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An analytical consideration of steady-state forced convection within a nanofluid-saturated metal foam

Published online by Cambridge University Press:  25 March 2015

W. Zhang ,
W. Li  and
A. Nakayama
W. Zhang
Affiliation:
Department of Mechanical Engineering, Shizuoka University, 3-5-1 Johoku, Naka-ku, Hamamatsu 432-8561, Japan
W. Li
Affiliation:
Department of Mechanical Engineering, Shizuoka University, 3-5-1 Johoku, Naka-ku, Hamamatsu 432-8561, Japan
A. Nakayama*
Affiliation:
Department of Mechanical Engineering, Shizuoka University, 3-5-1 Johoku, Naka-ku, Hamamatsu 432-8561, Japan School of Civil Engineering and Architecture, Wuhan Polytechnic University, Wuhan, Hubei 430023, China
*
†Email address for correspondence: [email protected]
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Abstract

An analytical consideration has been made to explore the velocity, temperature and nanoparticle distributions and heat transfer characteristics associated with thermal dispersion and nanoparticle mechanical dispersion within a nanofluid-saturated homogeneous metal foam. A volume-averaging theory was rigorously applied to integrate locally a set of governing equations based on the modified Buongiorno model at the pore scale. Thus, a macroscopic set of volume-averaged governing equations were derived allowing interstitial heat transfer between the nanofluid and metal phases. Unknown terms were modelled mathematically to obtain a closed set of volume-averaged governing equations. Subsequently, a pore-scale analysis was carried out to find possible functional forms for describing thermal dispersion and nanoparticle mechanical dispersion in a nanofluid-saturated metal foam. Using the resulting set of volume-averaged governing equations, forced convective flows in nanofluid-saturated metal foams were analytically investigated for the steady-state case. Eventually, it has been predicted that an unconventionally high level of the heat transfer rate (about 80 times more than the case of base fluid convection without a metal foam) may be achieved by combination of metal foam and nanofluid.

JFM classification

Convection: Convection Convection: Convection in porous media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 769 , 25 April 2015 , pp. 590 - 620
Copyright
© 2015 Cambridge University Press 

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References

Bianco, V., Chiacchio, F., Manca, O. & Nardini, S. 2009 Numerical investigation of nanofluids forced convection in circular tubes. Appl. Therm. Engng 29 (17–18), 3632–3642.Google Scholar
Buongiorno, J. 2006 Convective transport in nanofluids. Trans. ASME: J. Heat Transfer 128, 240–250.Google Scholar
Calmidi, V. V. & Mahajan, R. L. 1999 The effective thermal conductivity of high porosity fibrous metal foams. Trans. ASME: J. Heat Transfer 121, 466–471.Google Scholar
Calmidi, V. V. & Mahajan, R. L. 2000 Forced convection in high porosity metal foams. Trans. ASME: J. Heat Transfer 122, 557–565.Google Scholar
Cheng, P. 1978 Heat transfer in geothermal systems. Adv. Heat Transfer 14, 1–105.Google Scholar
Chien, R. & Chuang, J. 2007 Experimental microchannel heat sink performance studies using nanofluids. Intl J. Therm. Sci. 46, 57–66.CrossRefGoogle Scholar
Dukhan, N. 2013 Metal Foams: Fundamentals and Applications. DEStech Publications.Google Scholar
Fried, J. J. & Combarnous, M. A. 1971 Dispersion in porous media. Adv. Hydrosci. 7, 169–282.Google Scholar
Gelhar, L. W. & Carl, L. A. 1983 Three-dimensional stochastic analysis of macrodispersion in aquifers. Water Resour. Res. 19 (1), 161–180.CrossRefGoogle Scholar
Heris, S. Z., Esfahany, M. N. & Etemad, S. G. 2007 Experimental investigation of convective heat transfer of $\text{Al}_{2}\text{O}_{3}$ /water nanofluid in a circular tube. Intl J. Heat Fluid Flow 28, 203–210.CrossRefGoogle Scholar
Kuwahara, F., Yang, C., Ando, K. & Nakayama, A. 2011 Exact solutions for a thermal nonequilibrium model of fluid saturated porous media based on an effective porosity. Trans. ASME: J. Heat Transfer 133, 112602.Google Scholar
Launder, B. E. & Spalding, D. B. 1974 The numerical computation of turbulent flow. Comput. Meth. Appl. Mech. Engng 3, 269–289.Google Scholar
Lee, S. & Choi, S. U. S.1996 Application of metallic nanoparticle suspensions in advanced cooling systems. International Mechanical Engineering Congress and Exhibition, 17–22 November 1966, Atlanta, USA. pp. 1–12.Google Scholar
Lee, S., Choi, S. U. S., Li, S. & Eastman, J. A. 1999 Measuring thermal conductivity of fluids containing oxide nanoparticles. Trans. ASME: J. Heat Transfer 121, 280–289.Google Scholar
Li, W. & Nakayama, A. 2015 Temperature dependency of thermophysical properties in convective heat transfer enhancement in nanofluids. J. Thermophys. Heat Transfer 29 (2), (in press).CrossRefGoogle Scholar
Liang, C. Y. & Yang, W. J. 1975 Modified single blow technique for performance evaluation on heat transfer surfaces. Trans. ASME: J. Heat Transfer 97, 16–21.Google Scholar
Maiga, S. B., Palm, S. J., Nguyen, C. T., Roy, G. & Galanis, N. 2005 Heat transfer enhancement by using nanofluids in forced convection flows. Intl J. Heat Fluid Flow 26, 530–546.CrossRefGoogle Scholar
Nakayama, A. 1995 PC-Aided Numerical Heat Transfer and Convective Flow, pp. 49–50, 103–115. CRC Press.Google Scholar
Nakayama, A., Ando, K., Yang, C., Sano, Y., Kuwahara, F. & Liu, J. 2009 A study on interstitial heat transfer in consolidated and unconsolidated porous media. Heat Mass Transfer 45 (11), 1365–1372.Google Scholar
Nakayama, A., Kuwahara, F. & Hayashi, T. 2004 Numerical modelling for three-dimensional heat and fluid flow through a bank of cylinders in yaw. J. Fluid Mech. 498, 139–159.Google Scholar
Nakayama, A., Kuwahara, F. & Kodama, Y. 2006 An equation for thermal dispersion flux transport and its mathematical modelling for heat and fluid flow in a porous medium. J. Fluid Mech. 563, 81–96.Google Scholar
Ohsawa, S.2015 Three-dimensional simulation of heat and fluid flow in a nanofluid saturated metal foam. Master thesis, Graduate School of Engineering, Shizuoka University, Japan.Google Scholar
Pak, B. C. & Cho, Y. 1998 Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles. Exp. Heat Transfer 11, 151–170.CrossRefGoogle Scholar
Quintard, M. & Whitaker, S. 1993 One and two equation models for transient diffusion processes in two-phase systems. Adv. Heat Transfer 23, 369–465.Google Scholar
Quintard, M. & Whitaker, S. 1995 Local thermal equilibrium for transient heat conduction: theory and comparison with numerical experiments. Intl J. Heat Mass Transfer 38, 2779–2796.Google Scholar
Sakai, F., Li, W. & Nakayama, A.2014 A rigorous derivation and its applications of volume averaged transport equations for heat transfer in nanofluid saturated metal foam, Proceedings of the International Heat Transfer Conference, 10–15 August 2014, Kyoto, Japan.Google Scholar
Taylor, G. I. 1953 Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. Lond. A 219, 186–203.Google Scholar
Taylor, G. I. 1954 The dispersion of matter in turbulent flow through a pipe. Proc. R. Soc. Lond. A 223, 446–468.Google Scholar
Wang, J. & Kitanidis, P. K. 1999 Analysis of macrodispersion through volume averaging: comparison with stochastic theory. Stoch. Environ. Res. Risk Assess. 13, 66–84.Google Scholar
Xuan, Y. & Roetzel, W. 2000 Conceptions for heat transfer correlations of nanofluids. Intl J. Heat Mass Transfer 43, 3701–3707.Google Scholar
Yang, C., Ando, K. & Nakayama, A. 2011 A local thermal non-equilibrium analysis of fully developed forced convective flow in a tube filled with a porous medium. Trans. Porous Med. 89, 237–249.Google Scholar
Yang, C., Li, W. & Nakayama, A. 2013a Convective heat transfer of nanofluids in a concentric annulus. Intl J. Therm. Sci. 71, 249–257.Google Scholar
Yang, C., Li, W., Sano, Y., Mochizuki, M. & Nakayama, A. 2013b On the anomalous convective heat transfer enhancement in nanofluids: a theoretical answer to the nanofluids controversy. Trans. ASME: J. Heat Transfer 135, 054504.CrossRefGoogle Scholar
Yang, C., Liu, W. & Nakayama, A. 2009 Forced convective heat transfer enhancement in a tube with its core partially filled with a porous medium. Open Transp. Phenom. J. 1, 1–6.Google Scholar
Yang, C. & Nakayama, A. 2010 A synthesis of tortuosity and dispersion in effective thermal conductivity of porous media. Intl J. Heat Mass Transfer 53, 3222–3230.Google Scholar
Zhukauskas, A. 1987 Heat transfer from tubes in crossflow. Adv. Heat Transfer 18, 87–159.Google Scholar