A similarity solution is presented for the steady free convection boundary layer flow past a horizontal flat plate embedded in a porous medium filled with nanofluids. The model used for the nanofluid is the one which incorporates the effects of Brownian motion and thermophoresis. For the porous medium the Darcy-Boussinesq model is employed. This solution depends on a Lewis number , a buoyancy-ratio parameter , a Brownian motion parameter , and a thermophoresis parameter . The effects of these parameters on the velocity, temperature and nanoparticle fraction profiles are discussed. The dependency of the local Nusselt and Sherwood numbers on these four parameters is also investigated.
References
1.
Nield
, D. A.
, and Bejan
, A.
, 2006, Convection in Porous Media
, 3rd ed., Springer
, New York
.2.
Ingham
, D. B.
, and Pop
, I.
, eds., 2005, Transport Phenomena in Porous Media III
, Elsevier
, Oxford
.3.
Vafai
, K.
, ed., 2005, Handbook of Porous Media
, 2nd ed., Taylor & Francis
, New York
.4.
Vafai
, K.
, 2010, Porous Media: Applications in Biological Systems and Biotechnology
, CRC Press
, New York
.5.
Vadasz
, P.
, 2008, Emerging Topics in Heat and Mass Transfer in Porous Media
, Springer
, New York
.6.
Choi
, S. U. S.
, 1995, “Enhancing Thermal Conductivity of Fluids With Nanoparticles
,” Development and Applications of Non-Newtonian Flows
, D. A.
Siginer
and H. P.
Wang
, eds., ASME MD-Vol. 231 and FED-Vol. 66, USDOE, Washington, DC (United States), pp. 99
–105
.7.
Kang
, H. U.
, Kim
, S. H.
, and Oh
, J. M.
, 2006, “Estimation of Thermal Conductivity of Nanofluid Using Experimental Effective Particle Volume
,” Exp. Heat Transfer
, 19
, pp. 181
–191
.8.
Abu-Nada
, E.
, 2008, “Application of Nanofluids for Heat Transfer Enhancement of Separated Flows Encountered in a Backward Facing Step
,” Int. J. Heat Fluid Flow
, 29
, pp. 242
–249
.9.
Khanafer
, K.
, Vafai
, K.
, and Lightstone
, M.
, 2003, “Buoyancy-Driven Heat Transfer Enhancement in a Two-Dimensional Enclosure Utilizing Nanofluids
,” Int. J. Heat Mass Transfer
, 46
, pp. 3639
–3653
.10.
Maiga
, S. E. B.
, Palm
, S. J.
, Nguyen
, C. T.
, Roy
, G.
, and Galanis
, N.
, 2005, “Heat Transfer Enhancement by Using Nanofluids in Forced Convection Flows
,” Int. J. Heat Fluid Flow
, 26
, pp. 530
–546
.11.
Jou
, R. Y.
, and Tzeng
, S. C.
, 2006, “Numerical Research of Nature Convective Heat Transfer Enhancement Filled With Nanofluids in Rectangular Enclosures
,” Int. Commun. Heat Mass Transfer
, 33
, pp. 727
–736
.12.
Hwang
, K. S.
, Lee
, Ji -H.
, and Jang
, S. P.
, 2007, “Buoyancy-Driven Heat Transfer of Water-Based Al Nanofluids in a Rectangular Cavity
,” Int. J. Heat Mass Transfer
, 50
, pp. 4003
–4010
.13.
Tiwari
, R. K.
, and Das
, M. K.
, 2007, “Heat Transfer Augmentation in a Two-Sided Lid-Driven Differentially Heated Square Cavity Utilizing Nanofluids
,” Int. J. Heat Mass Transfer
, 50
, pp. 2002
–2018
.14.
Oztop
, H. F.
, and Abu-Nada
, E.
, 2008, “Numerical Study of Natural Convection in Partially Heated Rectangular Enclosures Filled With Nanofluids
,” Int. J. Heat Mass Transfer
, 29
, pp. 1326
–1336
.15.
Abu-Nada
, E.
, and Oztop
, H. F.
, 2009, “Effects of Inclination Angle on Natural Convection in Enclosures Filled With Cu-Water Nanofluid
,” Int. J. Heat Fluid Flow
, 30
, pp. 669
–678
.16.
Aminossadati
, S. M.
, and Ghasemi
, B.
, 2009, “Natural Convection Cooling of a Localized Heat Source at the Bottom of a Nanofluid-Filled Enclosure
,” Eur. J. Mech. B/Fluids
, 28
, pp. 630
–640
.17.
Ghasemi
, B.
, and Aminossadati
, S. M.
, 2010, “Periodic Natural Convection in a Nanofluid-Filled Enclosure With Oscillating Heat Flux
,” Int. J. Therm. Sci.
, 49
, pp. 1
–9
.18.
Muthtamilselvan
, M.
, Kandaswamy
, P.
, and Lee
, J.
, 2010, “Heat Transfer Enhancement of Copper-Water Nanofluids in a Lid-Driven Enclosure
,” Commun. Nonlinear Sci. Numer. Simul.
, 15
, pp. 1501
–1510
.19.
Duangthongsuk
, W.
, and Wongwises
, S.
, 2008, “Effect of Thermophysical Properties Models on the Predicting of the Convective Heat Transfer Coefficient for Low Concentration Nanofluid
,” Int. Commun. Heat Mass Transfer
, 35
, pp. 1320
–1326
.20.
Das
, S. K.
, Choi
, S. U. S.
, Yu
, W.
, and Pradet
, T.
, 2007, Nanofluids: Science and Technology
, Wiley
, New York
.21.
Buongiorno
, J.
, 2006, “Convective Transport in Nanofluids
,” ASME J. Heat Transfer
, 128
, pp. 240
–250
.22.
Daungthongsuk
, W.
, and Wongwises
, S.
, 2007, “A Critical Review of Convective Heat Transfer Nanofluids
,” Renewable Sustainable Energy Rev.
, 11
, pp. 797
–817
.23.
Trisaksri
, V.
, and Wongwises
, S.
, 2007, “Critical Review of Heat Transfer Characteristics of Nanofluids
,” Renewable Sustainable Energy Rev.
, 11
, pp. 512
–523
.24.
Wang
, X.-Q.
, and Mujumdar
, A. S.
, 2007, “Heat Transfer Characteristics of Nanofluids: A Review
,” Int. J. Therm. Sci.
, 46
, pp. 1
–19
.25.
Wang
, X. -Q. -Q.
, and Mujumdar
, A. S.
, 2008, “A Review on Nanofluids–Part I: Theoretical and Numerical Investigations
,” Braz. J. Chem. Eng.
, 25
, pp. 613
–630
.26.
Kakaç
, S.
, and Pramuanjaroenkij
, A.
, 2009, “Review of Convective Heat Transfer Enhancement With Nanofluids
,” Int. J. Heat Mass Transfer
, 52
, pp. 3187
–3196
.27.
Nield
, D. A.
, and Kuznetsov
, A. V.
, 2009, “The Cheng–Minkowycz Problem for Natural Convective Boundary-Layer Flow in a Porous Medium Saturated by a Nanofluid
,” Int. J. Heat Mass Transfer
, 52
, pp. 5792
–5795
.28.
Kuznetsov
, A. V.
, and Nield
, D. A.
, 2010, “Natural Convective Boundary-Layer Flow of a Nanofluid Past a Vertical Plate
,” Int. J. Therm. Sci.
, 49
, pp. 243
–247
.29.
Khan
, W. A.
, and Pop
, I.
, 2010, “Boundary-Layer Flow of a Nanofluid Past a Stretching Sheet
,” Int. J. Heat Mass Transfer
, 53
, pp. 2477
–2483
.30.
Cheng
, P.
, and Chang
, I.-D.
, 1976, “Buoyancy Induced Flows in a Saturated Porous Medium Adjacent to Impermeable Horizontal Surfaces
,” Int. J. Heat Mass Transfer
, 19
, pp. 1267
–1272
.31.
Chang
, I.-D.
, and Cheng
, P.
, 1983, “Matched Asymptotic Expansions for Free Convection About an Impermeable Horizontal Surface in a Porous Medium
,” Int. J. Heat Mass Transfer
, 26
, pp. 163
–173
.32.
Shiunlin
, D.-S.
, and Gebhart
, B.
, 1986, “Buoyancy-Induced Flow Adjacent to a Horizontal Surface Submerged in Porous Medium Saturated With Cold Water
,” Int. J. Heat Mass Transfer
, 29
, pp. 611
–623
.33.
Merkin
, J. H.
, and Zhang
, G.
, 1990, “On the Similarity Solutions for Free Convection in a Saturated Porous Medium Adjacent to Impermeable Horizontal Surfaces
,” Wärme-und Stoffübertr.
, 25
, pp. 179
–184
.34.
Chaudhary
, M. A.
, Merkin
, J. H.
, and Pop
, I.
, 1996, “Natural Convection From a Horizontal Permeable Surface in a Porous Medium–Numerical and Symptotic Solutions
,” Transp. Porous Media
, 22
, pp. 327
–344
.35.
Stewartson
, K.
, 1958, “On the Free Convection From a Horizontal Plate
,” J. Appl. Math. Phys. (ZAMP)
, 9
, pp. 276
–281
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