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Research Papers: Natural and Mixed Convection

Natural Convective Boundary Layer Flow of Nanofluids Above an Isothermal Horizontal Plate

[+] Author and Article Information
Kaustav Pradhan

Mechanical Engineering Department,
Indian Institute of Technology Kharagpur,
Kharagpur 721302, India
e-maiil: pradhan.kaustav@gmail.com

Subho Samanta

Mechanical Engineering Department,
Indian Institute of Technology Kharagpur,
Kharagpur 721302, India
e-mail: subhosamanta@iitkgp.ac.in

Abhijit Guha

Professor
Mechanical Engineering Department,
Indian Institute of Technology Kharagpur,
Kharagpur 721302, India
e-mail: a.guha@mech.iitkgp.ernet.in

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received July 4, 2013; final manuscript received June 20, 2014; published online July 29, 2014. Assoc. Editor: Ali Ebadian.

J. Heat Transfer 136(10), 102501 (Jul 29, 2014) (8 pages) Paper No: HT-13-1338; doi: 10.1115/1.4027909 History: Received July 04, 2013; Revised June 20, 2014

The natural convective boundary layer flow of a nanofluid over an isothermal horizontal plate is studied analytically. The model used for the nanofluid accounts for the effects of Brownian motion and thermophoresis. The analysis shows that the velocity, temperature, and nanoparticle volume fraction profiles in the respective boundary layers depend not only on the Prandtl number (Pr) and Lewis number (Le) but also on three additional dimensionless parameters: the Brownian motion parameter Nb, the buoyancy ratio parameter Nr and the thermophoresis parameter Nt. The velocity, temperature, and nanoparticle volume fraction profiles for the nanofluid are found to have a weak dependence on the values of Nb, Nr, and Nt. The effect of the above-mentioned parameters on the local skin-friction coefficient and Nusselt number has been studied extensively. It has been observed that as Nr increases, the local skin-friction coefficient decreases whereas local Nusselt number remains almost constant. As Nb or Nt increases, the local skin-friction coefficient increases whereas the local Nusselt number decreases.

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References

Florio, A., and Harnoy, A., 2007, “Combination Technique for Improving Natural Convection Cooling in Electronics,” Int. J. Therm. Sci., 46(1), pp. 76–92. [CrossRef]
Lim, K. O., Lee, K. S., and Song, T. H., 1999, “Primary and Secondary Instabilities in a Glass Melting Surface,” Numer. Heat Transfer, Part A, 36(3), pp. 309–325. [CrossRef]
Patil, P. M., and Kulkarni, P. S., 2008, “Effects of Chemical Reaction on Free Convective Flow of a Polar Fluid Through a Porous Medium in the Presence of Internal Heat Generation,” Int. J. Therm. Sci., 47(8), pp. 1043–1054. [CrossRef]
Saidur, R., Kazi, S. N., Hossain, M. S., Rahman, M. M., and Mohammed, H. A., 2011, “A Review on the Performance of Nanoparticles Suspended With Refrigerants and Lubricating Oils in Refrigeration Systems,” Renewable Sustainable Energy Rev., 15(1), pp. 310–323. [CrossRef]
Khanafer, K., and Vafai, K., 2011, “A Critical Synthesis of Thermophysical Characteristics of Nanofluids,” Int. J. Heat Mass Transfer, 54(19–20), pp. 4410–4428. [CrossRef]
Choi, S., 1995, “Enhancing Thermal Conductivity of Fluids With Nanoparticles,” Developments and Applications of Non-Neutonian Flows, D. A. Siginer and H. P., Wang, eds., American Society of Mechanical Engineers, New York, FED- Vol. 231/MD-Vol. 66, pp. 99–105.
Eastman, J. A., Choi, S. U. S., Li, S., Yu, W., and Thompson, L. J., 2001, “Anomalously Increased Effective Thermal Conductivities of Ethylene Glycol-Based Nanofluids Containing Copper Nanoparticles,” Appl. Phys. Lett., 78(6), pp. 718–720. [CrossRef]
Xuan, Y., and Li, Q., 2000, “Heat Transfer Enhancement of Nanofluids,” Int. J. Heat Fluid Flow, 21(1), pp. 58–64. [CrossRef]
Das, S. K., Choi, S. U. S., Yu, W., and Pradeep, T., 2007, Nanofluids: Science and Technology, 1st ed., Wiley, New York.
Guha, A., 1997, “A Unified Eulerian Theory of Turbulent Deposition to Smooth and Rough Surfaces,” J. Aerosol Sci., 28(8), pp. 1517–1537. [CrossRef]
Guha, A., 2008, “A Generalized Mass Transfer Law Unifying Various Particle Transport Mechanisms in Dilute Dispersions,” Heat Mass Transfer, 44(11), pp. 1289–1303. [CrossRef]
Guha, A., 2008, “Transport and Deposition of Particles in Turbulent and Laminar Flow,” Annu. Rev. Fluid Mech., 40, pp. 311–341. [CrossRef]
Buongiorno, J., 2006, “Convective Transport in Nanofluids,” ASME J. Heat Transfer, 128(3), pp. 240–250. [CrossRef]
Pak, B. C., and Cho, Y., 1998, “Hydrodynamic and Heat Transfer Study of Dispersed Fluids With Submicron Metallic Oxide Particles,” Exp. Heat Transfer, 11(2), pp. 151–170. [CrossRef]
Xuan, Y., and Li, Q., 2003, “Investigation on Convective Heat Transfer and Flow Features of Nanofluids,” ASME J. Heat Transfer, 125(1), pp. 151–155. [CrossRef]
Maxwell-Garnett, J. C., 1904, “Colours in Metal Glasses and in Metallic Films,” Philos. Trans. R. Soc. London, Ser. A, 203, pp. 385–420. [CrossRef]
Wang, B. X., Zhou, L. P., and Peng, X. F., 2003, “A Fractal Model for Predicting the Effective Thermal Conductivity of Liquid With Suspension of Nanoparticles,” Int. J. Heat Mass Transfer, 46(14), pp. 2665–2672. [CrossRef]
Khanafer, K., Vafai, K., and Lightstone, M., 2003, “Buoyancy Driven Heat Transfer Enhancement Utilizing Nanofluids,” Int. J. Heat Mass Transfer, 46(19), pp. 3639–3653. [CrossRef]
Putra, N., Roetzel, W., and Das, S. K., 2003, “Natural Convection of Nanofluids,” Heat Mass Transfer, 39(8–9), pp. 775–784. [CrossRef]
Wen, D., and Ding, Y., 2006, “Natural Convective Heat Transfer of Suspensions of Titanium Dioxide Nanoparticles (Nanofluids),” IEEE Trans. Nanotechnol., 5(3), pp. 220–227. [CrossRef]
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(2), pp. 243–247. [CrossRef]
Khan, W. A., and Aziz, A., 2011, “Natural Convection Flow of a Nanofluid Over a Vertical Plate With Uniform Surface Heat Flux,” Int. J. Therm. Sci., 50(7), pp. 1207–1214. [CrossRef]
Aziz, A., and Khan, W. A., 2012, “Natural Convective Boundary-Layer Flow of a Nanofluid Past a Convectively Heated Vertical Plate,” Int. J. Therm. Sci., 52(1), pp. 83–90. [CrossRef]
Kuznetsov, A. V., and Nield, D. A., 2011, “Double-Diffusive Natural Convective Boundary Layer Flow of a Nanofluid Past a Vertical Plate,” Int. J. Therm. Sci., 50(5), pp. 712–717. [CrossRef]
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(25–26), pp. 5792–5795. [CrossRef]
Nield, D. A., and Kuznetsov, A. V., 2011, “The Cheng-Minkowycz Problem for the Double-Diffusive Natural Convective Boundary-Layer Flow in a Porous Medium Saturated by a Nanofluid,” Int. J. Heat Mass Transfer, 54(1–3), pp. 374–378. [CrossRef]
Schlichting, H., and Gersten, H. K., 2004, Boundary Layer Theory, 8th ed., Springer, New Delhi, India.
Guha, A., 1998, “A Unified Theory for the Interpretation of Total Pressure and Temperature in Two-Phase Flows at Subsonic and Supersonic Speeds,” Proc. R. Soc. London, 454(1970), pp. 671–695. [CrossRef]
Guha, A., 1998, “A Simple Analytical Theory for Interpreting Measured Total Pressure in Multiphase Flows,” ASME J. Fluids Eng., 120(2), pp. 385–389. [CrossRef]
Guha, A., 1998, “Computation, Analysis and Theory of Two-Phase Flows,” Aeronaut. J., 102(1012), pp. 71–82.
Kleinstreuer, C., and Feng, Y., 2012, “Thermal Nanofluid Property Model With Application to Nanofluid Flow in a Parallel-Disk System—Part I: A New Thermal Conductivity Model for Nanofluid Flow,” ASME J. Heat Transfer, 134(5), p. 051002. [CrossRef]
Samanta, S., and Guha, A., 2012, “A Similarity Theory for Natural Convection From a Horizontal Plate for Prescribed Heat Flux or Wall Temperature,” Int. J. Heat Mass Transfer, 55(13–14), pp. 3857–3868. [CrossRef]
Bradie, B., 2007, A Friendly Introduction to Numerical Analysis, 1st ed., Pearson Education, New Delhi, India.
Rotem, Z., and Claassen, L., 1969, “Natural Convection Above Unconfined Horizontal Surfaces,” J. Fluid Mech., 39(1), pp. 173–192. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Physical model and the coordinate system

Grahic Jump Location
Fig. 2

Plots of the dimensionless similarity functions f(η), f'(η), θ(η), and ζ(η) for Pr=7, Nr=Nb=Nt=0.5 and Le=10. These represent the stream function, longitudinal velocity, temperature, and nanoparticle volume fraction, respectively. (Keys: ———— f(η), – – – – – f'(η), – · – · – · θ(η), ................ ζ(η).)

Grahic Jump Location
Fig. 3

Plots of the dimensionless similarity functions f'(η), θ(η), and ζ(η) for Pr=7, Nr=Nb=Nt=0.5 and two values of the Lewis number: (a) Le=10 and (b) Le=100. These represent the longitudinal velocity, temperature, and nanoparticle volume fraction, respectively. (Keys: ———— f'(η), – – – – – θ(η), – · – · – · ζ(η).)

Grahic Jump Location
Fig. 4

Variation of f ′(η) which determines the dimensionless longitudinal velocity for two values of Nr at Pr=7, Le=10, and Nb=Nt=0.5. (Keys: ———— Nr=10-5, – – – – – Nr=0.5.)

Grahic Jump Location
Fig. 5

Variation of θ(η) which determines the temperature distribution of the nanofluid for two values of Nb and Nt at Pr=7, Le=10, and Nr=0.5. (Keys: ———— Nb=Nt=10-5, – – – – – Nb=Nt=0.5.)

Grahic Jump Location
Fig. 6

Variation of ζ(η) which determines the nanoparticle volume fraction in the nanofluid for two values of Nb and Nt, at Pr=7, Nr=0.5 and two values of Lewis numbers. (Keys: ———— Nb=Nt=10-5, – – – – – Nb=Nt=0.5.)

Grahic Jump Location
Fig. 7

Variation of the reduced local Nusselt number with the Brownian motion parameter for Pr=7, Le=10 and three values of Nr and Nt

Grahic Jump Location
Fig. 8

Variation of the reduced local Nusselt number with the thermophoretic parameter for Pr=7, Le=10 and three values of Nr and Nb

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