In this paper, a
Lattice Boltzmann method was used to simulate the flow of temperature-sensitive
magnetic fluids in a micro porous cavity. According to Navier’s linear slip
length model, slip boundary conditions were used on all the walls of the micro
porous cavity. The effects of the horizontal slip length and the vertical slip
length on the flow and heat transfer characteristics were investigated. The results
showed that with the increase of the slip length, the velocities and their
gradients became smaller, so the convection was harder to occur, and the temperature
was more stable. On the walls, the effects of the slip lengths on the Nusselt
numbers at the edges and at the centers were different, so the local heat
transfer efficiencies were changed accordingly. It was also found that when the
horizontal slip length was set to be zero, the flow developed from one vertex
to two vortexes along the vertical direction with the increase of vertical slip
length. The corresponding critical vertical slip length first increased and
then decreased with the Rayleigh number and the magnetic Rayleigh number.
Cite this paper
Chen, X. , Jin, L. and Zhang, X. (2014). Slip Flow and Heat Transfer of Magnetic Fluids in Micro Porous Media Using a Lattice Boltzmann Method. Open Access Library Journal, 1, e1165. doi: http://dx.doi.org/10.4236/oalib.1101165.
Guo, Z. and Zhao, T.S. (2005) Lattice Boltzmann Simulation of Natural Convection
with Temperature-Dependent Viscosity in a Porous Cavity. Progress in Computational Fluid Dynamics, 5, 110-117. http://dx.doi.org/10.1504/PCFD.2005.005823
Park, J., Matsubara, M. and Li, X. (2007) Application of Lattice Boltzmann
Method to a Micro-Scale Flow Simulation in the Porous Electrode of a PEM Fuel
Cell. Journal of Power Sources, 173, 404-414. http://dx.doi.org/10.1016/j.jpowsour.2007.04.021
Wang, M. and Chen, S. (2007) Electroosmosis in Homogeneously
Charger Micro- and Nanoscale Random Porous Media. Journal of Colloid and Interface Science, 314, 264-273. http://dx.doi.org/10.1016/j.jcis.2007.05.043
Wang M., Kang Q., Viswanathan, H. and Robinson, B.A. (2010) Modeling
of Electro-Osmosis of Dilute Electrolyte Solutions in Silica Microporous Media. Journal of Geophysical Research, 115, B10205. http://dx.doi.org/10.1029/2010JB007460
Tang, G.H., Ye, P.X. and Tao, W.Q. (2010) Pressure-Driven and Electroosmotic Non-Newtonian Flows
through Microporous Media via Lattice Boltzmann Method. Journal of Non-Newtonian Fluid Mechanics, 165, 1536-1542.
Cottin-Bizonne
C., Cross B., Steinberger, A. and Charlaix, E. (2005) Boundary Slip on Smooth Hydrophobic Surfaces: Intrinsic
Effects and Possible Artifacts. Physical
Review Letters, 94, Article
ID: 056102. http://dx.doi.org/10.1103/PhysRevLett.94.056102
Shirani, E. and Jafari, S. (2007) Application of LBM in Simulation of Flow in Simple
Micro-Geometries and Micro Porous Media. African
Physical Review, 1, 0002.
Takenaka, S., Suga, K., Kinjo, T. and Hyodo, S. (2009) Flow Simulation in a
Sub-Micro Porous Medium by the Lattice Boltzmann and the Molecular Dynamics
Methods. The 7th International ASME Conference on Nanochannels, Microchannels and Minichannels, Pohang, 22-24 June
2009, 1-10.
Suga, K., Takenaka, S., Kinjo, T. and Hyodo, S. (2009) LBM and MD Simulations of a Flow in a Nano-Porous Medium. 2nd Asian Symposium on Computational Heat
Transfer and Fluid Flow, Jeju,
20-23 October 2009, 112-117.
Thompson, P.A. and Troian, S.M (1997) A General Boundary Condition for
Liquid Flow at Solid Surfaces. Nature, 389, 360-362. http://dx.doi.org/10.1038/38686
Sofonea, V. and Sekerka, R.F. (2005) Boundary Conditions for
the Upwind Finite Difference Lattice Boltzmann Model: Evidence of Slip Velocity
in Micro-Channel Flow. Journal of
Computational Physics, 207, 639-659. http://dx.doi.org/10.1016/j.jcp.2005.02.003
Chen, S. and Tian, Z. (2010) Simulation of Thermal
Micro-Flow Using Lattice Boltzmann Method with Langmuir Slip Model. International Journal of Heat and Fluid Flow, 31, 227-235. http://dx.doi.org/10.1016/j.ijheatfluidflow.2009.12.006
Yang, F. (2007) Flow Behavior of an Eyring Fluid in a Nanotube: The Effect
of the Slip Boundary Condition. Applied
Physics Letters, 90, Article
ID: 133105. http://dx.doi.org/10.1063/1.2717019
Larrode, F.E., Housiadas, C. and Drossinos, Y. (2000) Slip-Flow Heat Transfer in Circular Tubes. International Journal of Heat and Mass
Transfer, 43, 2669-2680. http://dx.doi.org/10.1016/S0017-9310(99)00324-5
Jin, L., Zhang, X. and Niu, X. (2011) Lattice Boltzmann Simulation for Temperature-Sensitive
Magnetic Fluids in a Porous Square Cavity. Journal
of Magnetism and Magnetic Materials, 324, 44-51. http://dx.doi.org/10.1016/j.jmmm.2011.07.033
Jin, L. and Zhang, X. (2013) Analysis of Temperature-Sensitive Magnetic Fluids in a Porous
Square Cavity Depending on Different Porosity and Darcy Number. Applied Thermal Engineering, 50, 1-11. http://dx.doi.org/10.1016/j.applthermaleng.2012.05.016