Abstract
Spectacular heat transfer enhancement has been measured in nanofluid suspensions. Attempts in explaining these experimental results did not yield yet a definite answer. Modelling the heat conduction process in nanofluid suspensions is being shown to be a special case of heat conduction in porous media subject to Lack of Local thermal equilibrium (LaLotheq). Similarly, the modelling of heat conduction in bi-composite systems is also equivalent to the applicable process in porous media. The chapter reviews the topic of heat conduction in porous media subject to Lack of Local thermal equilibrium (LaLotheq), introduces one of the most accurate methods of measuring the thermal conductivity, the transient hot wire method, and discusses its possible application to dual-phase systems. Maxwell’s concept of effective thermal conductivity is then introduced and theoretical results applicable for nanofluid suspensions are compared with published experimental data.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Reference
Alazmi, B. and Vafai, K. 2002 Constant wall heat flux boundary conditions in porous media under local thermal non-equilibrium conditions, Int. J. Heat Mass Transfer 45, 3071–3087.
Amiri, A. and Vafai, K. 1994 Analysis of dispersion effects and non-thermal equilibrium, non-Darcian, variable porosity incompressible flow through porous media, Int. J. Heat Mass Transfer 37, 934–954.
Assael, M.J., Dix, M., Gialou, K., Vozar, L., and Wakeham, W.A. 2002 Application of the transient hot-wire technique to the measurement of the thermal conductivity of solids, Int. J. Thermophys. 23, 615–633.
Assael, M.J., Chen, C.-F., Metaxa, I., and Wakeham, W.A. 2004 Thermal conductivity of suspensions of carbon nanotubes in water, Int. J. Thermophys. 25, 971–985.
Banu, N. and Rees, D.A.S. 2002 Onset of Darcy–Benard convection using a thermal non-equilibrium model, Int. J. Heat Mass Transfer 45, 2221–2238.
Batchelor, G.K. 1972 Sedimentation in a dilute dispersion of spheres, J. Fluid Mech. 52, 45–268.
Batchelor, G.K. and Green, J.T. 1972 The hydrodynamic interaction of two small freely-moving spheres in a linear flow field, J. Fluid Mech. 56, 375–400.
Baytas, A.C. and Pop, I. 2002 Free convection in a square porous cavity using a thermal nonequilibrium model, Int. J. Thermal Sci. 41, 861–870.
Bentley, J.P. 1984 Temperature sensor characteristics and measurement system design, J. Phys. E: Sci. Instrum. 17, 430–439.
Bonnecaze, R.T. and Brady, J.F. 1990 A method for determining the effective conductivity of dispersions of particles, Proc. R. Soc. Lond. A, 430, 285–313.
Bonnecaze, R.T. and Brady, J.F. 1991 The effective conductivity of random suspensions of spherical particles, Proc. R. Soc. Lond. A, 432, 445–465.
Chen, G. 1996 Nonlocal and nonequilibrium heat conduction in the vicinity of nanoparticles, J. Heat Transfer 118, 539–545.
Chen, G., 2000 Particularities of heat conduction in nanostructures, J. Nanoparticle Res.2, 199–204.
Chen, G. 2001 Balistic-diffusive heat-conduction equations, Phys. Rev. Lett. 86 (11), 2297–2300.
Choi, S.U.S., Zhang, Z.G., Yu, W., Lockwood, F.E., and Grulke, E.A. 2001 Anomalous thermal conductivity enhancement in nanotube suspensions, Appl. Phys. Lett., 79, 2252–2254.
Coquard, R., Bailis, D. 2006 Modeling of heat transfer in low-denisty EPS foams, J. Heat Transfer 128, 538–549.
Coquard, R., Bailis, D., and Quenard, D. 2006 Experimental and theoretical study of the hot-wire method applied to low-density thermal insulators, Int. J. Heat Mass Transfer 49, 4511–4524.
Davis, R.H. 1986 The effective thermal conductivity of a composite material with spherical inclusions, Int. J. Thermophys. 7, 609–620.
De Groot, J.J., Kestin, J., and Sookiazian, H. 1974 Instrument to measure the thermal conductivity of gases, Physica 75, 454–482.
Eastman, J.A., Choi, S.U.S., Li, S., Yu, W., and Thompson, L.J. 2001 Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles, Appl. Phys. Lett. 78, 718–720.
Hamilton, R.L. and Crosser, O.K. 1962 Thermal conductivity of heterogeneous two-component systems, I&EC Fundamentals 1, 187–191.
Hammerschmidt, U. and Sabuga, W., 2000 Transient hot wire (THW) method: Uncertainty assessment, Int. J. Thermophys. 21, 1255–1278.
Healy, J.J., de Groot, J.J. and Kestin, J. 1976 The theory of the transient hot-wire method for measuring thermal conductivity, Physica 82C, 392–408.
Huxtable, S.T., Cahill, D.G., Shenogin, S., Xue, L., Ozisik, R., Barone, P., Usrey, M., Strano, M.S., Siddons, G., Shim, M., and Keblinski, P. 2003 Interfacial heat flow in carbon nanotube suspensions, Nat. Mater. 2, 731–734.
Jang, S.P., and Choi, S.U.-S. 2004 Role of Brownian motion in the enhanced thermal conductivity of nanofluids, Appl. Phys. Lett. 84 (21), 4316–4318.
Jeffrey, D.J., 1973 Conduction through a random suspension of spheres, Proc. R. Soc. Lond. A, 335, 355–367.
Keblinski, P., Phillpot, S.R., Choi,\marginpar{\fbox{AQ1}} S.U.S. and Eastman, J.A. 2002 Mechanisms of heat flow in suspensions of nano-sized particles (nanofluids), Int. J. Heat Mass Transfer 45,855–863.
Kestin, J. and Wakeham, W.A. 1978 A contribution to the theory of the transient hot-wire technique for thermal conductivity measurements, Physica 92A, 102–116.
Kim, S.J. and Jang, S.P. 2002 Effects of Darcy number, the Prandtl number, and the Reynolds number on local thermal non-equilibrium, Int. J. Heat Mass Transfer 45,3885–3896.
Kuwahara, F., Shirota, M. and Nakayama, A. 2001 A numerical study of interfacial convective heat transfer coefficient in two-energy equation model for convection in porous media, Int. J. Heat Mass Transfer 44, 1153–1159.
Lage, J.L. 1999 The implications of the thermal equilibrium assumption for surrounding-driven steady conduction within a saturated porous medium layer, Int. J. Heat Mass Transfer 42,477–485.
Lee, S. Choi, S.U.-S. Li, S. and Eastman, J.A. 1999 Measuring thermal conductivity of fluids containing oxide nanoparticles, J. Heat Transfer 121, 280–289.
Li, C.H. and Peterson, G.P. 2006 Experimental investigation of temperature and volume fraction variations on the effective thermal conductivity of nanoparticle suspensions (nanofluids), J. Appl. Phys. 99, p. 084314.
Liu, M.S., Lin, M.C.C., Tsai, C.Y. and Wang, C.C. 2006 Enhancement of thermal conductivity with Cu for nanofluids using chemical reduction method, Int. J. Heat Mass Transfer 49, 3028–3033.
Lu, S. and Lin, H. 1996 Effective conductivity of composites containing aligned spheroidal inclusions of finite conductivity, J. Appl. Physics 79, 6761–6769.
Martinsons, C., Levick, A., and Edwards, G. 2001 Precise measurements of thermal diffusivity by photothermal radiometry for semi-infinite targets using accurately determined boundary conditions, Anal. Sci. 17, 114–117.
Maxwell, J.C. 1891 A Treatise on Electricity and Magnetism, 3rd edition, Clarendon Press, 1954 reprint, Dover, NY, pp. 435–441.
Minkowycz, W.J., Haji-Shiekh, A., and Vafai, K. 1999 On departure from local thermal equilibrium in porous media due to a rapidly changing heat source: The sparrow number, Int. J. Heat Mass Transfer 42, 3373–3385.
Nagasaka, Y. and Nagashima, A. 1981 Absolute measurement of the thermal conductivity of electrically conducting liquids by the transient hot-wire method, J. Phys. E: Sci. Instrum. 14, 1435–1440.
Nield, D.A., and Bejan, A. 2006 Convection in Porous Media, 3rd Edition, Springer-Verlag, New-York.
Nield, D.A. 1998 Effects of local thermal nonequilibrium in steady convective processes in a saturated porous medium: Forced convection in a channel, J. Porous Media 1, 181–186.
Nield, D.A. 2002 A note on the modeling of local thermal non-equilibrium in a structured porous medium, Int. J. Heat Mass Transfer 45, 4367–4368.
Nield, D.A., Kuznetsov, A.V. and Xiong, M. 2002 Effect of local thermal non-equilibrium on thermally developing forced convection in a porous medium, Int. J. Heat Mass Transfer 45, 4949–4955.
Özisik, M.N. 1993 Heat Conduction. 2nd edition, John Wiley & Sons, Inc., New York.
Prasher, R. Bhattacharya, P., and Phelan, P.E. 2005 Thermal conductivity of nanoscale colloidal solutions (Nanofluids), Phys. Rev. Lett. 94, p. 025901.
Putnam, S.A., Cahill, D.G., Braun, P.V., Ge, Z., and Shimmin, R.G 2006 Thermal conductivity of nanoparticle suspensions, J. Appl. Phys. 99, p. 084308.
Quintard, M. and Whitaker, S. 1995 Local thermal equilibrium for transient heat conduction: Theory and comparison with numerical experiments, Int. J. Heat Mass Transfer 38,2779–2796.
Rees, D.A.S. 2002 Vertical free convective boundary-layer flow in a porous medium using a thermal nonequilibrium model: Elliptical effects, Zeitchrift fur angewandte Mathematik und Physik ZAMP 53, 1–12.
Tzou, D.Y. 1997 Macro-to-Microscale Heat Transfer, The Lagging Behavior, Taylor & Francis, Washington, DC.
Tzou, D.Y. 1995 A unified field approach for heat conduction from macro-to-micro-scales, J. Heat Transfer 117, 8–16.
Vadasz, P. 2004 Absence of oscillations and resonance in porous media Dual–Phase–Lagging Fourier heat conduction, J. Heat Transfer 127, 307–314.
Vadasz, P. 2005a Explicit conditions for local thermal equilibrium in porous media heat conduction, Trans. Porous Media 59, 341–355.
Vadasz, P. 2005b Lack of oscillations in Dual–Phase–Lagging heat conduction for a porous slab subject to imposed heat flux and temperature, Int. J. Heat Mass Transfer 48, 2822–2828.
Vadasz, P. 2006a Exclusion of oscillations in heterogeneous and bi-composite media thermal conduction, Int. J. Heat Mass Transfer 49, 4886–4892.
Vadasz, P. 2006b Heat conduction in nanofluid suspensions, J. Heat Transfer 128, 465–477.
Vadasz, P. 2007a On the paradox of heat conduction in porous media subject to lack of local thermal equilibrium, Int. J. Heat Mass Transfer 50, 4131–4140.
Vadasz, P. 2007b Nanofluid suspensions: Possibility for heat transfer enhancement, in preparation.
Vadasz, J.J., Govender, S., and Vadasz, P. 2005 Heat transfer enhancement in nanofluids suspensions: possible mechanisms and explanations, Int. J. Heat Mass Transfer 48, 2673–2683.
Vadasz, P. and Nield, D.A. 2007 Extending the Duhamel theorem to dual phase applications, Int. J. Heat Mass Transfer, in press, doi:10.1016/j.ijheatmasstransfer.2007.03.054
Wakao, N., Kaguei, S. and Funazkri, T. 1979 Effect of fluid dispersion coefficients on particle-to-fluid heat transfer coefficients in packed beds, Chem. Engng. Sci. 34, 325–336.
Wakao, N. and Kaguei, S. 1982 Effect of fluid dispersion coefficients on particle-to-fluid heat transfer coefficients in packed beds, Heat and Mass Transfer in Packed Beds, Gordon and Breach, New York.
Xuan, Y. and Li, Q. 2000 Heat transfer enhancement of nanofluids, Int. J. Heat Mass Transfer 21, 58–64.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer Science+Business Media B.V
About this chapter
Cite this chapter
Vadász, P. (2008). Nanofluid Suspensions and Bi-composite Media as Derivatives of Interface Heat Transfer Modeling in Porous Media. In: Vadász, P. (eds) Emerging Topics in Heat and Mass Transfer in Porous Media. Theory and Applications of Transport in Porous Media, vol 22. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8178-1_12
Download citation
DOI: https://doi.org/10.1007/978-1-4020-8178-1_12
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-8177-4
Online ISBN: 978-1-4020-8178-1
eBook Packages: EngineeringEngineering (R0)