Lattice Boltzmann Simulation of Magnetic Field Direction Effect on Natural Convection of Nanofluid-Filled Cavity

Lattice Boltzmann Simulation of Magnetic Field Direction Effect on Natural Convection of Nanofluid-Filled Cavity

Ahmed Mahmoudi Imen Mejri Mohamed Ammar Abbassi Ahmed Omri

UR:Unité de Recherche Matériaux, Energie et Energies Renouvelables (MEER), Faculté des Sciences de Gafsa, B.P.19, Zarroug, Gafsa, 2112, Tunisie

Page: 
9-14
|
DOI: 
https://doi.org/10.18280/ijht.320102
| |
Published: 
31 December 2014
| Citation

OPEN ACCESS

Abstract: 

This paper examines the natural convection in a square enclosure filled with a water-Al $_{2} \mathrm{O}_{3}$ nanofluid and is subjected to a magnetic field. The bottom wall is uniformly heated and vertical walls are linearly heated whereas the top wall is well insulated. Lattice Boltzmann method (LBM) is applied to solve the coupled equations of flow and temperature fields. This study has been carried out for the pertinent parameters in the following ranges: Rayleigh number of the base fluid, $\mathrm{Ra}=10^{3}$ to $10^{5},$ Hartmann number varied from $\mathrm{Ha}=0$ to $60,$ the inclination angle of the magnetic field relative to the horizontal plane $\gamma=0^{\circ}$ to $180^{\circ}$ and the solid volume fraction of the nanoparticles between $\phi=0$ and $6 \%$. The results show that the heat transfer and fluid flow depends strongly upon the direction of magnetic field. In addition, according the Hartmann number, it observed that the magnetic field direction controls the effects of nanoparticles.

1. Introduction
2. Mathematical Formulation
3. Results and Discussion
4. Conclusions
Nomenclature
  References

[1] S. Ostrach,  Natural convection in enclosures, Journal of Heat Transfer, vol 110, pp. 1175-1190, 1988.

[2] M. Moreau, Magnetohydrodynamics, Kluwer Acadamic Publishers, The Netherlands, 1990 .

[3] H. Ozoe, K. Okada, The effect of the direction of the external magnetic field on the three dimensional natural convection in a cubical enclosure, International Journal of Heat and Mass Transfer, vol. 32, pp. 1939-1954,1989.

[4] Y. Al-Badawi and H. M. Duwairi . MHD Natural Convection in Iso-Flux Enclosures Filled With Porous Medium. Int. J. Heat Technol. Vol. 28 (2), pp. 87-91,2010.

[5] S. Abishek and S. S. Katte. Magnetohydrodynamic thermo-solutal buoyant darcy convection in a square enclosure. Int. J. Heat Technol, vol. 28(2), pp. 105-116,2010.

[6] E. Fattahi, M. Farhadi, K. Sedighi, H. Nemati, Lattice Boltzmann simulation of natural convection heat transfer in nanofluids, International Journal of Thermal Sciences, vol. 52, pp. 91-101,2012.

[7] G.H.R. Kefayati, S.F. Hosseinizaeh, M. Gorji, H. Sajiadi, Lattice Boltzmann simulation of natural convection in tall enclosures using water/SiO2 nanofluid, International Communications in Heat and Mass Transfer, vol. 38, pp. 798-805, 2011.

[8] F. Lai, Y. Yang, Lattice Boltzmann simulation of natural convection heat transfer of $\mathrm{Al}_{2} \mathrm{O}_{3} /$ water nanofluids in a square enclosure, International Journal of Thermal Sciences, vol. 50, pp. 1930 -1941,2011.

[9] A.H. Mahmoudi, M. Shahi, A.M. Shahedin, N. Hemati, Numerical modeling of natural convection in an open cavity with two vertical thin heat sources subjected to a nanofluid, International Communications in Heat and Mass Transfer, vol.38, pp. 110-118,2011.

[10] H. Nemati, M. Farhadi, K. Sedighi, M.M. Pirouz, E. Fattahi, Numerical simulation of fluid flow around two rotating side by side circular cylinders by Lattice Boltzmann method, International Journal of Computational Fluid Dynamics vol. 24, pp. 83-94,2010.

[11] M. Mehravaran, S.K. Hannani, Simulation of buoyant bubble motion in viscous flows employing lattice Boltzmann and level set methods, Scientia Iranica, vol. 18, pp. 231-240,2011.

[12] D. Martinez, S. Chen, W.H. Matthaeus, Lattice Boltzmann magneto hydrodynamics, Physics of Plasmas, vol. 1, pp. 1850-1867,1994.

[13] H. Nemati, M. Farhadi, K. Sedighi, E. Fattahi, A.A.R. Darzi, Lattice Boltzmann simulation of nanofluid in lid-driven cavity, International Communications in Heat and Mass Transfer, vol. 37, pp. 1528-1534,2010.

[14] B. Ghasemi, S.M. Aminossadati, A. Raisi, Magnetic field effect on natural convection in a nanofluidfilled square enclosure, International Journal of Thermal Sciences vol. 50, pp. 1748-1756,2011.