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Natural convection of multi-walled carbon nanotube–Fe3O4/water magnetic hybrid nanofluid flowing in porous medium considering the impacts of magnetic field-dependent viscosity

  • S. A. M. Mehryan
  • Mohsen Izadi
  • Zafar NamazianEmail author
  • Ali J. Chamkha
Article
  • 16 Downloads

Abstract

The study ahead deals with the natural convection of MWCN–Fe3O4/water magnetic hybrid nanofluid flowing in a porous medium. The flow domain is affected by an inclined magnetic field influencing the dynamic viscosity. The dependency of the flow and heat transfer characteristics on Rayleigh number, Ra = 103–106; Hartman number, Ha = 0–50; inclination angle of the magnetic field, ϕ = 0°–180°; magnetic number, δ0 = 0–2.0; porosity, ε = 0.1–0.9; Darcy number, Da = 10−7–10−1;and volume fraction of the composite nanoparticles, φ = 0, 0.1 and 0.3% is studied numerically. At low Rayleigh number Ra = 104, dispersing the nanocomposite particles increases the average Nusselt number Nuavg, while that decreases the Nuavg when Ra = 105 and 106. The dependency of viscosity on the magnetic field decreases the Nuavg at 0° < ϕ < 135°, which is due to an increase in overall viscosity of the nanofluid. After that (ϕ ≥ 135°), the average Nusselt number is greatly enhanced by increasing ϕ from 135° up to 180°. There is no meaningful change in average Nusselt number of the hybrid nanofluid by increasing the inclination angle of magnetic field in the absence of magnetic field-dependent viscosity (δ0 = 0).

Keywords

MWCN–Fe3O4/water hybrid nanofluid MFD viscosity Porous medium Magnetic field 

List of symbols

Bo

Applied magnetic field

g

Gravitational acceleration

L

Cavity size

Ha

Hartmann number

k

Thermal conductivity

K

Permeability

p

Dimensional pressure

P

Non-dimensional pressure

Pr

Prandtl number

Ra

Thermal Rayleigh number

T

Temperature

x, y

Dimensional Cartesian coordinates

X, Y

Dimensionless Cartesian coordinates

u, v

Components of velocity in x- and y-directions, respectively

Greek symbols

α

Thermal diffusivity

β

Thermal expansion coefficient

θ

Non-dimensional temperature

ε

Porosity

μ

Dynamic viscosity

φ

Volume fraction of nanoparticles

ϕ

Angle of magnetic field

σ

Electrical conductivity

ν

Kinematic viscosity

ρ

Density

Subscripts

bf

Base fluid

c

Cold

h

Hot

hnf

Hybrid nanofluid

np

Nanoparticles

s

Solid

Notes

References

  1. 1.
    Mehryan SA, Kashkooli FM, Soltani M, Raahemifar K. Fluid flow and heat transfer analysis of a nanofluid containing motile gyrotactic micro-organisms passing a nonlinear stretching vertical sheet in the presence of a non-uniform magnetic field; numerical approach. PLoS ONE. 2016;11:e0157598.CrossRefGoogle Scholar
  2. 2.
    Izadi M, Behzadmehr A, Jalali-Vahida D. Numerical study of developing laminar forced convection of a nanofluid in an annulus. Int J Therm Sci. 2009;48:2119–29.CrossRefGoogle Scholar
  3. 3.
    Izadi M, Shahmardan MM, Maghrebi MJ, Behzadmehr A. Numerical study of developed laminar mixed convection of Al2O3/water nanofluid in an annulus. Chem Eng Commun. 2013;200:878–94.CrossRefGoogle Scholar
  4. 4.
    Izadi M, Behzadmehr A, Shahmardan MM. Effects of inclination angle on laminar mixed convection of a nanofluid flowing through an annulus. Chem Eng Commun. 2015;202:1693–702.CrossRefGoogle Scholar
  5. 5.
    Khanafer K, Vafai K, Lightstone M. Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. Int J Heat Mass Transf. 2003;46:3639–53.CrossRefGoogle Scholar
  6. 6.
    Chamkha AJ, Doostanidezfuli A, Izadpanahi E, Ghalambaz M. Phase-change heat transfer of single/hybrid nanoparticles-enhanced phase-change materials over a heated horizontal cylinder confined in a square cavity. Adv Powder Technol. 2017;28:385–97.CrossRefGoogle Scholar
  7. 7.
    Ghalambaz M, Doostani A, Izadpanahi E, Chamkha AJ. Phase-change heat transfer in a cavity heated from below: the effect of utilizing single or hybrid nanoparticles as additives. J Taiwan Inst Chem Eng. 2017;72:104–15.CrossRefGoogle Scholar
  8. 8.
    Noghrehabadi A, Izadpanahi E, Ghalambaz M. Analyze of fluid flow and heat transfer of nanofluids over a stretching sheet near the extrusion slit. Comput Fluids. 2014;100:227–36.CrossRefGoogle Scholar
  9. 9.
    Izadi M, Shahmardan MM, Behzadmehr A. Richardson number ratio effect on laminar mixed convection of a nanofluid flow in an annulus. Int J Comput Methods Eng Sci Mech. 2013;14:304–16.CrossRefGoogle Scholar
  10. 10.
    Izadi M, Behzadmehr A, Shahmardan MM. Effects of discrete source-sink arrangements on mixed convection in a square cavity filled by nanofluid. Korean J Chem Eng. 2014;31:12–9.CrossRefGoogle Scholar
  11. 11.
    Mehryan S, Izadi M, Chamkha AJ, Sheremet MA. Natural convection and entropy generation of a ferrofluid in a square enclosure under the effect of a horizontal periodic magnetic field. J Mol Liq. 2018;263:510–25.CrossRefGoogle Scholar
  12. 12.
    Mohebbi R, Izadi M, Chamkha AJ. Heat source location and natural convection in a C-shaped enclosure saturated by a nanofluid. Phys Fluids. 2017;29:122009.CrossRefGoogle Scholar
  13. 13.
    Ghalambaz M, Sabour M, Pop I. Free convection in a square cavity filled by a porous medium saturated by a nanofluid: viscous dissipation and radiation effects. Int J Eng Sci Technol. 2016;19:1244–53.CrossRefGoogle Scholar
  14. 14.
    Ghalambaz M, Sheremet MA, Pop I. Free convection in a parallelogrammic porous cavity filled with a nanofluid using Tiwari and Das’ nanofluid model. PLoS ONE. 2015;10:e0126486.CrossRefGoogle Scholar
  15. 15.
    Pop I, Ghalambaz M, Sheremet M. Free convection in a square porous cavity filled with a nanofluid using thermal non equilibrium and Buongiorno models. Int J Numer Methods Heat Fluid Flow. 2016;26:671–93.CrossRefGoogle Scholar
  16. 16.
    Sabour M, Ghalambaz M, Chamkha A. Natural convection of nanofluids in a cavity: criteria for enhancement of nanofluids. Int J Numer Methods Heat Fluid Flow. 2017;27:1504–34.CrossRefGoogle Scholar
  17. 17.
    Sabour M, Ghalambaz M. Natural convection in a triangular cavity filled with a nanofluid-saturated porous medium using three heat equation model. Can J Phys. 2016;94:604–15.CrossRefGoogle Scholar
  18. 18.
    Tahmasebi A, Mahdavi M, Ghalambaz M. Local thermal nonequilibrium conjugate natural convection heat transfer of nanofluids in a cavity partially filled with porous media using Buongiorno’s model. Numer Heat Transf Part A Appl. 2018;73:254–76.CrossRefGoogle Scholar
  19. 19.
    Zaraki A, Ghalambaz M, Chamkha AJ, Ghalambaz M, de Rossi D. Theoretical analysis of natural convection boundary layer heat and mass transfer of nanofluids: effects of size, shape and type of nanoparticles, type of base fluid and working temperature. Adv Powder Technol. 2015;26:935–46.CrossRefGoogle Scholar
  20. 20.
    Zargartalebi H, Ghalambaz M, Sheremet MA, Pop I. Unsteady free convection in a square porous cavity saturated with nanofluid: the case of local thermal nonequilibrium and Buongiorno’s mathematical models. J Porous Media. 2017;20:999–1016.CrossRefGoogle Scholar
  21. 21.
    Rashidi S, Mahian O, Languri EM. Applications of nanofluids in condensing and evaporating systems. J Therm Anal Calorim. 2018;131:2027–39.CrossRefGoogle Scholar
  22. 22.
    Rashidi S, Karimi N, Mahian O, Esfahani JA. A concise review on the role of nanoparticles upon the productivity of solar desalination systems. J Therm Anal Calorim. 2018;135:1145–59.CrossRefGoogle Scholar
  23. 23.
    Rashidi S, Akbarzadeh M, Karimi N, Masoodi R. Combined effects of nanofluid and transverse twisted-baffles on the flow structures, heat transfer and irreversibilities inside a square duct: a numerical study. Appl Therm Eng. 2018;130:135–48.CrossRefGoogle Scholar
  24. 24.
    Laein RP, Rashidi S, Esfahani JA. Experimental investigation of nanofluid free convection over the vertical and horizontal flat plates with uniform heat flux by PIV. Adv Powder Technol. 2016;27:312–22.CrossRefGoogle Scholar
  25. 25.
    Shirejini SZ, Rashidi S, Esfahani JA. Recovery of drop in heat transfer rate for a rotating system by nanofluids. J Mol Liq. 2016;220:961–9.CrossRefGoogle Scholar
  26. 26.
    Maskaniyan M, Rashidi S, Esfahani JA. A two-way couple of Eulerian–Lagrangian model for particle transport with different sizes in an obstructed channel. Powder Technol. 2017;312:260–9.CrossRefGoogle Scholar
  27. 27.
    Bovand M, Rashidi S, Ahmadi G, Esfahani JA. Effects of trap and reflect particle boundary conditions on particle transport and convective heat transfer for duct flow: a two-way coupling of Eulerian–Lagrangian model. Appl Therm Eng. 2016;108:368–77.CrossRefGoogle Scholar
  28. 28.
    Kayhani MH, Soltanzadeh H, Heyhat MM, Nazari M, Kowsary F. Experimental study of convective heat transfer and pressure drop of TiO2/water nanofluid. Int Commun Heat Mass Transf. 2012;39:456–62.CrossRefGoogle Scholar
  29. 29.
    Nazari M, Ashouri M, Kayhani MH, Tamayol A. Experimental study of convective heat transfer of a nanofluid through a pipe filled with metal foam. Int J Therm Sci. 2015;88:33–9.CrossRefGoogle Scholar
  30. 30.
    Mehryan SA, Kashkooli FM, Ghalambaz M, Chamkha AJ. Free convection of hybrid Al2O3–Cu water nanofluid in a differentially heated porous cavity. Adv Powder Technol. 2017;28:2295–305.CrossRefGoogle Scholar
  31. 31.
    Öğüt EB. Natural convection of water-based nanofluids in an inclined enclosure with a heat source. Int J Therm Sci. 2009;48:2063–73.CrossRefGoogle Scholar
  32. 32.
    Mehryan SA, Izadpanahi E, Ghalambaz M, Chamkha AJ. Mixed convection flow caused by an oscillating cylinder in a square cavity filled with Cu–Al2O3/water hybrid nanofluid. J Therm Anal Calorim. 2019.  https://doi.org/10.1007/s10973-019-08012-2.Google Scholar
  33. 33.
    Maskaniyan M, Nazari M, Rashidi S, Mahian O. Natural convection and entropy generation analysis inside a channel with a porous plate mounted as a cooling system. Therm Sci Eng Prog. 2018;6:186–93.CrossRefGoogle Scholar
  34. 34.
    Armaghani T, Maghrebi MJ, Chamkha AJ, Nazari M. Effects of particle migration on nanofluid forced convection heat transfer in a local thermal non-equilibrium porous channel. J Nanofluids. 2014;3:51–9.CrossRefGoogle Scholar
  35. 35.
    Armaghani T, Chamkha AJ, Maghrebi M, Nazari M. Numerical analysis of a nanofluid forced convection in a porous channel: a new heat flux model in LTNE condition. J Porous Media. 2014;17:637–46.CrossRefGoogle Scholar
  36. 36.
    Nazari M, Maghrebi MJ, Armaghani T, Chamkha AJ. New models for heat flux splitting at the boundary of a porous medium: three energy equations for nanofluid flow under local thermal nonequilibrium conditions. Can J Phys. 2014;92:1312–9.CrossRefGoogle Scholar
  37. 37.
    Hoghoughi G, Izadi M, Oztop HF, Abu-Hamdeh N. Effect of geometrical parameters on natural convection in a porous undulant-wall enclosure saturated by a nanofluid using Buongiorno’s model. J Mol Liq. 2018;255:148–59.CrossRefGoogle Scholar
  38. 38.
    Izadi M, Hoghoughi G, Mohebbi R, Sheremet M. Nanoparticle migration and natural convection heat transfer of Cu–water nanofluid inside a porous undulant-wall enclosure using LTNE and two-phase model. J Mol Liq. 2018;261:357–72.CrossRefGoogle Scholar
  39. 39.
    Izadi M, Sinaei S, Mehryan SAM, Oztop HF, Abu-Hamdeh N. Natural convection of a nanofluid between two eccentric cylinders saturated by porous material: Buongiorno’s two phase model. Int J Heat Mass Transf. 2018;127:67–75.CrossRefGoogle Scholar
  40. 40.
    Mehryan SA, Ghalambaz M, Izadi M. Conjugate natural convection of nanofluids inside an enclosure filled by three layers of solid, porous medium and free nanofluid using Buongiorno’s and local thermal non-equilibrium models. J Therm Anal Calorim. 2019;135:1047–67.CrossRefGoogle Scholar
  41. 41.
    Bourantas GC, Skouras ED, Loukopoulos VC, Burganos VN. Heat transfer and natural convection of nanofluids in porous media. Eur J Mech B Fluids. 2014;43:45–56.CrossRefGoogle Scholar
  42. 42.
    Izadi M, Mehryan S, Sheremet MA. Natural convection of CuO–water micropolar nanofluids inside a porous enclosure using local thermal non-equilibrium condition. J Taiwan Inst Chem Eng. 2018;88:89–103.CrossRefGoogle Scholar
  43. 43.
    Rashidi S, Esfahani JA, Maskaniyan M. Applications of magnetohydrodynamics in biological systems: a review on the numerical studies. J Magn Magn Mater. 2017;439:358–72.CrossRefGoogle Scholar
  44. 44.
    Rashidi S, Bovand M, Esfahani JA. Opposition of magnetohydrodynamic and Al2O3–water nanofluid flow around a vertex facing triangular obstacle. J Mol Liq. 2016;215:276–84.CrossRefGoogle Scholar
  45. 45.
    Bovand M, Rashidi S, Esfahani JA. Optimum interaction between magnetohydrodynamics and nanofluid for thermal and drag management. J Thermophys Heat Transf. 2016;31:218–29.CrossRefGoogle Scholar
  46. 46.
    Izadi M, Mohebbi R, Delouei AA, Sajjadi H. Natural convection of a magnetizable hybrid nanofluid inside a porous enclosure subjected to two variable magnetic fields. Int J Mech Sci. 2019;151:154–69.CrossRefGoogle Scholar
  47. 47.
    Sajjadi H, Delouei AA, Izadi M, Mohebbi R. Investigation of MHD natural convection in a porous media by double MRT lattice Boltzmann method utilizing MWCNT–Fe3O4/water hybrid nanofluid. Int J Heat Mass Transf. 2019;132:1087–104.CrossRefGoogle Scholar
  48. 48.
    Mehryan SA, Sheremet MA, Soltani M, Izadi M. Natural convection of magnetic hybrid nanofluid inside a double-porous medium using two-equation energy model. J Mol Liq. 2019;277:959–70.CrossRefGoogle Scholar
  49. 49.
    Ramanathan A, Suresh G. Effect of magnetic field dependent viscosity and anisotropy of porous medium on ferroconvection. Int J Eng Sci. 2004;42:411–25.CrossRefGoogle Scholar
  50. 50.
    Sharma RC. The effect of magnetic field dependent viscosity on thermosolutal convection in a ferromagnetic fluid saturating a porous medium. Transp Porous Media. 2005;60:251–74.CrossRefGoogle Scholar
  51. 51.
    Sekar R, Raju K. Effect of magnetic field dependent viscosity on Soret-driven ferrothermohaline convection saturating an anisotropic porous medium of sparse particle suspension. World J Eng. 2014;11:213–28.CrossRefGoogle Scholar
  52. 52.
    Nanjundappa C, Shivakumara I, Srikumar K. Effect of MFD viscosity on the onset of ferromagnetic fluid layer heated from below and cooled from above with constant heat flux. Meas Sci Rev. 2009;9:75–80.CrossRefGoogle Scholar
  53. 53.
    Ram P, Bhandari A, Sharma K. Effect of magnetic field-dependent viscosity on revolving ferrofluid. J Magn Magn Mater. 2010;322:3476–80.CrossRefGoogle Scholar
  54. 54.
    Sheikholeslami M, Rashidi MM, Hayat T, Ganji DD. Free convection of magnetic nanofluid considering MFD viscosity effect. J Mol Liq. 2016;218:393–9.CrossRefGoogle Scholar
  55. 55.
    Maghrebi MJ, Nazari M, Armaghani T. Forced convection heat transfer of nanofluids in a porous channel. Transp Porous Media. 2012;93:401–13.CrossRefGoogle Scholar
  56. 56.
    Rashidi S, Eskandarian M, Mahian O, Poncet S. Combination of nanofluid and inserts for heat transfer enhancement. J Therm Anal Calorim. 2019;135:437–60.CrossRefGoogle Scholar
  57. 57.
    Rashidi S, Bovand M, Esfahani JA, Ahmadi G. Discrete particle model for convective Al2O3–water nanofluid around a triangular obstacle. Appl Therm Eng. 2016;100:39–54.CrossRefGoogle Scholar
  58. 58.
    Sheikholeslami M, Mehryan SA, Shafee A, Sheremet MA. Variable magnetic forces impact on magnetizable hybrid nanofluid heat transfer through a circular cavity. J Mol Liq. 2018;277:388–96.CrossRefGoogle Scholar
  59. 59.
    Sheikholeslami M, Vajravelu K. Nanofluid flow and heat transfer in a cavity with variable magnetic field. Appl Math Comput. 2017;298:272–82.Google Scholar
  60. 60.
    Khalid A, Khan I, Khan A, Shafie S, Tlili I. Case study of MHD blood flow in a porous medium with CNTS and thermal analysis. Case Stud Therm Eng. 2018;12:374–80.CrossRefGoogle Scholar
  61. 61.
    Rao SS. The finite element method in engineering. New York: Elsevier; 2010.Google Scholar
  62. 62.
    Donea J, Huerta A. Finite element methods for flow problems. New York: Wiley; 2003.CrossRefGoogle Scholar
  63. 63.
    Wriggers P. Nonlinear finite element methods. New York: Springer; 2008.Google Scholar
  64. 64.
    Kahveci K. Natural convection in a partitioned vertical enclosure heated with a uniform heat flux. J Heat Transf. 2007;129:717–26.CrossRefGoogle Scholar
  65. 65.
    Cesini G, Paroncini M, Cortella G, Manzan M. Natural convection from a horizontal cylinder in a rectangular cavity. Int J Heat Mass Transf. 1999;42:1801–11.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  • S. A. M. Mehryan
    • 1
  • Mohsen Izadi
    • 2
  • Zafar Namazian
    • 1
    Email author
  • Ali J. Chamkha
    • 3
    • 4
  1. 1.Young Researchers and Elite Club, Yasooj BranchIslamic Azad UniversityYasoojIran
  2. 2.Mechanical Engineering Department, Faculty of EngineeringLorestan UniversityKhorramabadIran
  3. 3.Mechanical Engineering Department, Prince Mohammad Endowment for Nanoscience and TechnologyPrince Mohammad Bin Fahd UniversityAl-KhobarSaudi Arabia
  4. 4.RAK Research and Innovation CenterAmerican University of Ras Al KhaimahRas Al KhaimahUnited Arab Emirates

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