Thermal instability in a porous medium layer saturated by a nanofluid. (English) Zbl 1177.80047

Summary: The onset of convection in a horizontal layer of a porous medium saturated by a nanofluid is studied analytically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The analysis reveals that for a typical nanofluid (with large Lewis number) the prime effect of the nanofluids is via a buoyancy effect coupled with the conservation of nanoparticles, the contribution of nanoparticles to the thermal energy equation being a second-order effect. It is found that the critical thermal Rayleigh number can be reduced or increased by a substantial amount, depending on whether the basic nanoparticle distribution is top-heavy or bottom-heavy, by the presence of the nanoparticles. Oscillatory instability is possible in the case of a bottom-heavy nanoparticle distribution.


80A20 Heat and mass transfer, heat flow (MSC2010)
76S05 Flows in porous media; filtration; seepage
60J65 Brownian motion
76R10 Free convection
82D80 Statistical mechanics of nanostructures and nanoparticles
Full Text: DOI


[1] S. Choi, Enhancing thermal conductivity of fluids with nanoparticle, in: D.A. Siginer, H.P. Wang (Eds.), Developments and Applications of Non-Newtonian Flows, ASME FED, vol. 231/ MD-vol. 66, 1995, pp. 99 – 105.
[2] Masuda, H.; Ebata, A.; Teramae, K.; Hishinuma, N.: Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles, Netsu bussei 7, 227-233 (1993)
[3] J. Buongiorno, W. Hu, Nanofluid coolants for advanced nuclear power plants, Paper No. 5705, in: Proceedings of ICAPP’05, Seoul, May 15 – 19, 2005.
[4] Kleinstreuer, C.; Li, J.; Koo, J.: Microfluidics of nano-drug delivery, Int. J. Heat mass transfer 51, 5590-5597 (2008) · Zbl 1151.80309
[5] Buongiorno, J.: Convective transport in nanofluids, ASME J. Heat transfer 128, 240-250 (2006)
[6] Tzou, D. Y.: Instability of nanofluids in natural convection, ASME J. Heat transfer 130, 072401 (2008) · Zbl 1143.80330
[7] Tzou, D. Y.: Thermal instability of nanofluids in natural convection, Int. J. Heat mass transfer 51, 2967-2979 (2008) · Zbl 1143.80330
[8] Kim, J.; Kang, Y. T.; Choi, C. K.: Analysis of convective instability and heat transfer characteristics of nanofluids, Phys. fluids 16, 2395-2401 (2004) · Zbl 1186.76282
[9] Kim, J.; Choi, C. K.; Kang, Y. T.; Kim, M. G.: Effects of thermodiffusion and nanoparticles on convective instabilities in binary nanofluids, Nanoscale microscale thermophys. Eng. 10, 29-39 (2006)
[10] Kim, J.; Kang, Y. T.; Choi, C. K.: Analysis of convective instability and heat transfer characteristics of nanofluids, Int. J. Refrig. 30, 323-328 (2007)
[11] Tsai, T. H.; Chien, R.: Performance analysis of nanofluid-cooled microchannel heat sinks, Int. J. Heat fluid flow 28, 1013-1026 (2007)
[12] Chamkha, A. J.; Pop, I.: Effect of thermophoresis particle deposition in free convection boundary layer from a vertical flat plate embedded in a porous medium, Int. commun. Heat mass transfer 31, 421-430 (2004)
[13] D.A. Nield, A.V. Kuznetsov, The onset of convection in a nanofluid layer, ASME J. Heat Transfer, submitted for publication. · Zbl 1193.76052
[14] Nield, D. A.; Bejan, A.: Convection in porous media, (2006) · Zbl 1256.76004
[15] Kuznetsov, A. V.; Avramenko, A. A.: Effect of small particles on the stability of bioconvection in a suspension of gyrotactic microorganisms in a layer of finite length, Int. commun. Heat mass transfer 31, 1-10 (2004)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.