Advertisement

Journal of Thermal Analysis and Calorimetry

, Volume 136, Issue 4, pp 1723–1735 | Cite as

MHD forced convection of MWCNT–Fe3O4/water hybrid nanofluid in a partially heated τ-shaped channel using LBM

  • Yuan Ma
  • Rasul MohebbiEmail author
  • M. M. Rashidi
  • Zhigang Yang
Article

Abstract

Forced convection heat transfer of multi-wall carbon nanotubes–iron oxide nanoparticles/water hybrid nanofluid (MWCNT–Fe3O4/water hybrid nanofluid) inside a partially heated τ-shaped channel has been numerically investigated. The effect of magnetic field is taken into account. The governing equations are solved by the lattice Boltzmann method in the domain, and the results were compared with other numerical methods by an excellent agreement between them. The effects of parameters such as Hartmann number (0 ≤ Ha ≤ 60), volume fraction of nanoparticles (0 ≤ ϕ ≤ 0.003) and different location of two heaters on the fluid flow and heat transfer are studied. The results indicate that for all cases, the average Nusselt number of each heater increases as the volume fraction of nanoparticles increases. The heat transfer characteristics were significantly affected by the arrangement of the two heaters. The heaters located on the left half of the top wall is convection-dominant mechanism, and the conduction heat transfer is the primary mechanism when the heater is on the right half of the top wall. The average Nusselt number increases as Ha increases for the heater of dominating convection mechanism but decreases for the heater of dominating conduction mechanism.

Keywords

Forced convection heat transfer Nanofluid τ-shaped channel LBM Magnetic field 

List of symbols

X1, X2

Positions of the heaters

h

Width of the channel

H

Height of the channel

ei

Discrete lattice velocity in direction

f

Density distribution function

feq

Equilibrium density distribution function

Ha

Hartmann number

Nu

Nusselt number

U, V

Non-dimensional velocity components

Pr

Prandtl number

L

Length of the heaters

W

Length of the channel

θ

Orientation of the magnetic field

cs

Speed of sound in Lattice scale

g

Energy distribution function

geq

Equilibrium energy distribution function

kB

Boltzmann constant

T

Fluid temperature

k

Thermal conductivity

Ra

Rayleigh number

Greek symbols

ωi

Mass function in direction i

ϕ

Volume fraction

τc

Relaxation time for temperature

α

Thermal diffusivity

ρ

Density

τv

Relaxation time for flow

β

Thermal expansion coefficient

μ

Dynamic viscosity

Subscripts

loc

Local

s

Solid particles

nf

Nanofluid

c

Cold

ave

Average

f

Fluid

h

Hot

i

Move direction of single particle

Notes

Acknowledgements

This work was supported by the Shanghai Automotive Wind Tunnel Technical Service Platform (16DZ2290400). The computing facility of Shanghai Key Laboratory of Vehicle Aerodynamics and Vehicle Thermal Management Systems is gratefully acknowledged.

References

  1. 1.
    Nasrin R, Rahim NA, Fayaz H, et al. Water/MWCNT nanofluid based cooling system of PVT: experimental and numerical research. Renew Energy. 2018;121:286–300.CrossRefGoogle Scholar
  2. 2.
    Ghadikolaei SS, Hosseinzadeh K, Ganji DD, et al. Fe3O4–(CH2OH)2 nanofluid analysis in a porous medium under MHD radiative boundary layer and dusty fluid. J Mol Liq. 2018;258:172–85.CrossRefGoogle Scholar
  3. 3.
    Shi X, Li S, Wei Y, et al. Numerical investigation of laminar convective heat transfer and pressure drop of water-based Al2O3 nanofluids in a microchannel. Int Commun Heat Mass Transf. 2018;90:111–20.CrossRefGoogle Scholar
  4. 4.
    Ma Y, Mohebbi R, Rashidi MM, Yang Z. Simulation of nanofluid natural convection in a U-shaped cavity equipped by a heating obstacle: effect of cavity’s aspect ratio. J Taiwan Inst Chem Eng. 2018.  https://doi.org/10.1016/j.jtice.2018.07.026.Google Scholar
  5. 5.
    Ma Y, Mohebbi R, Rashidi MM, Manca O, Yang Z. Numerical investigation of MHD effects on nanofluid heat transfer in a baffled U-shaped enclosure using lattice Boltzmann method. J Therm Anal Calorimetry. 2018;12:1.  https://doi.org/10.1007/s10973-018-7518-y.Google Scholar
  6. 6.
    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
  7. 7.
    Mohammed HA, Bhaskaran G, Shuaib NH, et al. Heat transfer and fluid flow characteristics in microchannels heat exchanger using nanofluids: a review. Renew Sustain Energy Rev. 2011;15(3):1502–12.CrossRefGoogle Scholar
  8. 8.
    Kumar NTR, Bhramara P, Sundar LS, et al. Heat transfer, friction factor and effectiveness of Fe3O4 nanofluid flow in an inner tube of double pipe U-bend heat exchanger with and without longitudinal strip inserts. Exp Therm Fluid Sci. 2017;85:331–43.CrossRefGoogle Scholar
  9. 9.
    Karimi A, Afrand M. Numerical study on thermal performance of an air-cooled heat exchanger: effects of hybrid nanofluid, pipe arrangement and cross section. Energy Convers Manag. 2018;164:615–28.CrossRefGoogle Scholar
  10. 10.
    Mohebbi R, Lakzayi H, Sidik NAC, et al. Lattice Boltzmann method based study of the heat transfer augmentation associated with Cu/water nanofluid in a channel with surface mounted blocks. Int J Heat Mass Transf. 2018;117:425–35.CrossRefGoogle Scholar
  11. 11.
    Mohebbi R, Rashidi MM, Izadi M, et al. Forced convection of nanofluids in an extended surfaces channel using lattice Boltzmann method. Int J Heat Mass Transf. 2018;117:1291–303.CrossRefGoogle Scholar
  12. 12.
    Cong Qi, Liang Lin, Rao Zhonghao. Study on the flow and heat transfer of liquid metal based nanofluid with different nanoparticle radiuses using two-phase lattice Boltzmann method. Int J Heat Mass Transf. 2016;94:316–26.CrossRefGoogle Scholar
  13. 13.
    Ma Y, Mohebbi R, Rashidi MM, et al. Study of nanofluid forced convection heat transfer in a bent channel by means of lattice Boltzmann method. Phys Fluids. 2018;30(3):032001.CrossRefGoogle Scholar
  14. 14.
    Safari A, Saffar-Avval M, Amani E. Numerical investigation of turbulent forced convection flow of nano fluid in curved and helical pipe using four-equation model. Powder Technol. 2018;328:47–53.CrossRefGoogle Scholar
  15. 15.
    Ahmed M, Eslamian M. Laminar forced convection of a nanofluid in a microchannel: effect of flow inertia and external forces on heat transfer and fluid flow characteristics. Appl Therm Eng. 2015;78:326–38.CrossRefGoogle Scholar
  16. 16.
    Raisi A, Aminossadati SM, Ghasemi B. An innovative nanofluid-based cooling using separated natural and forced convection in low Reynolds flows. J Taiwan Inst Chem Eng. 2016;62:259–66.CrossRefGoogle Scholar
  17. 17.
    Abedini A, Armaghani T, Chamkha AJ. MHD free convection heat transfer of a water–Fe3O4 nanofluid in a baffled C-shaped enclosure. J Therm Anal Calorimetry. 2018.  https://doi.org/10.1007/s10973-018-7225-8.Google Scholar
  18. 18.
    Selimefendigil F, Oztop HF, Chamkha AJ. MHD mixed convection in a nanofluid filled vertical lid-driven cavity having a flexible fin attached to its upper wall. J Therm Anal Calorimetry. 2018.  https://doi.org/10.1007/s10973-018-7036-y.Google Scholar
  19. 19.
    Selimefendigil F, Chamkha AJ. Magnetohydrodynamics mixed convection in a power law nanofluid-filled triangular cavity with an opening using Tiwari and Das’ nanofluid model. J Therm Anal Calorimetry. 2018.  https://doi.org/10.1007/s10973-018-7037-x.Google Scholar
  20. 20.
    Sheikholeslami M, Vajravelu K, Rashidi MM. Forced convection heat transfer in a semi annulus under the influence of a variable magnetic field. Int J Heat Mass Transf. 2016;92:339–48.CrossRefGoogle Scholar
  21. 21.
    Rashidi MM, Abelman S, Mehr NF. Entropy generation in steady MHD flow due to a rotating porous disk in a nanofluid. Int J Heat Mass Transf. 2013;62:515–25.CrossRefGoogle Scholar
  22. 22.
    Elshehabey HM, Ahmed SE. MHD mixed convection in a lid-driven cavity filled by a nanofluid with sinusoidal temperature distribution on the both vertical walls using Buongiorno’s nanofluid model. Int J Heat Mass Transf. 2015;88:181–202.CrossRefGoogle Scholar
  23. 23.
    Sheikholeslami M, Bhatti MM. Forced convection of nanofluid in presence of constant magnetic field considering shape effects of nanoparticles. Int J Heat Mass Transf. 2017;111:1039–49.CrossRefGoogle Scholar
  24. 24.
    Ma Y, Mohebbi R, Rashidi MM, et al. Numerical simulation of flow over a square cylinder with upstream and downstream circular bar using lattice Boltzmann method. Int J Mod Phys C. 2018;12:1.  https://doi.org/10.1142/s0129183118500304.Google Scholar
  25. 25.
    Ma Y, Rashidi MM, Yang Z. Numerical simulation of flow past a square cylinder with a circular bar upstream and a splitter plate downstream. J Hydrodyn. 2018.  https://doi.org/10.1007/s42241-018-0087-5.Google Scholar
  26. 26.
    Nazari M, Mohebbi R, Kayhani MH. Power-law fluid flow and heat transfer in a channel with a built-in porous square cylinder: Lattice Boltzmann simulation. J Nonnewton Fluid Mech. 2014;204:38–49.CrossRefGoogle Scholar
  27. 27.
    Nazari M, Kayhani MH, Mohebbi R. Heat transfer enhancement in a channel partially filled with a porous block: lattice Boltzmann method. Int J Mod Phys C. 2013;24(09):1350060.CrossRefGoogle Scholar
  28. 28.
    Mohebbi R, Nazari M, Kayhani MH. Comparative study of forced convection of a power-law fluid in a channel with a built-in square cylinder. J Appl Mech Tech Phys. 2016;57(1):55–68.CrossRefGoogle Scholar
  29. 29.
    Mohebbi R, Rashidi MM. Numerical simulation of natural convection heat transfer of a nanofluid in an L-shaped enclosure with a heating obstacle. J Taiwan Inst Chem Eng. 2017;72:70–84.CrossRefGoogle Scholar
  30. 30.
    Mohebbi R, Heidari H. Lattice Boltzmann simulation of fluid flow and heat transfer in a parallel-plate channel with transverse rectangular cavities. Int J Mod Phys C. 2017;28(03):1750042.CrossRefGoogle Scholar
  31. 31.
    Tao S, He Q, Chen B, Yang X, Huang S. One-point second-order curved boundary condition for lattice Boltzmann simulation of suspended particles. Comput Math Appl. 2018;12:1.  https://doi.org/10.1016/j.camwa.2018.07.013.Google Scholar
  32. 32.
    Chen CL, Chang SC, Chang CK. Lattice Boltzmann simulation for mixed convection of nanofluids in a square enclosure. Appl Math Model. 2015;39(8):2436–51.CrossRefGoogle Scholar
  33. 33.
    Mishra L, Baranwal AK, Chhabra RP. Laminar forced convection in power-law fluids from two heated cylinders in a square duct. Int J Heat Mass Transf. 2017;113:589–612.CrossRefGoogle Scholar
  34. 34.
    Sheikholeslami M, Hayat T, Alsaedi A. Numerical simulation for forced convection flow of MHD CuO–H2O nanofluid inside a cavity by means of LBM. J Mol Liq. 2018;249:941–8.CrossRefGoogle Scholar
  35. 35.
    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(12):122009.CrossRefGoogle Scholar
  36. 36.
    Izadi M, Mohebbi R, Karimi D, et al. Numerical simulation of natural convection heat transfer inside a shaped cavity filled by a MWCNT–Fe3O4/water hybrid nanofluids using LBM. Chem Eng Process Process Intensif. 2018;125:56–66.CrossRefGoogle Scholar
  37. 37.
    Ma Y, Mohebbi R, Rashidi MM, Yang Z. Effect of hot obstacle position on natural convection heat transfer of MWCNTs–water nanofluid in U-shaped enclosure using lattice Boltzmann method. Int J Numer Methods Heat Fluid Flow. 2018.Google Scholar
  38. 38.
    Izadi M, Mohebbi R, Chamkha A, Pop I. Effects of cavity and heat source aspect ratios on natural convection of a nanofluid in a C-shaped enclosure using lattice Boltzmann method. Int J Numer Methods Heat Fluid Flow. 2018.Google Scholar
  39. 39.
    Mohebbi R, Izadi M, Amiri Delouei A, Sajjadi H. Effect of MWCNT–Fe3O4/water hybrid nanofluid on the thermal performance of ribbed channel with apart sections of heating and cooling. J Therm Anal Calorimetry. 2018.  https://doi.org/10.1007/s10973-018-7483-5.Google Scholar
  40. 40.
    Sundar LS, Singh MK, Sousa ACM. Enhanced heat transfer and friction factor of MWCNT–Fe3O4/water hybrid nanofluids. Int Commun Heat Mass Transf. 2014;52:73–83.CrossRefGoogle Scholar
  41. 41.
    Kefayati GHR. Natural convection of ferrofluid in a linearly heated cavity utilizing LBM. J Mol Liq. 2014;191:1–9.CrossRefGoogle Scholar
  42. 42.
    Asadi Abchouyeh M, Mohebbi R, Solaymani Fard O. Lattice Boltzmann simulation of nanofluid natural convection heat transfer in a channel with a sinusoidal obstacle. Int J Mod Phys C. 2018.  https://doi.org/10.1142/S0129183118500791.Google Scholar
  43. 43.
    Mohamad AA, Kuzmin A. A critical evaluation of force term in lattice Boltzmann method, natural convection problem. Int J Heat Mass Transf. 2010;53(5–6):990–6.CrossRefGoogle Scholar
  44. 44.
    Bhatnagar PL, Gross EP, Krook M. A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys Rev. 1954;94(3):511.CrossRefGoogle Scholar
  45. 45.
    Chen S, Doolen GD. Lattice Boltzmann method for fluid flows. Annu Rev Fluid Mech. 1998;30(1):329–64.CrossRefGoogle Scholar
  46. 46.
    Qian YH, d’Humières D, Lallemand P. Lattice BGK models for Navier–Stokes equation. EPL (Europhys Lett). 1992;17(6):479.CrossRefGoogle Scholar
  47. 47.
    Yan YY, Zu YQ. Numerical simulation of heat transfer and fluid flow past a rotating isothermal cylinder—a LBM approach. Int J Heat Mass Transf. 2008;51(9):2519–36.CrossRefGoogle Scholar
  48. 48.
    Zou Q, He X. On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Phys Fluids. 1997;9(6):1591–8.CrossRefGoogle Scholar
  49. 49.
    Mohamad AA. Applied lattice Boltzmann method for transport phenomena, momentum, heat and mass transfer. Can J Chem Eng. 2007;85(6):946.Google Scholar
  50. 50.
    Santra AK, Sen S, Chakraborty N. Study of heat transfer due to laminar flow of copper–water nanofluid through two isothermally heated parallel plates. Int J Therm Sci. 2009;48(2):391–400.CrossRefGoogle Scholar
  51. 51.
    Ghasemi B, Aminossadati SM, Raisi A. Magnetic field effect on natural convection in a nanofluid-filled square enclosure. Int J Therm Sci. 2011;50(9):1748–56.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  • Yuan Ma
    • 1
    • 2
  • Rasul Mohebbi
    • 3
    Email author
  • M. M. Rashidi
    • 4
  • Zhigang Yang
    • 1
    • 2
    • 5
  1. 1.Shanghai Automotive Wind Tunnel CenterTongji UniversityShanghaiChina
  2. 2.Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management SystemsShanghaiChina
  3. 3.School of EngineeringDamghan UniversityDamghanIran
  4. 4.Department of Civil Engineering, School of EngineeringUniversity of BirminghamBirminghamUK
  5. 5.Beijing Aeronautical Science and Technology Research InstituteBeijingChina

Personalised recommendations