F. M. Hady, F. S. Ibrahim, S. M. Abdel-Gaied, M. R. Eid. Boundary-Layer Non-Newtonian Flow Over a Vertical Plate in a Porous Medium Saturated With a Nanofluid[J]. Applied Mathematics and Mechanics, 2011, 32(12): 1472-1480. doi: 10.3879/j.issn.1000-0887.2011.12.007
Citation: F. M. Hady, F. S. Ibrahim, S. M. Abdel-Gaied, M. R. Eid. Boundary-Layer Non-Newtonian Flow Over a Vertical Plate in a Porous Medium Saturated With a Nanofluid[J]. Applied Mathematics and Mechanics, 2011, 32(12): 1472-1480. doi: 10.3879/j.issn.1000-0887.2011.12.007

Boundary-Layer Non-Newtonian Flow Over a Vertical Plate in a Porous Medium Saturated With a Nanofluid

doi: 10.3879/j.issn.1000-0887.2011.12.007
  • Received Date: 2010-12-13
  • Rev Recd Date: 2011-09-19
  • Publish Date: 2011-12-15
  • The free convective heat transfer to the power-law non-Newtonian from a vertical plate in a porous medium saturated with nanofluid under laminar conditions was investigated. It was considered that the non-Newtonian nanofluid obeys the mathematical model of power-law. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The partial differential system governing the problem was transformed into an ordinary system via a usual similarity transformation. The numerical solutions of the resulting ordinary system were obtained. These solutions depend on the power-law index n, Lewis number Le, buoyancy-ratio number Nr, Brownian motion number Nb and thermophoresis number Nt. For various values of n and Le, the effect of the influence parameters on the fluid behavior as well as the reduced Nusselt number was presented and discussed.
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  • [1]
    Lee S, Choi S U S,Eastman J A. Measuring thermal conductivity of fluids containing oxide nanoparticles[J]. Trans ASME, J Heat Transfer, 1999, 121(2): 280-289.
    [2]
    Xuan Y, Li Q. Heat transfer enhancement of nanofluids[J]. Int J Heat Fluid Flow, 2000, 21(1): 58-64. doi: 10.1016/S0142-727X(99)00067-3
    [3]
    Xuan Y, Roetzel W. Conceptions for heat transfer correlation of nanofluids[J]. Int J Heat Mass Transfer, 2000, 43(19): 3701-3707. doi: 10.1016/S0017-9310(99)00369-5
    [4]
    Eastman J A, Choi S U S,Li S, Yu W,Thompson L J. Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles[J]. Appl Phys Lett, 2001, 78(6): 718-720. doi: 10.1063/1.1341218
    [5]
    Xie H, Wang J, Xi T G, Liu Y,Ai F. Thermal conductivity enhancement of suspensions containing nanosized alumina particles[J]. J Appl Phys,2002, 91(7): 4568-4572. doi: 10.1063/1.1454184
    [6]
    Wang B X, Zhou L P,Peng X F. A fractal model for predicting the effective thermal conductivity of liquid with suspension of nanoparticles[J]. Int J Heat Mass Transfer, 2003, 46(14):2665-2672. doi: 10.1016/S0017-9310(03)00016-4
    [7]
    Wen D S,Ding Y L. Effective thermal conductivity of aqueous suspensions of carbon nanotubes (carbon nanotube nanofluids)[J]. J Thermophysics Heat Transfer, 2004, 18(4): 481-485. doi: 10.2514/1.9934
    [8]
    Hong T K, Yang H S, Choi C J. Study of the enhanced thermal conductivity of Fe nanofluids[J]. J Appl Phys, 2005, 97(6):1-4.
    [9]
    Daungthongsuk W,Wongwises S. A critical review of convective heat transfer of nanofluids[J]. Renewable Sustainable Energy Reviews, 2007, 11(5): 797-817. doi: 10.1016/j.rser.2005.06.005
    [10]
    Zhou D W. Heat transfer enhancement of copper nanofluid with acoustic cavitation[J]. Int J Heat Mass Transfer, 2004, 47(14/16): 3109-3117.
    [11]
    Choi S. Enhancing thermal conductivity of fluids with nanoparticle[C]Siginer D A, Wang H P. Developments and Applications of Non-Newtonian Flows. ASME MD 231 and FED 66, 1995: 99-105.
    [12]
    Xuan Y, Li Q. Investigation on convective heat transfer and flow features of nanofluids[J]. J Heat Transfer, 2003, 125(1): 151-155. doi: 10.1115/1.1532008
    [13]
    Buongiorno J. Convective transport in nanofluids[J]. J Heat Transfer, 2006, 128(3): 240-250.
    [14]
    Wang X Q, Mujumdar A S. Heat transfer characteristics of nanofluids: a review[J]. Int J Thermal Sci, 2007, 46(1): 1-19.
    [15]
    Hady F M, Mohamed R A, Mahdy A. Non-Darcy natural convection flow along a vertical wavy plate embedded in a non-Newtonian fluid saturated porous medium[J]. Int J Appl Mech Eng, 2008, 13(1): 91-100.
    [16]
    Hady F M, Ibrahim F S. Forced convection heat transfer on a flat plate embedded in porous media for power-law fluids[J]. Trans Porous Media, 1997, 28(2): 125-134.
    [17]
    Mahdy A, Hady F M. Effect of thermophoretic particle deposition in non-Newtonian free convection flow over a vertical plate with magnetic field effect[J]. J Non-Newtonian Fluid Mech, 2009, 161(1/3): 37- 41.
    [18]
    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]. J Geophysical Research, 1977, 82(14): 2040-2044. doi: 10.1029/JB082i014p02040
    [19]
    Cheng P, Chang I D. Buoyancy induced flows in a saturated porous medium adjacent to impermeable horizontal surfaces[J]. Int J Heat Mass Transfer, 1976, 19: 1267-1272. doi: 10.1016/0017-9310(76)90078-8
    [20]
    Lesnic D, Ingham D B, Pop I. Free convection boundary layer flow along a vertical surface in a porous medium with Newtonian heating[J]. Int J Heat Mass Transfer, 1999, 42(14): 2621-2627.
    [21]
    Lesnic D, Ingham D B, Pop I. Free convection from a horizontal surface in a porous medium with Newtonian heating[J]. Trans Porous Media, 2000, 3(3): 227-235.
    [22]
    Rastogi S K, Poulikakos D. Double-diffusion from a vertical surface in a porous region saturated with a non-Newtonian fluid[J]. Int J Heat Mass Transfer, 1995, 38(5): 935-946.
    [23]
    Nield D A, Kuznetsov A V. Thermal instability in a porous medium layer saturated by a nanofluid[J]. Int J Heat Mass Transfer, 2009, 52(25/26): 5796-5801. doi: 10.1016/j.ijheatmasstransfer.2009.07.023
    [24]
    Nield D A, Kuznetsov A V. Thermal instability in a porous medium layer saturated by a nanofluid: Brinkman model[J]. Trans Porous Media, 2010, 81(3): 409-422.
    [25]
    Nield D A, Kuznetsov A V. The Cheng-Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid[J]. Int J Heat Mass Transfer, 2009, 52(25/26): 5792-5795. doi: 10.1016/j.ijheatmasstransfer.2009.07.024
    [26]
    Hamad M A A, Bashir M A. Boundary-layer flow and heat transfer of a power law non-Newtonian over a vertical stretching sheet[J]. World Appl Sci J, 2009, 7(special Issue for appl math): 172-178.
    [27]
    Khan W A, Pop I. Boundary-layer flow of a nanofluid past a stretching sheet[J]. Int J Heat Mass Transfer, 2010, 53(11/12): 2477-2483.
    [28]
    Hamad M A A, Pop I, Ismail A I Md. Local similarity solutions for the free convective boundary-layer flow over a vertical semi-infinite cylinder embedded in a porous medium saturated with a nanofluid[J]. Australian J Basic Appl Sci, 2011, 5: 147-156.
    [29]
    Hojjat M, Etemad S Gh, Bagheri R. Laminar heat transfer of non-Newtonian nanofluids in a circular tube[J]. Korean J Chem Eng, 2010, 27(5) :1391-1396. doi: 10.1007/s11814-010-0250-3
    [30]
    Hojjat M, Etemad S Gh, Bagheri R, Thibault J. Laminar convective heat transfer of non-Newtonian nanofluids with constant wall temperature[J]. Heat Mass Transfer, 2011, 47(2): 203-209. doi: 10.1007/s00231-010-0710-7
    [31]
    Hojjat M, Etemad S Gh, Bagheri R, Thibault J. Rheological characteristics of non-Newtonian nanofluids: experimental investigation[J]. Int Commun Heat Mass Transfer, 2011, 38(2): 144-148.
    [32]
    Hojjat M, Etemad S Gh, Bagheri R, Thibault J. Convective heat transfer of non-Newtonian nanofluids through a uniformly heated circular tube[J]. Int J Thermal Sci, 2011, 50(4): 525-531.
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