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Influence of Wall Conductivites on a Fully Developed Mixed-Convection Magnetohydrodynamic Nanofluid Flow in a Vertical Channel

  • S. Das
  • B. Tarafdar
  • R. N. Jana
  • O. D. Makinde
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  • 19 Downloads

A fully developed mixed-convection nanofluid flow in a vertical channel with variable thermal and electrical wall conductivities in the presence of a uniform transverse magnetic field is studied. The working fluid is a homogeneous mixture of a base fluid (water) and metallic nanoparticles of three different kinds, namely, copper, alumina, and titanium dioxide. The fluid is also electrically conducting in the presence of an applied magnetic field. The flow is characterized by a moderate magnetic Reynolds number. An induced magnetic field is present. The effects of the pertinent parameters on the nanofluid temperature, velocity, and induced magnetic field strength, as well as on the shear stress and heat transfer rate at the channel wall, are shown. In the case of a negative vertical temperature gradient (heating from below), there exists a critical Rayleigh number at which the fluid becomes unstable. This number is also found as a function of the wall conductivities.

Keywords

fully developed flow mixed convection nanofluids wall conductivity channel 

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References

  1. 1.
    S. U. S. Choi, Enhancing thermal conductivity of fluids with nanoparticles, in D. A. Siginer and H. P. Wang (Eds.), Developments and Applications of Non-Newtonian Flows, Proc. ASME, 66, 99–105 (1995).Google Scholar
  2. 2.
    X. Wang, X. Xu, and S. U. S. Choi, Thermal conductivity of nanoparticle fluid mixture, J. Thermophys. Heat Transf., 13, 474–480 (1999).CrossRefGoogle Scholar
  3. 3.
    S. U. S. Choi, Z. G. Zhang, W. Yu, F. E. Lockwood, and E. A. Grulke, Anomalous thermal conductivity enhancement in nanotube suspensions, Appl. Phys. Lett., 79, 2252–2254 (2001).CrossRefGoogle Scholar
  4. 4.
    J. Y. T. Kang Ki and C. K. Choi, Analysis of convective instability and heat transfer characteristics of nanofluids, Phys. Fluids, 16, 2395–2401 (2004).CrossRefzbMATHGoogle Scholar
  5. 5.
    J. Buongiorno, Convective transport in nanofluids, ASME J. Heat Transf., 128, 240–250 (2006).CrossRefGoogle Scholar
  6. 6.
    S. K. Das, S. U. S. Choi, W. Yu, and T. Pradeep, Nanofluids: Science and Technology, Wiley, New Jersey (2007).CrossRefGoogle Scholar
  7. 7.
    V. Trisaksri and S. Wongwises, Critical review of heat transfer characteristics of nanofluids, Renew. Sustain. Energy Rev., 11, 512–523 (2007).CrossRefGoogle Scholar
  8. 8.
    W. N. Gill and E. Del Casal, A theoretical investigation of natural convection effects in forced horizontal flows, AIChE J., 8, 513–518 (1962).CrossRefGoogle Scholar
  9. 9.
    S. Ostrach, Combined natural- and forced-convection laminar flow and heat transfer of fluid with and without heat sources in channels with linearly varying wall temperatures, NACA TN 3141 (1954).Google Scholar
  10. 10.
    W. T. Snyder, The influence of wall conductance on magnetohydrodynamic channel flow heat transfer, J. Heat Transf., 8, 552–558 (1964).CrossRefGoogle Scholar
  11. 11.
    A. S. Lavine, Analysis of fully developed opposing mixed convection between inclined parallel plates, Wärme Stoffübert., 23, 249–257 (1988).CrossRefGoogle Scholar
  12. 12.
    D. Hall, G. C. Vliet, and T. L. Bergman, Natural convection cooling of vertical rectangular channels in air considering radiation and wall conduction, J. Electron. Packag., 121, 75–84 (1999).CrossRefGoogle Scholar
  13. 13.
    R. Greif, I. S. Habib, and J. C. Lin, Laminar convection of a radiating gas in a vertical channel, J. Fluid Mech., 46, 513 (1971).CrossRefGoogle Scholar
  14. 14.
    C. P. Yu and K. K. Yang, Effect of wall conductances on convective magnetohydrodynamic channel flow, Appl. Sci. Res., 20, 16–23 (1969).CrossRefzbMATHGoogle Scholar
  15. 15.
    P. S. Gupta and A. S. Gupta, Radiation effect on hydromagnetic convection in a vertical channel, Int. J. Heat Mass Transf., 17, 1437–1442 (1973).CrossRefzbMATHGoogle Scholar
  16. 16.
    N. Datta and R. N. Jana, Effect of wall conductances on hydromagnetic convection of a radiating gas in a vertical channel, Int. J. Heat Mass Transf., 19, 1015–1019 (1974).CrossRefzbMATHGoogle Scholar
  17. 17.
    A. Barletta, E. Magyari, and B. Keller, Dual mixed convection flows in a vertical channel, Int. J. Heat Mass Transf., 48, 4835–4845 (2005).CrossRefzbMATHGoogle Scholar
  18. 18.
    M. Guria, B. K. Das, R. N. Jana, and S. K. Ghosh, Effects of wall conductance on MHD fully developed flow with asymmetric heating of the wall, Int. J. Fluid Mech. Res., 34, 521–534 (2007).CrossRefGoogle Scholar
  19. 19.
    X. Hang and I. Pop, Fully developed mixed convection flow in a vertical channel filled with nanofluids, Int. Commun. Heat Mass Transf., 39, 1086–1092 (2012).CrossRefGoogle Scholar
  20. 20.
    T. Grosan and I. Pop, Fully developed mixed convection in a vertical channel filled by a nanofluid, J. Heat Transf., 134, No. 8, 082501 (2012).CrossRefGoogle Scholar
  21. 21.
    H. Xu, T. Fan, and I. Pop, Analysis of mixed convection flow of a nanofluid in a vertical channel with the Buongiorno mathematical model, Int. Commun. Heat Mass Transf., 44, 15–22 (2013).CrossRefGoogle Scholar
  22. 22.
    M. Fakour, A. Vahabzadeh, and D. D. Ganji, Scrutiny of mixed convection flow of a nanofluid in a vertical channel, Int. J. Case Studies Therm. Eng., 4, 15–23 (2014).CrossRefGoogle Scholar
  23. 23.
    S. Das, R. N. Jana, and O. D. Makinde, Mixed convective magnetohydrodynamic flow in a vertical channel filled with nanofluids, Eng. Sci. Tech. Int. J., 18, 244–255 (2015).CrossRefGoogle Scholar
  24. 24.
    S. Kakaç and A. Pramuanjaroenkij, Review of convective heat transfer enhancement with nanofluids, Int. J. Heat Mass Transf., 52, 3187–3196 (2009).CrossRefzbMATHGoogle Scholar
  25. 25.
    H. F. Oztop and E. Abu-Nada, Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids, Int. J. Heat Fluid Flow, 29, 1326–1336 (2009).CrossRefGoogle Scholar
  26. 26.
    L. N. Tao, On combined free and forced convection in channels, ASME J. Heat Transf., 82, 233–238 (1960).CrossRefGoogle Scholar
  27. 27.
    S. K. Ghosh, O. A. Bég, J. Zueco, and V. R. Prasad, Transient hydromagnetic flow in a rotating channel permeated by an inclined magnetic field with magnetic induction and Maxwell displacement current effects, Z. Angew. Math. Phys., 61, 147–169 (2010).MathSciNetCrossRefzbMATHGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • S. Das
    • 1
  • B. Tarafdar
    • 1
  • R. N. Jana
    • 2
  • O. D. Makinde
    • 3
  1. 1.Department of MathematicsUniversity of Gour BangaMaldaIndia
  2. 2.Department of Applied MathematicsVidyasagar UniversityMidnaporeIndia
  3. 3.Faculty of Military ScienceStellenbosch UniversitySaldanhaSouth Africa

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