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Lattice Boltzmann Simulation of MHD Natural Convection in a Nanofluid-Filled Enclosure with Non-Uniform Heating on Both Side Walls

Authors: Imen Mejri, Ahmed Mahmoudi, Mohamed A. Abbassi, Ahmed Omri

Abstract:

This paper examines the natural convection in a square enclosure filled with a water-Al2O3 nanofluid and is subjected to a magnetic field. The side walls of the cavity have spatially varying sinusoidal temperature distributions. The horizontal walls are adiabatic. 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, Ra=103 to 106, Hartmann number varied from Ha=0 to 90, phase deviation (γ=0, π/4, π/2, 3π/4 and π) and the solid volume fraction of the nanoparticles between Ø = 0 and 6%. The results show that the heat transfer rate increases with an increase of the Rayleigh number but it decreases with an increase of the Hartmann number. For γ=π/2 and Ra=105 the magnetic field augments the effect of nanoparticles. At Ha=0, the greatest effects of nanoparticles are obtained at γ = 0 and π/4 for Ra=104 and 105 respectively.

 

Keywords: Lattice Boltzmann Method, magnetic field, Natural convection, nanofluid, Sinusoidal temperature distribution.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1090444

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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 and 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] J.P. Garandet, T. Alboussiere and R. Moreau, "Buoyancy driven convection in a rectangular enclosure with a transverse magnetic field”, International Journal of Heat and Mass Transfer, vol. 35, pp. 741-748, 1992.
[5] M. Venkatachalappa and C.K. Subbaraya, "Natural convection in a rectangular enclosure in the presence of a magnetic field with uniform heat flux from the side walls”, Acta Mechanica, vol. 96, pp. 13-26, 1993.
[6] S. Alchaar, P. Vasseur and E. Bilgen, "Natural convection heat transfer in a rectangular enclosure with a transverse magnetic field”, Journal of Heat Transfer, vol. 117, pp. 668-673, 1995.
[7] N. Rudraiah, R.M. Barron, M. Venkatachalappa and C.K. Subbaraya, "Effect of a magnetic field on free convection in a rectangular enclosure”, International Journal of Engineering Science, vol. 33, pp. 1075-1084, 1995.
[8] K. Khanafer, K. Vafai and M. Lightstone, "Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids”, International Journal of Heat and Mass Transfer, vol. 46, pp. 3639-3653, 2003.
[9] K. Kahveci, "Buoyancy driven heat transfer of nanofluids in a tilted enclosure”, Journal of Heat Transfer, vol. 132, pp. 062501, 2010.
[10] N. Putra, W. Roetzel and S.K. Das, "Natural convection of nano-fluids”, Heat and Mass Transfer, vol. 39, pp. 775-784, 2003.
[11] D. Wen and Y. Ding, "Formulation of nanofluids for natural convective heat transfer applications”, International Journal of Heat and Fluid Flow, vol. 26, pp. 855-864, 2005.
[12] M. Pirmohammadi and M. Ghassemi, "Effect of magnetic field on convection heat transfer inside a tilted square enclosure”, International Communications in Heat and Mass Transfer, vol. 36, pp. 776-780, 2009.
[13] M.C. Ece and E. Buyuk, "Natural-convection flow under a magnetic field in an inclined rectangular enclosure heated and cooled on adjacent walls”, Fluid Dynamics Research, vol. 38, pp. 564-590, 2006.
[14] M. Sathiyamoorthy and A. Chamkha, "Effect of magnetic field on natural convection flow in a liquid gallium filled square cavity for linearly heated side wall(s)”, International Journal of Thermal Sciences, vol. 49, pp. 1856-1865, 2010.
[15] S. Sivasankaran and C.J. Ho, "Effect of temperature dependent properties on MHD convection of water near its density maximum in a square cavity”, International Journal of Thermal Sciences, vol. 47, pp. 1184-1194, 2008.
[16] D. Wen and Y. Ding, "Formulation of nanofluids for natural convective heat transfer applications”, International Journal of Heat and Fluid Flow, vol. 26, pp. 855–864, 2005.
[17] H.F. Oztop and E. Abu-Nada, "Numerical study of natural convection in partially heated rectangular enclosure filled with nanofluids”, International Journal of Heat and Fluid Flow, vol. 29, pp. 1326–1336, 2008.
[18] E. Abu-Nada, "Effects of variable viscosity and thermal conductivity of Al2O3–water nanofluid on heat transfer enhancement in natural convection”, International Journal of Heat and Fluid Flow, vol. 30, pp. 679–690, 2009.
[19] E. Abu-Nada, "Effects of variable viscosity and thermal conductivity of CuO–water nanofluid on heat transfer enhancement in natural convection: mathematical model and simulation”, ASME Journal of Heat Transfer, vol. 132, pp. 052401, 2010.
[20] E. Abu-Nada, Z. Masoud, H. Oztop and A. Campo, "Effect of nanofluid variable properties on natural convection in enclosures”, International Journal of Thermal Sciences, vol. 49, pp. 479–491, 2010.
[21] E. Abu-Nada and A. Chamkha, "Effect of nanofluid variable properties on natural convection in enclosures filled with a CuO–EG–water nanofluid”, International Journal of Thermal Sciences, vol. 49, pp. 2339–2352, 2010.
[22] E. Abu-Nada and A. Chamkha, "Mixed convection flow in a lid-driven inclined square enclosure filled with a nanofluid”, European Journal of Mechanics B Fluids, vol. 29, pp. 472–482, 2010.
[23] Pravez Alam, Ashok Kumar, S. Kapoor and S.R. Ansari, "Numerical investigation of natural convection in a rectangular enclosure due to partial heating and cooling at vertical walls”, Communications in Nonlinear Science and Numerical Simulation, vol. 17, pp. 2403–2414, 2012.
[24] E. Fattahi, M. Farhadi, K. Sedighi and H. Nemati, "Lattice Boltzmann simulation of natural convection heat transfer in nanofluids”, International Journal of Thermal Sciences, vol. 52, pp. 91-101, 2012.
[25] G.H.R. Kefayati, S.F. Hosseinizaeh, M. Gorji and H. Sajjadi, "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.
[26] F. Lai and Y. Yang, "Lattice Boltzmann simulation of natural convection heat transfer of Al2O3/water nanofluids in a square enclosure”, International Journal of Thermal Sciences, vol. 50, pp. 1930-1941, 2011.
[27] A.H. Mahmoudi, M. Shahi, A.M. Shahedin and 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.
[28] GH. R. Kefayati, M. Gorji, D. D. Ganji and H. Sajjadi, "Investigation of Prandtl number effect on natural convection MHD in an open cavity by Lattice Boltzmann Method”, Engineering Computations, vol. 30, pp. 97-116, 2013.
[29] GH. R. Kefayati, M. Gorji, H. Sajjadi and D.D. Ganji, "Lattice Boltzmann simulation of MHD mixed convection in a lid-driven square cavity with linearly heated wall”, Scientia Iranica, vol. 19, pp. 1053–1065, 2012.
[30] H. Nemati, M. Farhadi, K. Sedighi , M.M. Pirouz and 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.
[31] M. Mehravaran and 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.
[32] M. M. Pirouz, M. Farhadi, K. Sedighi, H. Nemati and E. Fattahi, "Lattice Boltzmann simulation of conjugate heat transfer in a rectangular channel with wall-mounted obstacles”, Scientia Iranica, Transaction B: Mechanical Engineering, vol. 18, pp. 213–221, 2011.
[33] A.A. Mohamad, "Applied Lattice Boltzmann Method for transport phenomena, momentum”, Heat and mass transfer, Sure, Calgary, 2007.
[34] S. Succi, "The lattice Boltzmann equation for fluid dynamics and beyond”, Clarendon Press, Oxford, London, 2001.
[35] D. Martinez, S. Chen and W.H. Matthaeus, "Lattice Boltzmann magneto hydrodynamics”, Physics of Plasmas, vol. 1, pp. 1850–1867, 1994.
[36] H. Nemati, M. Farhadi, K. Sedighi, E. Fattahi and 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.
[37] Y. Xuan and W. Roetzel, "Conceptions for heat transfer correlation of nanofluids”, International Journal of Heat and Mass Transfer, vol. 43, pp. 3701-3707, 2000.
[38] H.C. Brinkman, "The viscosity of concentrated suspensions and solution”, The Journal of Chemical Physics, vol. 20, pp. 571-581, 1952.
[39] J.C. Maxwell, "A Treatise on Electricity and Magnetism”, vol. II, Oxford University Press, Cambridge, UK, 1873, pp. 54.
[40] Q.H. Deng and J. Chang, "Natural convection in a rectangular enclosure with sinusoidal temperature distributions on both sidewalls”, Numer. Heat Transfer A, vol. 54, pp. 507–524, 2008.
[41] B. Ghasemi, S.M. Aminossadati and A. Raisi, "Magnetic field effect on natural convection in a nanofluid-filled square enclosure”, International Journal of Thermal Sciences, vol. 50, pp. 1748-1756, 2011.
[42] M. Jahanshahi , S.F. Hosseinizadeh , M. Alipanah , A. Dehghani and G.R. Vakilinejad "Numerical simulation of free convection based on experimental measured conductivity in a square cavity using Water/SiO2 nanofluid”, International Communications in Heat and Mass Transfer, vol. 37, pp. 687–694, 2010.