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Effect of a Magnetic Field on Natural Convection in a Nanofluid-Filled Enclosure with a Linearly Heated Wall Using LBM

  • Research Article - Mechanical Engineering
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Abstract

In this paper, effect of a magnetic field on natural convection flow in a nanofluid-filled enclosure with a linearly heated wall has been analyzed with a new attitude to Lattice Boltzmann method. The cavity is filled with water and nanoparticles of Cu in the presence of the magnetic field. This study has been carried out for the pertinent parameters in the following ranges: the Rayleigh number of base fluid, Ra = 103–105, the volumetric fraction of nanoparticles between 0 and 15 % with interval 5 %. The Hartmann number varied from Ha = 0 to 90 with interval 30, while magnetic field is considered at the direction of the cavity horizontal. Results show that the heat transfer decreases by increment of Hartmann number for various Rayleigh numbers. Heat transfer increases with growth of the volume fractions, but this growth is various for different Rayleigh numbers. The magnetic field augments the effect of nanoparticles at high Rayleigh numbers (Ra = 105), while the effect declines in the presence of the magnetic field for low Rayleigh numbers (Ra = 103 and 104).

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Abbreviations

B :

Magnetic field

c :

Lattice speed

c i :

Discrete particle speeds

c p :

Specific heat at constant pressure

F :

External forces

f :

Density distribution functions

f eq :

Equilibrium density distribution functions

g :

Internal energy distribution functions

g eq :

Equilibrium internal energy distribution functions

g y :

Gravity

M :

Lattice number

Ma :

Mach number

Nu :

Nusselt number

Pr :

Prandtl number

R :

Constant of the gases

Ra :

Rayleigh number \({\left({Ra=\frac{\beta g_y H^3(T_{\rm H} =T_{\rm C})}{\upsilon\alpha}}\right)}\)

T :

Temperature

x, y :

Cartesian coordinates

u :

Magnitude velocity

ω i :

Weighted factor in direction i

β :

Thermal expansion coefficient

τ c :

Relaxation time for temperature

τ v :

Relaxation time for flow

ϑ :

Kinematic viscosity

Δx :

Lattice spacing

Δt :

Time increment

α :

Thermal diffusivity

ϕ :

Volume fraction

μ :

Dynamic viscosity

ψ :

Stream function value

γ :

Inclination angle of magnetic field

avg:

Average

C:

Cold

H:

Hot

f:

Fluid

nf:

Nanofluid

References

  1. Sazia, I.; Mohamad, A.A.: Suppressing free convection from a flat plate with poor conductor ribs. Int. J. Heat Mass Transfer 42(1), 2041–2051 (1999)

    Google Scholar 

  2. Le Quere, P.; Humphrey, J.A.C.; Sherman, F.S.: Numerical calculation of thermally driven two dimensional unsteady laminar flow in cavities of rectangular cross section. Numer. Heat Transfer 4, 249–283 (1981)

    Google Scholar 

  3. Chan, Y.L.; Tien, C.L.: A numerical study of two-dimensional natural convection in square open cavities. Numer. Heat Transfer 8, 65–80 (1985)

    Google Scholar 

  4. Mohamad, A.A.: Natural convection in open cavities and slots, Numer. Heat Transfer 27, 705–716 (1995)

    Google Scholar 

  5. Sathiyamoorthy, M.; Basak, T.; Roy, S.; Pop, I.: Steady natural convection flows in a square cavity with linearly heated side wall(s). Int. J. Heat Mass Transfer 50, 766–775 (2007)

    Google Scholar 

  6. Kahveci, K.; Oztuna, S.: MHD natural convection flow and heat transfer in a laterally heated partitioned enclosure. Eur. J. Mech. B Fluids 28, 744–752 (2009)

    Google Scholar 

  7. Pirmohammadi, M.; Ghassemi, M.: Effect of magnetic field on convection heat transfer inside a tilted square enclosure. Int. Commun. Heat Mass Transfer 36, 776–780 (2009)

    Google Scholar 

  8. Sathiyamoorthy, M.; Chamkha, A.: Effect of magnetic field on natural convection flow in a liquid gallium filled square cavity for linearly heated side wall(s). Int. J. Thermal Sci. 49, 1856–1865 (2010)

    Google Scholar 

  9. Sivasankaran, S.; Malleswaran, A.; Lee, J.; Sundar, P.: Hydro-magnetic combined convection in a lid-driven cavity with sinusoidal boundary conditions on both sidewalls. Int. J. Heat Mass Transfer 54, 512–525 (2011)

    Google Scholar 

  10. Rahman, M.M.; Parvin, S.; Saidur, R.; Rahim, N.A.: Magnetohydrodynamic mixed convection in a horizontal channel with an open cavity. Int. Commun. Heat Mass Transfer 38, 184–193 (2011)

    Google Scholar 

  11. Oztop, H.F.; Zhao, Z.; Yu, B.: Conduction-combined forced and natural convection in lid-driven enclosures divided by a vertical solid partition. Int. Commun. Heat Mass Transfer 36, 661–668 (2009)

    Google Scholar 

  12. Oztop, H.F.; Al-Salem, K.; Pop, I.: MHD mixed convection in a lid-driven cavity with corner heater. Int. J. Heat Mass Transfer 54, 3494–3504 (2011)

    Google Scholar 

  13. Nasrin, R.; Parvin, S.: Hydromagnetic effect on mixed convection in a lid-driven cavity with sinusoidal corrugated bottom surface. Int. Commun. Heat Mass Transfer 38, 781–789 (2011)

    Google Scholar 

  14. Parida, S.K.; Acharya, M.; Dash, G.C.; Panda, S.: MHD heat and mass transfer in a rotating system with periodic suction. Arab. J. Sci. Eng. 36, 1139–1151 (2011)

    Google Scholar 

  15. Sivasankaran, S.; Lee, J.; Bhuvaneswari, M.: Effect of a partition on hydro-magnetic convection in an enclosure. Arab. J. Sci. Eng. 36, 1393–1406 (2011)

    Google Scholar 

  16. Jahanshahi, M.; Hosseinizadeh, S.F.; Alipanah, M.; Dehghani, A.; Vakilinejad, G.R.: Numerical simulation of free convection based on experimental measured conductivity in a square cavity using Water/SiO2 nanofluid. Int. Commun. Heat Mass Transfer 37, 687–694 (2010)

    Google Scholar 

  17. Yang, Y.; Zhang, Z.G.; Grulke, E.A.; Anderson, W.B.; Wu, G.: Heat transfer properties of nanoparticle-in-fluid dispersions (nanofluids) in laminar flow. Int. J. Heat Mass Transfer 48, 1107–1116 (2005)

    Google Scholar 

  18. Khanafer, K.; Vafai, K.; Lightstone, M.: Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. Int. J. Heat Mass Transfer 46, 3639–3653 (2003)

    Google Scholar 

  19. Wen, D.; Ding, Y.: Formulation of nanofluids for natural convective heat transfer applications. Int. J. Heat Fluid Flow 26(6), 855–864 (2005)

    Google Scholar 

  20. Ho, C.J.; Chen, M.W.; Li, Z.W.: Numerical simulation of natural convection of nanofluid in a square enclosure: effects due to uncertainties of viscosity and thermal conductivity. Int. J. Heat Mass Transfer 51, 4506–4516 (2008)

    Google Scholar 

  21. Santra, A.K.; Sen, S.; Chakraborty, N.: Study of heat transfer augmentation in a differentially heated square cavity using copper-water nanofluid. Int. J. Thermal Sci. 47, 1113–1122 (2008)

    Google Scholar 

  22. Makind, O.D.; Aziz, A.: Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition. Int. J. Thermal Sci. 50, 1326–1332 (2011)

    Google Scholar 

  23. Motsumi, T.G.; Makinde, O.D.: Effects of thermal radiation and viscous dissipation on boundary layer flow of nanofluids over a permeable moving flat plate. Phys. Scr. 86, 045003 (2012)

    Google Scholar 

  24. Moradi, A.; Alsaedi, A.; Hayat, T.: Investigation of nanoparticles effect on the Jeffery Hamel flow. Arab. J. Sci. Eng. (2012)

  25. Ghasemi, B.; Aminossadati, S.M.; Raisi, A.: Magnetic field effect on natural convection in a nanofluid-filled square enclosure. Int. J. Thermal Sci., 1–9 (2011)

  26. Mohamad, A.A.; Kuzmin, A.: A critical evaluation of force term in lattice Boltzmann method, natural convection problem. Int. J. Heat Mass Transfer 53, 990–996 (2010)

    Google Scholar 

  27. Mohamad, A.A.; Bennacer, R.; El-Ganaoui, M.: Double dispersion, natural convection in an open end cavity simulation via Lattice Boltzmann Method. Int. J. Thermal Sci. 49, 1944–1953 (2010)

    Google Scholar 

  28. Sajjadi, H.; Gorji, M.; Hosseinzadeh, S.F.; Kefayati, G.R.; Ganji, D.D.: Numerical analysis of turbulent natural convection in square cavity using large-eddy simulation in Lattice Boltzmann method. IJST Trans. Mech. Eng. 35, 133–142 (2011)

    Google Scholar 

  29. Sidik, N.A.C.; Sahat, I.M.: Finite difference and cubic interpolated profile lattice Boltzmann method for prediction of two-dimensional lid-driven shallow cavity flow. Arab. J. Sci. Eng. 37, 1101–1110 (2012)

    Google Scholar 

  30. Kefayati, Gh.R.; Hosseinizadeh, S.F.; Gorji, M.; Sajjadi, H.: Lattice Boltzmann simulation of natural convection in tall enclosures using water/SiO2 nanofluid. Int. Commun. Heat Mass Transfer 38, 798–805 (2011)

    Google Scholar 

  31. Kefayati, Gh.R.; Hosseinizadeh, S.F.; Gorji, M.; Sajjadi, H.: Lattice Boltzmann simulation of natural convection in an open enclosure subjugated to Water/copper nanofluid. Int. J. Thermal Sci. 52, 91–101 (2012)

    Google Scholar 

  32. Kefayati, Gh.R.: Lattice Boltzmann simulation of natural convection in a square cavity with a linearly heated wall using nanofluid. Arab. J. Sci. Eng. (accepted)

  33. Sajjadi, H.; Gorji, M.; Kefayati, Gh.R.; Ganji, D.D.: Lattice Boltzmann simulation of turbulent natural convection in tall enclosures using Cu/water nanofluid. Numer. Heat Transfer Part A 62, 512–530 (2012)

  34. Kefayati, Gh.R.; Gorji, M.; Ganji, D.D.; Sajjadi, H.: Investigation of Prandtl number effect on natural convection MHD in an open cavity by Lattice Boltzmann Method. Eng. Comput. 30, 97–116 (2013)

    Google Scholar 

  35. Kefayati, Gh.R.; Gorji, M.; Sajjadi, H.; Ganji, D.D.: Lattice Boltzmann simulation of MHD mixed convection in a lid-driven square cavity with linearly heated wall. Sci. Iran. 19(4), 1053–1065 (2012)

    Google Scholar 

  36. Kefayati, Gh.R.: Effect of a magnetic field on natural convection in an open cavity subjugated to Water/alumina nanofluid using Lattice Boltzmann Method. Int. Commun. Heat Mass Transfer 40(1), 67–77 (2013)

    Google Scholar 

  37. Kefayati, Gh.R.: Lattice Boltzmann simulation of natural convection in nanofluid-filled tall enclosures at presence of magnetic field. Theor. Comput. Fluid Dyn. (in press)

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Authors and Affiliations

  1. School of Computer Science, Engineering and Mathematics, Flinders University, Adelaide, Australia

    Gh. R. Kefayati

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Kefayati, G.R. Effect of a Magnetic Field on Natural Convection in a Nanofluid-Filled Enclosure with a Linearly Heated Wall Using LBM. Arab J Sci Eng 39, 4151–4163 (2014). https://doi.org/10.1007/s13369-014-1031-9

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  • DOI: https://doi.org/10.1007/s13369-014-1031-9

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