Lattice Boltzmann simulation of MHD natural convection in a nanofluid-filled cavity with linear temperature distribution

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 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, Ra = 103 to 105, Hartmann number varied from Ha = 0 to 60, the inclination angle of the magnetic field relative to the horizontal plane γ = 0° to 180° and the solid volume fraction of the nanoparticles between ϕ = 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. Also for Ra ≥ 5 × 104 and for the range of Hartmann number study, we note that the heat transfer and fluid flow depend 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]  Pravez Alam,et al.  Numerical investigation of natural convection in a rectangular enclosure due to partial heating and cooling at vertical walls , 2012 .

[2]  Mohsen Jahanshahi,et al.  Numerical simulation of free convection based on experimental measured conductivity in a square cavity using Water/SiO2 nanofluid , 2010 .

[3]  Eiyad Abu-Nada,et al.  Effects of variable viscosity and thermal conductivity of Al2O3-water nanofluid on heat transfer enhancement in natural convection , 2009 .

[4]  J. Maxwell.  A Treatise on Electricity and Magnetism , 1873, Nature.

[5]  K. Kahveci.  Buoyancy Driven Heat Transfer of Nanofluids in a Tilted Enclosure , 2010 .

[6]  S. Hannani,et al.  Simulation of buoyant bubble motion in viscous flows employing lattice Boltzmann and level set methods , 2011 .

[7]  H. Sajjadi,et al.  Lattice Boltzmann simulation of natural convection in tall enclosures using water/SiO2 nanofluid , 2011 .

[8]  Davood Domiri Ganji,et al.  Investigation of Prandtl number effect on natural convection MHD in an open cavity by lattice Boltzmann method , 2012 .

[9]  Hiroyuki Ozoe,et al.  The effect of the direction of the external magnetic field on the three-dimensional natural convection in a cubical enclosure , 1989 .

[10]  Ali J. Chamkha,et al.  Effect of magnetic field on natural convection flow in a liquid gallium filled square cavity for linearly heated side wall(s) , 2010 .

[11]  W. Roetzel,et al.  Conceptions for heat transfer correlation of nanofluids , 2000 .

[12]  R. Moreau,et al.  Buoyancy driven convection in a rectangular enclosure with a transverse magnetic field , 1992 .

[13]  H. Sajjadi,et al.  Lattice Boltzmann simulation of natural convection in an open enclosure subjugated to water/copper nanofluid , 2012 .

[14]  Mina Shahi,et al.  Numerical modeling of natural convection in an open cavity with two vertical thin heat sources subjected to a nanofluid , 2011 .

[15]  M. Farhadi,et al.  Numerical simulation of fluid flow of two rotating side-by-side circular cylinders by Lattice Boltzmann method , 2010 .

[16]  K. Khanafer,et al.  BUOYANCY-DRIVEN HEAT TRANSFER ENHANCEMENT IN A TWO-DIMENSIONAL ENCLOSURE UTILIZING NANOFLUIDS , 2003 .

[17]  D. Martínez,et al.  Lattice Boltzmann magnetohydrodynamics , 1994, comp-gas/9401002.

[18]  Saiied M. Aminossadati,et al.  Magnetic field effect on natural convection in a nanofluid-filled square enclosure , 2011 .

[19]  J. Boon.  The Lattice Boltzmann Equation for Fluid Dynamics and Beyond , 2003 .

[20]  Yulong Ding,et al.  Experimental investigation into convective heat transfer of nanofluids at the entrance region under laminar flow conditions , 2004 .

[21]  S. Ostrach.  Natural convection in enclosures , 1988 .

[22]  Ching-Jenq Ho,et al.  Effect of temperature dependent properties on MHD convection of water near its density maximum in a square cavity , 2008 .

[23]  W. Roetzel,et al.  Natural convection of nano-fluids , 2003 .

[24]  Majid Ghassemi,et al.  Effect of magnetic field on convection heat transfer inside a tilted square enclosure , 2009 .

[25]  Ronald M. Barron,et al.  Effect of a magnetic field on free convection in a rectangular enclosure , 1995 .

[26]  Mehmet Cem Ece,et al.  Natural-convection flow under a magnetic field in an inclined rectangular enclosure heated and cooled on adjacent walls , 2006 .

[27]  D. Ganji,et al.  Lattice Boltzmann simulation of MHD mixed convection in a lid-driven square cavity with linearly heated wall , 2012 .

[28]  E. Bilgen,et al.  Natural Convection Heat Transfer in a Rectangular Enclosure With a Transverse Magnetic Field , 1995 .

[29]  Ali J. Chamkha,et al.  Effect of nanofluid variable properties on natural convection in enclosures filled with a CuO–EG–Water nanofluid , 2010 .

[30]  Yulong Ding,et al.  Formulation of nanofluids for natural convective heat transfer applications , 2005 .

[31]  M. Farhadi,et al.  Lattice Boltzmann simulation of conjugate heat transfer in a rectangular channel with wall-mounted obstacles , 2011 .

[32]  Ali J. Chamkha,et al.  Mixed convection flow in a lid-driven inclined square enclosure filled with a nanofluid , 2010 .

[33]  Ziyad N. Masoud,et al.  Effect of nanofluid variable properties on natural convection in enclosures , 2010 .

[34]  M. Farhadi,et al.  Lattice Boltzmann simulation of nanofluid in lid-driven cavity , 2010 .

[35]  H. Oztop,et al.  Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids , 2008 .

[36]  Tanmay Basak,et al.  Steady natural convection flows in a square cavity with linearly heated side wall(s) , 2007 .

[37]  M. Farhadi,et al.  Lattice Boltzmann simulation of natural convection heat transfer in nanofluids , 2012 .

[38]  H. Brinkman.  The Viscosity of Concentrated Suspensions and Solutions , 1952 .

[39]  Yue-Tzu Yang,et al.  Lattice Boltzmann simulation of natural convection heat transfer of Al2O3/water nanofluids in a square enclosure , 2011 .

[40]  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 , 2010 .

[41]  C. K. Subbaraya,et al.  Natural convection in a rectangular enclosure in the presence of a magnetic field with uniform heat flux from the side walls , 1993 .