Korean Chemical Engineering Research

The Korean Institute of Chemical Engineers (한국화학공학회)
권호 표지
DOI QR코드

DOI QR Code

Analysis of Forced Convection Heat Transfer for Axial Annular Flow of Giesekus Viscoelastic Fluid

  • Received : 2014.04.21
  • Accepted : 2014.07.23
  • Published : 2015.02.01
Download PDF
⟨ Previous Next ⟩

Abstract

Analytical solutions for the forced convection heat transfer of viscoelastic fluids obeying the Giesekus model are obtained in a concentric annulus under laminar flow for both thermal and hydrodynamic fully developed conditions. Boundary conditions are assumed to be (a) constant fluxes at the walls and (b) constant temperature at the walls. Temperature profiles and Nusselt numbers are derived from dimensionless energy equation. Subsequently, effects of elasticity, mobility parameter and viscous dissipation are discussed. Results show that by increasing elasticity, Nusselt number increases. However, this trend is reversed for constant wall temperature when viscous dissipation is weak. By increasing viscous dissipation, the Nusselt number decreases for the constant flux and increases for the constant wall temperature. For the wall cooling case, when the viscous dissipation exceeds a critical value, the generated heat overcomes the heat which is removed at the walls, and fluid heats up longitudinally.

Keywords

References

  1. Shah, R. K. and London, A. L., Laminar Flow Forced Convection in Ducts, Academic Press, New York(1978).
  2. Coelho, P. M. and Pinho, F. T., Int. J. Heat Mass Transfer, 49, 3349(2006). https://doi.org/10.1016/j.ijheatmasstransfer.2006.03.017
  3. Manglik, R. M. and Fang, P., Int. J. Heat Fluid Flow, 16, 298 (1995). https://doi.org/10.1016/0142-727X(95)00030-T
  4. Fang P., Manglik, R. M. and Jog, M. A., J. Non-Newton. Fluid Mech., 84, 1(1999). https://doi.org/10.1016/S0377-0257(98)00145-1
  5. Raju, K. K. and Devanathan, R., Rheol. Acta., 10, 484(1971). https://doi.org/10.1007/BF03396398
  6. Hong, S. N. and Matthews, J. C., Int. J. Heat Mass Transfer, 12, 1699(1969). https://doi.org/10.1016/0017-9310(69)90101-X
  7. Batra, R. L. and Sudarsan, V. R., Comput. Meth. Appl. Mech. Eng., 95, 1(1992). https://doi.org/10.1016/0045-7825(92)90078-X
  8. Tanaka, M. and Mitsuishi, N., Heat Transfer Jpn. Res., 4, 26(1975).
  9. Jambal, O., Shigechi, T., Davaa, G. and Momoki, S., Int. Comm. Heat Mass Transfer, 32, 1174(2005). https://doi.org/10.1016/j.icheatmasstransfer.2005.07.003
  10. Pinho, F. T. and Oliveira, P. J., Int. J. Heat Mass Transfer, 43, 2273(2000). https://doi.org/10.1016/S0017-9310(99)00303-8
  11. Coelho, P. M., Pinho, F. T. and Oliveira, P. J., Int. J. Heat Mass Transfer, 45, 1413(2002). https://doi.org/10.1016/S0017-9310(01)00236-8
  12. Hashemabadi, S. H., Etemad, S. Gh., Narenji, M. R. G. and Thibault, J., Int. Commun. Heat Mass Transfer, 30, 197(2003). https://doi.org/10.1016/S0735-1933(03)00030-7
  13. Hashemabadi, S. H., Etemad, S. Gh. and Thibault, J., Int. J. Heat Mass Transfer, 47, 3985(2004). https://doi.org/10.1016/j.ijheatmasstransfer.2004.03.026
  14. Coelho, P. M., Pinho, F. T. and Oliveira, P. J., Int. J. Heat Mass Transfer, 46, 3865(2003). https://doi.org/10.1016/S0017-9310(03)00179-0
  15. Oliveira, P. J., Coelho, P. M. and Pinho, F. T., J. Non-Newton. Fluid Mech., 121, 69(2004). https://doi.org/10.1016/j.jnnfm.2004.04.005
  16. Pinho, F. T. and Coelho, P. M., J. Non-Newton. Fluid Mech., 138, 7(2006). https://doi.org/10.1016/j.jnnfm.2006.04.002
  17. Khatibi, A. M., Mirzazadeh, M. and Rashidi, F., Heat Mass Transfer, 46, 405(2010). https://doi.org/10.1007/s00231-010-0582-x
  18. Giesekus, H., J. Non-Newton. Fluid Mech., 11, 69(1982) . https://doi.org/10.1016/0377-0257(82)85016-7
  19. Giesekus, H., J. Non-Newton. Fluid Mech., 12, 367(1983). https://doi.org/10.1016/0377-0257(83)85009-5
  20. Kakac, S. and Yener, Y., Convective Heat Transfer, CRC Press (1995).
  21. Bird, R. B., Amstrong, R. C. and Hassager, O., Dynamics of Polymeric Liquids: Fluid Mechanics, Vol. 1, Wiley, New York(1977).
  22. Mohseni, M. M. and Rashidi, F., J. Non-Newton. Fluid Mech., 165, 1550(2010). https://doi.org/10.1016/j.jnnfm.2010.07.012
  23. Bejan, A., Convection Heat Transfer, Wiley, New York(1995).
  24. Bhatara, G., Shaqfeh, E. S. G. and Khomami, B., J. Rheol., 49, 929(2005). https://doi.org/10.1122/1.2000969

Cited by

  1. Heat Transfer of Bingham Fluids in an Annular Duct with Viscous Dissipation pp.1521-0537, 2017, https://doi.org/10.1080/01457632.2017.1388943
  2. Effects of elasticity on unsteady forced convective heat transfer of viscoelastic fluid around a cylinder in the presence of viscous dissipation vol.32, pp.8, 2020, https://doi.org/10.1063/5.0009948