0
Research Papers: Porous Media

Parametric Study of Rarefaction Effects on Micro- and Nanoscale Thermal Flows in Porous Structures

[+] Author and Article Information
A. H. Meghdadi Isfahani

Department of Mechanical Engineering,
Islamic Azad University,
Najafabad Branch,
Najafabad 8514143131, Iran
e-mails: amir_meghdadi@pmc.iaun.ac.ir;
amir_meghdadi@yahoo.com

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received September 8, 2016; final manuscript received March 11, 2017; published online May 9, 2017. Assoc. Editor: Peter Vadasz.

J. Heat Transfer 139(9), 092601 (May 09, 2017) (9 pages) Paper No: HT-16-1563; doi: 10.1115/1.4036525 History: Received September 08, 2016; Revised March 11, 2017

Hydrodynamics and heat transfer in micro/nano channels filled with porous media for different porosities and Knudsen numbers, Kn, ranging from 0.1 to 10, are considered. The performance of standard lattice Boltzmann method (LBM) is confined to the microscale flows with a Knudsen number less than 0.1. Therefore, by considering the rarefaction effect on the viscosity and thermal conductivity, a modified thermal LBM is used, which is able to extend the ability of LBM to simulate wide range of Knudsen flow regimes. The present study reports the effects of the Knudsen number and porosity on the flow rate, permeability, and mean Nusselt number. The Knudsen's minimum effect for micro/nano channels filled with porous media was observed. In addition to the porosity and Knudsen number, the obstacle sizes have important role in the heat transfer, so that enhanced heat transfer is observed when the obstacle sizes decrease. For the same porosity and Knudsen number, the inline porous structure has the highest heat transfer performance.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Ai, Y. , Yalcin, S. E. , Gu, D. , Baysal, O. , Baumgart, H. , Qian, S. , and Beskok, A. , 2010, “ A Low-Voltage Nano-Porous Electroosmotic Pump,” J. Colloid Interface Sci., 350(2), pp. 465–470. [CrossRef] [PubMed]
Jiang, R. H. , Lin, C. F. , Yang, C. C. , Fan, F. H. , Huang, Y. C. , Tseng, W.-P. , Cheng, P. F. , Wu, K. C. , and Wang, J. H. , 2012, “ InGaN Light-Emitting Diode With a Nanoporous/Air-Channel Structure,” Appl. Phys. Express, 6(1), p. 012103. [CrossRef]
Kondrashova, D. , Lauerer, A. , Mehlhorn, D. , Jobic, H. , Feldhoff, A. , Thommes, M. , Chakraborty, D. , Gommes, C. , Zecevic, J. , Jongh, P. , Bunde, A. , Kärger, J. , and Valiullin, R. , 2017, “ Scale-Dependent Diffusion Anisotropy in Nanoporous Silicon,” Sci. Rep., 7, p. 40207. [CrossRef] [PubMed]
Ohba, T. , 2016, “ Limited Quantum Helium Transportation Through Nano-Channels by Quantum Fluctuation,” Sci. Rep., 6(1), p. 28992. [CrossRef] [PubMed]
Jeong, N. , Choi, D. H. , and Lin, C. L. , 2006, “ Prediction of Darcy-Forchheimer Drag for Micro-Porous Structures of Complex Geometry Using the Lattice Boltzmann Method,” J. Micromech. Microeng., 16(10), pp. 2240–2250. [CrossRef]
Yuranov, I. , Renken, A. , and Kiwi-Minsker, L. , 2005, “ Zeolite/Sintered Metal Fibers Composites as Effective Structured Catalyst,” Appl. Catal., 281(55), pp. 55–60.
Kiwi-Minsker, L. , and Renken, A. , 2005, “ Microstructured Reactors for Catalytic Reactions,” Catal. Today, 110(2), pp. 2–14.
Assis, O. B. G. , and Claro, L. C. , 2003, “ Immobilized Lysozyme Protein on Fibrous Medium: Preliminary Results for Microfilteration Applications,” Electron. J. Biotechnol., 6(2), epub.
Brask, A. , Goranovic, G. , Jensen, M. J. , and Bruus, H. , 2005, “ A Novel Electro-Osmotic Pump Design for Nonconducting Liquids: Theoretical Analysis of Flow Rate–Pressure Characteristics and Stability,” J. Micromech. Microeng., 15(4), pp. 883–891. [CrossRef]
Bazant, M. Z. , and Squires, T. M. , 2004, “ Induced-Charge Electrokinetic Phenomena: Theory and Microfluidic Applications,” Phys. Rev. Lett., 92(6), p. 066101.
Oddy, M. H. , Santiago, J. G. , and Michelsen, J. C. , 2001, “ Electrokinetic Instability Micromixing,” Anal. Chem., 73(24), pp. 5822–5832. [CrossRef] [PubMed]
Biddiss, E. , Erickson, D. , and Li, D. Q. , 2004, “ Heterogeneous Surface Charge Enhanced Micromixing for Electrokinetic Flows,” Anal. Chem., 7(11), pp. 3208–3213. [CrossRef]
Wong, P. K. , Wang, J. T. , Deval, J. H. , and Ho, C. M. , 2004, “ Electrokinetics in Micro Devices for Biotechnology Applications,” IEEE/ASME Trans. Mechatronics, 9(2), pp. 366–376. [CrossRef]
Jiang, P. X. , Fan, M. H. , Si, G. S. , and Ren, Z. P. , 2001, “ Thermal-Hydraulic Performance of Small Scale Micro-Channel and Porous-Media Heat-Exchangers,” Int. J. Heat Mass Transfer, 44(5), pp. 1039–1051. [CrossRef]
Mahdavi, M. , Saffar-Avval, M. , Tiari, S. , and Mansoori, Z. , 2014, “ Entropy Generation and Heat Transfer Numerical Analysis in Pipes Partially Filled With Porous Medium,” Int. J. Heat Mass Transfer, 79, pp. 496–506. [CrossRef]
Rong, F. , Zhang, W. , Shi, B. , and Guo, Z. , 2014, “ Numerical Study of Heat Transfer Enhancement in a Pipe Filled With Porous Media by Axisymmetric TLB Model Based on GPU,” Int. J. Heat Mass Transfer, 70, pp. 1040–1049. [CrossRef]
Buonomo, B. , Manca, O. , and Lauriat, G. , 2014, “ Forced Convection in Micro-Channels Filled With Porous Media in Local Thermal Non-Equilibrium Conditions,” Int. J. Therm. Sci., 77, pp. 206–222. [CrossRef]
Shokouhmand, H. , Meghdadi Isfahani, A. H. , and Shirani, E. , 2010, “ Friction and Heat Transfer Coefficient in Micro and Nano Channels Filled With Porous Media for Wide Range of Knudsen Number,” Int. Commun. Heat Mass Transfer, 37(7), pp. 890–894. [CrossRef]
Karniadakis, G. , Beskok, A. , and Aluru, N. , 2005, Microflows and Nanoflows Fundamentals and Simulation, Springer, New York.
Abolfazli Esfahani, J. , and Norouzi, A. , 2014, “ Two Relaxation Time Lattice Boltzmann Model for Rarefied Gas Flows,” Physica A, 393, pp. 51–61. [CrossRef]
Liu, X. , and Guo, Z. , 2013, “ A Lattice Boltzmann Study of Gas Flows in a Long Micro-Channel,” Comput. Math. Appl., 65(2), pp. 186–193. [CrossRef]
Gokaltun, S. , and Dulikravich, G. S. , 2014, “ Lattice Boltzmann Method for Rarefied Channel Flows With Heat Transfer,” Int. J. Heat Mass Transfer, 78, pp. 796–804. [CrossRef]
Islam, M. S. , Caulkin, R. , Jia, X. , Fairweather, M. , and Williams, R. A. , 2012, “ Prediction of the Permeability of Packed Beds of Non-Spherical Particles,” Comput. Aided Chem. Eng., 30, pp. 1088–1092.
Lopez, P. , and Bayazitoglu, Y. , 2013, “ An Extended Thermal Lattice Boltzmann Model for Transition Flow,” Int. J. Heat Mass Transfer, 65, pp. 374–380. [CrossRef]
Chikatamarla, S. S. , and Karlin, I. V. , 2006, “ Entropy and Galilean Invariance of Lattice Boltzmann Theories,” Phys. Rev. Lett., 97(19), p. 190601. [CrossRef] [PubMed]
Ansumali, S. , Karlin, I. V. , Arcidiacono, S. , Abbas, A. , and Prasianakis, N. I. , 2007, “ Hydrodynamics Beyond Navier–Stokes: Exact Solution to the Lattice Boltzmann Hierarchy,” Phys. Rev. Lett., 98(12), p. 124502. [CrossRef] [PubMed]
Kim, S. H. , Pitsch, H. P. , and Boyd, I. D. , 2008, “ Accuracy of Higher-Order Lattice Boltzmann Methods for Microscale Flows With Finite Knudsen Numbers,” J. Comput. Phys., 227(19), pp. 8655–8671. [CrossRef]
Zhang, Y. H. , Gu, X. J. , Barber, R. W. , and Emerson, D. R. , 2006, “ Capturing Knudsen Layer Phenomena Using a Lattice Boltzmann Model,” Phys. Rev. E., 74(4), p. 046704. [CrossRef]
Tang, G. H. , Zhang, Y. H. , and Emerson, D. R. , 2008, “ Lattice Boltzmann Models for Nonequilibrium Gas Flows,” Phys. Rev. E., 77(4), p. 046701. [CrossRef]
Tang, G. H. , Zhang, Y. H. , Gu, X. J. , and Emerson, D. R. , 2008, “ Lattice Boltzmann Modeling Knudsen Layer Effect in Non-Equilibrium Flows,” EPL, 83(4), p. 40008. [CrossRef]
Homayoon, A. , Meghdadi Isfahani, A. H. , Shirani, E. , and Ashrafizadeh, M. , 2011, “ A Novel Modified Lattice Boltzmann Method for Simulation of Gas Flows in Wide Range of Knudsen Number,” Int. Commun. Heat Mass Transfer, 38(6), pp. 827–832. [CrossRef]
Shokouhmand, H. , and Meghdadi Isfahani, A. H. , 2011, “ An Improved Thermal Lattice Boltzmann Model for Rarefied Gas Flows in Wide Range of Knudsen Number,” Int. Commun. Heat Mass Transfer, 38(10), pp. 1463–1469. [CrossRef]
Zhuo, C. , and Zhong, C. , 2013, “ Filter-Matrix Lattice Boltzmann Model for Microchannel Gas Flows,” Phys. Rev. E, 88(5), p. 053311. [CrossRef]
Liou, T.-M. , and Lin, C.-T. , 2013, “ Study on Microchannel Flows With a Sudden Contraction–Expansion at a Wide Range of Knudsen Number Using Lattice Boltzmann Method,” Microfluid. Nanofluid., 16(1), pp. 315–327.
Li, Q. , He, Y. L. , Tang, G. H. , and Tao, W. Q. , 2011, “ Lattice Boltzmann Modeling of Microchannel Flows in the Transition Flow Regime,” Microfluid. Nanofluid., 10(3), pp. 607–618. [CrossRef]
Kalarakis, A. N. , Michalis, V. K. , Skouras, E. D. , and Burganos, V. N. , 2012, “ Mesoscopic Simulation of Rarefied Flow in Narrow Channels and Porous Media,” Transp. Porous Media, 94(1), pp. 385–398. [CrossRef]
Jin, Y. , Uth, M. F. , and Kuznetsov, A. V. , 2015, “ Numerical Investigation of the Possibility of Macroscopic Turbulence in Porous Media: A Direct Numerical Simulation Study,” J. Fluid Mech., 766, pp. 76–103. [CrossRef]
Uth, M. F. , Jin, Y. , and Kuznetsov, A. V. , 2016, “ A Direct Numerical Simulation Study on the Possibility of Macroscopic Turbulence in Porous Media: Effects of Different Solid Matrix Geometries, Solid Boundaries, and Two Porosity Scales,” Phys. Fluids, 28(6), p. 065101. [CrossRef]
Klinkenberg, L. J. , 1941, “ The Permeability of Porous Media to Liquids and Gases,” Drilling and Productions Practices, American Petroleum Institute, New York.
Scheidegger, A. E. , 1972, The Physics of Flow Through Porous Media, 3rd ed., University of Toronto Press, Toronto, ON, Canada.
Peng, Y. , 2005, “ Thermal Lattice Boltzmann Two-Phase Flow Model for Fluid Dynamics,” Ph.D. thesis, University of Pittsburgh, Pittsburgh, PA.
Cercignani, C. , 1988, The Boltzmann Equations and Its Applications, Springer-Verlag, New York.
He, X. Y. , Chen, S. Y. , and Doolen, G. D. , 1998, “ A Novel Thermal Model for the Lattice Boltzmann Method in Incompressible Limit,” J. Comput. Phys., 146(1), pp. 282–300. [CrossRef]
Succi, S. , 2001, The Lattice Boltzmann Equation: for Fluid Dynamics and Beyond, Oxford University Press, Oxford, UK.
Succi, S. , 2002, “ Mesoscopic Modeling of Slip Motion at Fluid-Solid Interfaces With Heterogeneous Catalysis,” J. Phys. Rev. Lett., 89(6), p. 064502. [CrossRef]
Lim, C. Y. , Shu, C. , Niu, X. D. , and Chew, Y. T. , 2002, “ Application of Lattice Boltzmann Method to Simulate Microchannel Flows,” J. Phys. Fluids., 14(7), pp. 2299–2308. [CrossRef]
Verhaeghe, F. , Luo, L. S. , and Blanpain, B. , 2009, “ Lattice Boltzmann Modeling of Microchannel Flow in Slip Flow Regime,” J. Comput. Phys., 228(1), pp. 147–157. [CrossRef]
Pan, C. , Luo, L. S. , and Miller, C. T. , 2006, “ An Evaluation of Lattice Boltzmann Schemes for Porous Medium Flow Simulation,” Comput. Fluids, 35(8–9), pp. 898–909. [CrossRef]
Tang, G. H. , Tao, W. Q. , and He, Y. L. , 2005, “ Gas Slippage Effect on Microscale Porous Flow Using the Lattice Boltzmann Method,” Phys. Rev. E, 72(5), p. 056301. [CrossRef]
Ergun, S. , 1952, “ Fluid Flow Through Packed Columns,” Chem. Eng. Prog., 48(2), pp. 89–94.
Bear, J. , 1972, Dynamic of Fluids in Porous Media, Elsevier, Amsterdam, The Netherlands.
Niu, X. D. , Chew, Y. T. , and Shu, C. , 2004, “ A Lattice Boltzmann BGK Model for Simulation of Micro Flows,” Europhys. Lett., 67(4), p. 600. [CrossRef]
Niu, X. D. , Shu, C. , and Chew, Y. T. , 2007, “ A Thermal Lattice Boltzmann Model With Diffuse Scattering Boundary Condition for Micro Thermal Flows,” Comput. Fluids, 36(2), pp. 273–281. [CrossRef]
Hadjiconstantinou, N. G. , and Simek, O. , 2002, “ Constant-Wall-Temperature Nusselt Number in Micro and Nano-Channels,” ASME J. Heat Transfer, 124(2), pp. 356–364. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

The simulated porous structure: (a) ε=0.881, (b) ε=0.861, (c) ε=0.825, (d) ε=0.732, (e) inline ε=0.877, and (f) staggered ε=0.897

Grahic Jump Location
Fig. 2

Volumetric flow rate as a function of exit

Grahic Jump Location
Fig. 3

The volume flow rate versus the pressure gradient. Labels ε=0.877(L) and ε=0.897(S) represent the results of inline and staggered porous structures, respectively.

Grahic Jump Location
Fig. 4

Knudsen minimum effect

Grahic Jump Location
Fig. 5

The Knudsen number influence on Darcy number

Grahic Jump Location
Fig. 6

Nondimensional pressure drop versus Reynolds number

Grahic Jump Location
Fig. 7

Pressure drops considering the compressibility versus Reynolds number

Grahic Jump Location
Fig. 8

Nusselt number obtained from the DSMC and the new LBM (Pr = 2/3)

Grahic Jump Location
Fig. 9

The heat transfer control volume

Grahic Jump Location
Fig. 10

The Knudsen number effect on the mean temperature along the channel for pi/po=1.1

Grahic Jump Location
Fig. 11

The effect of Knudsen number at the channel outlet on the average Nusselt number

Grahic Jump Location
Fig. 12

The porosity effect on the mean Nusselt number

Grahic Jump Location
Fig. 13

The porosity effect on the mean temperature distribution along the channel

Grahic Jump Location
Fig. 14

The particle size effect of the mean temperature distribution along the channel

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In