hybrid nanofluid flow and heat transfer in a split lid-driven square cavity with Y-shaped obstacle. Phys Fluids2020; 32(9): 093609.
44.
RehmanNMahmoodRHussain MajeedA, et al. Finite element analysis on entropy generation in MHD iron(III) oxide-water NanoFluid equipped in partially heated fillet cavity. J Magn Magn Mater2023; 565: 170269.
45.
KoreiZBerrahilFFilaliA, et al. Thermo-magnetic convection analysis of magnetite ferrofluid in an arc-shaped lid-driven electronic chamber with partial heating. J Therm Anal Calorim2023; 148(6): 2585–2604.
46.
HossainAAneeMJThohuraS, et al. Finite difference simulation of free convection of non-Newtonian nanofluids with radiation effects over a truncated wavy cone. Pramana - J Phys2023; 97(4): 168.
47.
AhadJIHossainAParvinA, et al. Magnetohydrodynamics thermosolutal convection of hybrid MWCNT-Fe3O4-water nanofluid along a vertical wavy surface with wall heat and mass flux. Partial Differ Equ Appl Math2024; 10: 100667.
48.
PaulAKanti DasTNathJM. Numerical investigation on the thermal transportation of MHD Cu/Al2 O3-H2O casson-hybrid-nanofluid flow across an exponentially stretching cylinder incorporating heat source. Phys Scr2022; 97(8): 085701.
49.
SheikholeslamiM. Numerical approach for MHD Al2O3-water nanofluid transportation inside a permeable medium using innovative computer method. Comput Methods Appl Mech Eng2019; 344: 306–318.
50.
SheikholeslamiMEllahiR. Three dimensional mesoscopic simulation of magnetic field effect on natural convection of nanofluid. Int J Heat Mass Transf2015; 89: 799–808.
51.
RebeyASajadiSM. Examine the lattice Boltzmann method for the mixed convection simulation of water/Al2O3 nanofluid in a 2D rectangular cavity under radiation with isothermal semicircular obstacles. Eng Anal Bound Elem2023; 149: 27–37.
52.
ZhouJAliMAAlizadehA, et al. Numerical study of mixed convection flow of two-phase nanofluid in a two-dimensional cavity with the presence of a magnetic field by changing the height of obstacles with artificial intelligence: Investigation of entropy production changes and Bejan number. Eng Anal Bound Elem2023; 148: 52–61.
53.
NematiMDavoodabadi FarahaniSArmaghaniT. A LBM entropy calculation caused by hybrid nanofluid mixed convection under the effect of changing the kind of magnetic field and other active/passive methods. J Magn Magn Mater2023; 566: 170277.
54.
AnqiAE. The use of staggered grid in numerical solution of nanofluid convection within a rectangular chamber with semicircular fins and the use of artificial neural networks in optimizing dimensionless numbers. Eng Anal Bound Elem2023; 146: 418–435.
55.
BarnoonPToghraieDDehkordiRB, et al. MHD mixed convection and entropy generation in a lid-driven cavity with rotating cylinders filled by a nanofluid using two phase mixture model. J Magn Magn Mater2019; 483: 224–248.
56.
NabweyHARashadAMMansourMA, et al. Magneto-nanofluid flow via mixed convection inside E-shaped square chamber. Symmetry2022; 14(6): 1159.
57.
TiwariRKDasMK. Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids. Int J Heat Mass Transf2007; 50(9–10): 2002–2018.
58.
HappelJBrennerH. Low Reynolds number hydrodynamics. Englewood Cliffs, NJ: Prentice Hall Inc., 1965, p.331.
59.
BatchelorGK. The stress system in a suspension of force-free particles. J Fluid Mech1970; 41(3): 545–570.
60.
GibanovNSSheremetMAOztopHF, et al. Convective heat transfer in a lid-driven cavity with a heat-conducting solid backward step under the effect of buoyancy force. Int J Heat Mass Transf2017; 112: 158–168.
61.
DubeyAVasuB. Finite element analysis of MHD blood flow in stenosed coronary artery with the suspension of nanoparticles. In: International conference on mathematical modelling and scientific computation, July 2018, pp.219–239. Singapore: Springer.
62.
FarooqMAhmadSJavedM, et al. Analysis of Cattaneo-Christov heat and mass fluxes in the squeezed flow embedded in porous medium with variable mass diffusivity. Results Phys2017; 7: 3788–3796.
63.
SheikholeslamiMVajraveluK. Nanofluid flow and heat transfer in a cavity with variable magnetic field. Appl Math Comput2017; 298: 272–282.
64.
RashidiMMSadriMSheremetMA. Numerical simulation of hybrid nanofluid mixed convection in a lid-driven square cavity with magnetic field using high-order compact scheme. Nanomater2021; 11(9): 2250.
65.
ShulepovaEVSheremetMAOztopHF, et al. Mixed convection of Al2O3–H2O nanoliquid in a square chamber with complicated fin. Int J Mech Sci2020; 165: 105192.
DubeyAVasuBAnwar BégO, et al. Computational fluid dynamic simulation of two-fluid non-Newtonian nanohemodynamics through a diseased artery with a stenosis and aneurysm. Comput Methods Biomech Biomed Eng2020; 23(8): 345–371.
68.
DubeyAVasuBBégOA, et al. Finite element computation of magneto-hemodynamic flow and heat transfer in a bifurcated artery with saccular aneurysm using the Carreau-Yasuda biorheological model. Microvasc Res2021; 138: 104221.
69.
VasuBDubeyABégOA. Finite element analysis of non-Newtonian magnetohemodynamic flow conveying nanoparticles through a stenosed coronary artery. Heat Transf Asian Res2020; 49(1): 33–66.
70.
HussainSÖztopHFMehmoodK, et al. Effects of inclined magnetic field on mixed convection in a nanofluid filled double lid-driven cavity with volumetric heat generation or absorption using finite element method. Chin J Phys2018; 56(2): 484–501.
71.
HussainSJamalMGeridonmezBP. Impact of fins and inclined magnetic field in double lid-driven cavity with Cu–water nanofluid. Int J Therm Sci2021; 161: 106707.
72.
WernerCGorlaRSR. Probabilistic study of bone remodeling using finite element analysis. Int J Appl Mech Eng2013; 18(3): 911–921.
73.
BatheKJ. Finite element procedures. Klaus-Jurgen Bathe, UK: Prentice Hall, 2006.
74.
AhmedSChenZMXuH, et al. Mixed convection flow in a square lid-driven cavity subject to inclined magnetic field with highly accurate wavelet-homotopy solutions. Comput Math Appl2024; 162: 33–51.
