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The Cheng-Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid. (English) Zbl 1177.80046
Summary: The Cheng-Minkowycz problem of natural convection past a vertical plate, in a porous medium saturated by a nanofluid, is studied analytically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. For the porous medium the Darcy model is employed. A similarity solution is presented. This solution depends on a Lewis number Le, a buoyancy-ratio number Nr, a Brownian motion number Nb, and a thermophoresis number Nt. The dependency of the Nusselt number on these four parameters is investigated.

MSC:
80A20 Heat and mass transfer, heat flow (MSC2010)
76R10 Free convection
76S05 Flows in porous media; filtration; seepage
60J65 Brownian motion
82D80 Statistical mechanics of nanostructures and nanoparticles
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[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, in: Proceedings of ICAPP ’05, Paper no. 5705, Seoul, May 15 – 19, 2005.
[4] Buongiorno, J.: Convective transport in nanofluids, ASME J. Heat transfer 128, 240-250 (2006)
[5] Cheng, P.; Minkowycz, W. J.: Free convection about a vertical flat plate embedded in a porous medium with application to heat transfer from a dike, J. geophys. Res. 82, 2040-2044 (1977)
[6] Bejan, A.: Convection heat transfer, (2004) · Zbl 1079.76648
[7] Bejan, A.; Khair, K. R.: Heat and mass transfer by natural convection in a porous medium, Int. J. Heat mass transfer 28, 909-919 (1985) · Zbl 0564.76085
[8] Nield, D. A.; Bejan, A.: Convection in porous media, (2006) · Zbl 1256.76004
[9] Wang, X. Q.; Mujumdar, A. S.: Heat transfer characteristics of nanofluids: a review, Int. J. Thermal sci. 46, 1-19 (2007)
[10] Tzou, D. Y.: Instability of nanofluids in natural convection, ASME J. Heat transfer 130, #072401 (2008) · Zbl 1143.80330
[11] Tzou, D. Y.: Thermal instability of nanofluids in natural convection, Int. J. Heat mass transfer 51, 2967-2979 (2008) · Zbl 1143.80330
[12] D.A. Nield, A.V. Kuznetsov, The onset of convection in a nanofluid layer, ASME J. Heat Transfer, submitted for publication. · Zbl 1193.76052
[13] Nield, D. A.; Kuznetsov, A. V.: Thermal instability in a porous medium layer saturated by a nanofluid, Int. J. Heat mass transfer 52, 5796-5801 (2009) · Zbl 1177.80047
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