Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-19T05:15:15.820Z Has data issue: false hasContentIssue false
  • English
  • Français

Lattice Boltzmann Modeling of Thermal Conduction in Composites with Thermal Contact Resistance

Published online by Cambridge University Press:  30 April 2015

Chiyu Xie ,
Jinku Wang ,
Dong Wang ,
Ning Pan  and
Moran Wang
Chiyu Xie
Affiliation:
Department of Engineering Mechanics and CNMM, Tsinghua University, Beijing 100084, China
Jinku Wang
Affiliation:
National Institute of Metrology, Beijing 100084, China
Dong Wang
Affiliation:
School of Materials Science, Wuhan Textile University, Wuhan, Hubei 430200, China
Ning Pan
Affiliation:
Nanomaterials in Environment, Agriculture & Technology (NEAT), University of California, Davis, CA 95616, USA
Moran Wang*
Affiliation:
Department of Engineering Mechanics and CNMM, Tsinghua University, Beijing 100084, China School of Materials Science, Wuhan Textile University, Wuhan, Hubei 430200, China
*
*Corresponding author. Email addresses: [email protected] (C. Xie), [email protected] (J. Wang), [email protected] (D. Wang), [email protected] (N. Pan), [email protected] (M. Wang)
Get access

Abstract

The effective thermal conductivity of composite materials with thermal contact resistance at interfaces is studied by lattice Boltzmann modeling in this work. We modified the non-dimensional partial bounce-back scheme, proposed by Han et al. [Int. J. Thermal Sci., 2008. 47: 1276-1283], to introduce a real thermal contact resistance at interfaces into the thermal lattice Boltzmann framework by re-deriving the redistribution function of heat at the phase interfaces for a corrected dimensional formulation. The modified scheme was validated in several cases with good agreement between the simulation results and the corresponding theoretical solutions. Furthermore, we predicted the effective thermal conductivities of composite materials using this method where the contact thermal resistance was not negligible, and revealed the effects of particle volume fraction, thermal contact resistance and particle size. The results in this study may provide a useful support for materials design and structure optimization.

Keywords

65.80.-gLattice Boltzmann methodpartial bounce-back schemethermal contact resistanceeffective thermal conductivity
Type
Research Article
Information
Communications in Computational Physics , Volume 17 , Issue 4 , April 2015 , pp. 1037 - 1055
Copyright
Copyright © Global-Science Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Sartre, V., Lallemand, M., Enhancement of thermal contact conductance for electronic systems, Applied Thermal Engineering, 21 (2001) 221–235.CrossRefGoogle Scholar
[2]Grujicic, M., Zhao, C.L., Dusel, E.C., The effect of thermal contact resistance on heat management in the electronic packaging, Applied Surface Science, 246 (2005) 290–302.CrossRefGoogle Scholar
[3]Hasselman, D.P.H., Johnson, L.F, Effective Thermal Conductivity of Composites with Interfacial Thermal Barrier Resistance, Journal of Composite Materials, 21 (1987) 508–515.Google Scholar
[4]Nan, C.-W., Birringer, R., Clarke, D.R., Gleiter, H., Effective thermal conductivity of particulate composites with interfacial thermal resistance, Journal of Applied Physics, 81 (1997) 6692–6699.Google Scholar
[5]Sridhar, M.R., Yovanovicht, M.M, Review of elastic and plastic contact conductance models: Comparison with experiment, Journal of Thermophysics and Heat Transfer, 8 (1994) 633–640.Google Scholar
[6]Clausing, A.M., Chao, B.T, Thermal Contact Resistance in a Vacuum Environment, Journal of Heat Transfer, 87 (1965) 243–250.Google Scholar
[7]Bahrami, M., Culham, J.R., Yananovich, M.M., Schneider, G.E., Review of thermal joint resistance models for nonconforming rough surfaces, Applied Mechanics Reviews, 59 (2006) 1–12.Google Scholar
[8]Chen, S., Doolen, G.D, Lattice boltzmann method for fluid flows, Annual Review of Fluid Mechanics, 30 (1998) 329–364.Google Scholar
[9]Aidun, C.K., Clausen, J.R, Lattice-Boltzmann method for complex flows, Annual Review of Fluid Mechanics, 42 (2010) 439–472.Google Scholar
[10]Chen, S., Chen, H., Martnez, D., Matthaeus, W., Lattice Boltzmann model for simulation of magnetohydrodynamics, Physical Review Letters, 67 (1991) 3776–3779.Google Scholar
[11]Martinez, D.O., Shiyi, C., Matthaeus, W.H., Lattice Boltzmann thermohydrodynamics, Physics of Plasmas, 1 (1994) 1850–1867.Google Scholar
[12]He, X., Li, N., Lattice Boltzmann simulation of electrochemical systems, Computer Physics Communications, 129 (2000) 158–166.CrossRefGoogle Scholar
[13]Breyiannis, G., Valougeorgis, D., Lattice kinetic simulations in three-dimensional magneto-hydrodynamics, Physical Review E, 69 (2004) 065702.Google Scholar
[14]Wang, J., Wang, M., Li, Z., Lattice Boltzmann simulations of mixing enhancement by the electro-osmotic flow in microchannels, Modern Physics Letters B, 19 (2005) 1515–1518.Google Scholar
[15]Guo, Z., Zhao, T.S., Shi, Y., A lattice Boltzmann algorithm for electro-osmotic flows in microfluidic devices, The Journal of Chemical Physics, 122 (2005) 144907.Google Scholar
[16]Wang, J., Wang, M., Li, Z., Lattice Poisson-Boltzmann simulations of electro-osmotic flows in microchannels, Journal of Colloid and Interface Science, 296 (2006) 729–736.Google Scholar
[17]Wang, M., Kang, Q., Electrokinetic transport in microchannels with random roughness, Analytical Chemistry, 81 (2009) 2953–2961.Google Scholar
[18]Alexander, F.J., Chen, S., Sterling, J.D., Lattice Boltzmann thermohydrodynamics, Physical Review E, 47 (1993) R2249-R2252.Google Scholar
[19]McNamara, G., Alder, B., Analysis of the lattice Boltzmann treatment of hydrodynamics, Physica A: Statistical Mechanics and its Applications, 194 (1993) 218–228.Google Scholar
[20]Chen, Y., Ohashi, H., Akiyama, M., Thermal lattice Bhatnagar-Gross-Krook model without nonlinear deviations in macrodynamic equations, Physical Review E, 50 (1994) 2776–2783.CrossRefGoogle ScholarPubMed
[21]Shan, X., Simulation of Rayleigh-Bénard convection using a lattice Boltzmann method, Physical Review E, 55 (1997) 2780–2788.Google Scholar
[22]Eggels, J.G.M., Somers, J.A, Numerical simulation of free convective flow using the lattice-Boltzmann scheme, International Journal of Heat and Fluid Flow, 16 (1995) 357–364.Google Scholar
[23]He, X., Chen, S., Doolen, G.D., A novel thermal model for the lattice Boltzmann method in incompressible limit, Journal of Computational Physics, 146 (1998) 282 – 300.Google Scholar
[24]Peng, Y., Shu, C., Chew, Y.T., Simplified thermal lattice Boltzmann model for incompressible thermal flows, Physical Review E, 68 (2003) 026701.Google Scholar
[25]Wang, J., Wang, M., Li, Z., A lattice Boltzmann algorithm for fluid-solid conjugate heat transfer, International Journal of Thermal Sciences, 46 (2007) 228–234.CrossRefGoogle Scholar
[26]Wang, M., Wang, J., Pan, N., Chen, S., Mesoscopic predictions of the effective thermal conductivity for microscale random porous media, Physical Review E, 75 (2007) 036702.Google Scholar
[27]Wang, M., He, J., Yu, J., Pan, N., Lattice Boltzmann modeling of the effective thermal conductivity for fibrous materials, International Journal of Thermal Sciences, 46 (2007) 848–855.Google Scholar
[28]Wang, M., Wang, J., Pan, N., Chen, S., He, J., Three-dimensional effect on the effective thermal conductivity of porous media, Journal of Physics D: Applied Physics, 40 (2007) 260–265.Google Scholar
[29]Wang, M., Kang, Q., Pan, N., Thermal conductivity enhancement of carbon fiber composites, Applied Thermal Engineering, 29 (2009) 418–421.Google Scholar
[30]Wang, M., Pan, N., Modeling and prediction of the effective thermal conductivity of random open-cell porous foams, International Journal of Heat and Mass Transfer, 51 (2008) 1325–1331.Google Scholar
[31]Wang, M.R., Pan, N., Wang, J.K., Chen, S.Y., Mesoscopic simulations of phase distribution effects on the effective thermal conductivity of microgranular porous media, Journal of Colloid and Interface Science, 311 (2007) 562–570.Google Scholar
[32]Midttomme, K., Roaldset, E., The effect of grain size on thermal conductivity of quartz sands and silts, Petroleum Geoscience, 4 (1998) 165–172.Google Scholar
[33]Liang, J.Z., Li, F.H, Measurement of thermal conductivity of hollow glass-bead-filled polypropylene composites, Polymer Testing, 25 (2006) 527–531.Google Scholar
[34]Alvarez, F.X., Jou, D., Sellitto, A., Pore-size dependence of the thermal conductivity of porous silicon: A phonon hydrodynamic approach, Applied Physics Letters, 97 (2010) 033103.Google Scholar
[35]Zhao, J.J., Thermophysical Properties and Heat Transfer Mechanisms of Microscale and Nanoscale Structures in Aerogel-based Composite Insulators, in: Thermal Engineering, Vol. Ph.D, Tsinghua University, Beijing, China, 2012.Google Scholar
[36]Gailite, L., Scopelliti, P.E., Sharma, V.K., Indrieri, M., Podestà, A., Tedeschi, G., Milani, P., Nanoscale Roughness Affects the Activity of Enzymes Adsorbed on Cluster-Assembled Titania Films, Langmuir, 30 (2014) 5973–5981.Google Scholar
[37]Ma, X., Qu, X., Zhang, Q., Chen, F., Analysis of interfacial action of rectorite/thermoplastic polyurethane nanocomposites by inverse gas chromatography and molecular simulation, Polymer, 49 (2008) 3590–3600.Google Scholar
[38]Wang, M., Wang, X.M., Wang, J.K., Pan, N., Grain size effects on effective thermal conductivity of porous materials with internal thermal contact resistance, Journal of Porous Media, 16 (2013) 1043–1048.Google Scholar
[39]Yoshida, H., Kobayashi, T., Hayashi, H., Kinjo, T., Washizu, H., Fukuzawa, K., Boundary condition at a two-phase interface in the lattice Boltzmann method for the convection-diffusion equation, Physical Review E, 90 (2014) 013303.Google Scholar
[40]Han, K., Feng, Y.T., Owen, D.R.J., Modelling of thermal contact resistance within the framework of the thermal lattice Boltzmann method, International Journal of Thermal Sciences, 47 (2008) 1276–1283.Google Scholar
[41]Wang, M., Pan, N., Predictions of effective physical properties of complex multiphase materials, Materials Science and Engineering: R: Reports, 63 (2008) 1–30.Google Scholar
[42]D’Orazio, A., Succi, S., Boundary conditions for thermal lattice Boltzmann simulations, Computational Science – ICCS 2003, Lecture Notes in Computer Science, 2657 (2003) 977–986.CrossRefGoogle Scholar
[43]Chen, X., Han, P., A note on the solution of conjugate heat transfer problems using SIMPLE-like algorithms, International Journal of Heat and Fluid Flow, 21 (2000) 463467.Google Scholar
[44]Wang, M., Pan, N., Wang, J., Chen, S., Mesoscopic simulations of phase distribution effects on the effective thermal conductivity of microgranular porous media, Journal of Colloid and Interface Science, 311 (2007) 562–570.CrossRefGoogle ScholarPubMed
[45]Zou, Q., He, X., On pressure and velocity boundary conditions for the lattice Boltzmann BGK model, Physics of Fluids, 9 (1997) 1591–1598.Google Scholar