Skip to main content
SpringerLink
Log in

Influence of Temperature and Pressure on Viscoelastic Fluid Flow in a Plane Channel

  • TRANSFER PROCESSES IN RHEOLOGICAL MEDIA
  • Published:
Journal of Engineering Physics and Thermophysics Aims and scope

The hydrodynamics of a steady-state nonisothermal flow of a viscoelastic polymer medium in a plane channel and heat transfer in it under boundary conditions of the first kind have been investigated. Fluid flow with a low Reynolds number and a high Péclet number was investigated, which made it possible to neglect the gravity and inertial forces, as well as the longitudinal thermal conductivity of the medium. From the rheological viewpoint, the polymer melt represents a viscoelastic fluid; therefore the Phan-Thien–Tanner fluid model was used as a rheological model of the fluid, with viscosity depending on temperature and pressure. A high-viscosity medium was considered; therefore a dissipation term was included into the equation of the energy of its flow. With the use of the indicated rheological model the velocity profile of fluid flow was obtained in an explicit form from the equation of fluid motion. It has been established that the dependence of the fluid viscosity on temperature and pressure exerts a noticeable influence on the distribution of the Nusselt number and of bulk temperature of the fluid along the channel length. It is shown that account for the temperature dependence of fluid viscosity leads to a decrease in the role of energy dissipation of its flow in the process of flow heating and that, conversely, the dependence of the fluid viscosity on pressure considerably enhances the dissipation effect. The problem has been solved numerically by the method of finite differences.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. V. Baranov, Nonisothermal flow of rheologically complex media under conditions of chemical transformations, Mekh. Kompoz. Mater. Konstr., 16, No. 3, 384–399 (2010).

    Google Scholar 

  2. P. J. Oliveira and F. T. Pinho, Plane contraction flow of upper convected Maxwell and Phan-Thien–Tanner fluids as predicted by a finite-volume method, J. Non-Newtonian Fluid Mech., 88, Nos. 1–2, 63–88 (1999).

    Article  Google Scholar 

  3. M. Aboubacar, H. Matallah, and M. F. Webster, Highly elastic solutions for Oldroyd-B and Phan-Thien–Tanner fl uids with a fi nite volume/element method: planar contraction flows, J. Non-Newtonian Fluid Mech., 103, No. 1, 65–103 (2002).

    Article  Google Scholar 

  4. S. H. Hashemabadi, S. G. Etemad, and J. Thibault, Analytical solution for dynamic pressurization of viscoelastic fluids, Int. J. Heat Fluid Flow, 24, 137–144 (2003).

    Article  Google Scholar 

  5. M. S. Alves, P. J. Oliveira, and F. T. Pinho, Benchmark solutions for the flow of Oldroyd-B and PTT fluids in planar contractions, J. Non-Newtonian Fluid Mech., 110, No. 1, 45–75 (2003).

    Article  Google Scholar 

  6. D. O. Cruz and F. T. Pinho, Skewed Poiseuille–Couette fl ows of sPTT fluids in concentric annuli and channels, J. Non- Newtonian Fluid Mech., 121, No. 1, 1–14 (2004).

    Article  Google Scholar 

  7. S. H. Hashemabadi and S. M. Mirnajafi zadeh, Analytical solution of simplified Than-Thien–Tanner fluid between nearly parallel plates of a small inclination, J. Appl. Sci., 7, No. 9, 1271–1278 (2007).

    Article  Google Scholar 

  8. Cao Wei, Shen Changyu, and Zhang Chujie. Computing flow-induced stresses of injection molding based on the Phan-Thien–Tanner model, Arch. Appl. Mech., 78, No. 5, 363–377 (2008).

  9. R. J. Poole and M. A. Alves, Velocity overshoots in gradual contraction flows, J. Non-Newtonian Fluid Mech., 160, No. 1, 47–54 (2009).

    Article  Google Scholar 

  10. T. Chinyoka, Poiseuille flow of reactive Phan-Thien–Tanner liquids in 1D channel flow, Trans. ASME, J. Heat Transf., 132, No. 11, 111701/1–111701/7 (2010).

    Article  Google Scholar 

  11. K. Yapici, B. Karasozen, and Yu. Uludag, Numerical analysis of viscoelastic fluids in steady pressure-driven channel flow, Trans. ASME, J. Fluids Eng., 134, No. 5, 051206/1–051206/9 (2012).

    Article  Google Scholar 

  12. Luis L. Ferras, Joao M. Nobrega, and T. Pinho Fernando, Analytical solutions for channels flows of Phan-Thien–Tanner and Giesekus fluids slip, J. Non-Newtonian Fluid Mech., 171–172, 97–105 (2012).

  13. D. V. Anan'ev and A. A. Kainova, Heat transfer and hydrodynamics in the Phan-Thien–Tanner laminar viscoelastic fluid flow in a convergent channel, Izv. Ross. Akad. Nauk, Énergetika, No. 5, 51–64 (2014).

    Google Scholar 

  14. D. V. Anan'ev, G. R. Khalitova, and U. K. Vachagina, Hydrodynamics and heat transfer in laminar viscoelastic fluid flow in a plane-slotted channel, Teplofi z. Aéromekh., 22, No. 1, 49–60 (2015).

    Google Scholar 

  15. E. K. Vachagina, A. I. Kaidyrov, A. A. Kainova, and G. R. Khalitova, Viscoelastic fluid flow in a prismatic channel of square cross section considering rubber mixtures as an example, Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 1, 9–17 (2016).

    Google Scholar 

  16. A. V. Baranov and N. A. Anisimova, Rheological characteristic features of polymer compositions in the processing processes, Mekh. Kompoz. Mater. Konstr., 14, No. 2, 188–206 (2008).

    Google Scholar 

  17. D. M. Binding, M. A. Couch, and K. Walters, The pressure dependence of the shear and elongational of polymer melts, J. Non-Newtonian Fluid Mech., 79, Nos. 2–3, 137–155 (1998).

    Article  Google Scholar 

  18. Mehrdad Massoudi and Tran X. Phuoc, Unsteady shear flow of fluids with pressure-dependent viscosity, Int. J. Eng. Sci., 44, Nos. 13–14, 915–926 (2006).

    Article  MathSciNet  Google Scholar 

  19. R. R. Huilgol and Z. You, On the importance of the pressure dependence of viscosity in steady non-isothermal shearing flows, J. Non-Newtonian Fluid Mech., 136, Nos. 2–3, 106–117 (2006).

    Article  Google Scholar 

  20. A. Kalogirou, S. Poyiadji, and G. C. Georgiou, Incompressible Poiseuille flows of Newtonian liquids with a pressuredependent viscosity, J. Non-Newtonian Fluid Mech., 166, Nos. 7–8, 413–419 (2011).

    Article  Google Scholar 

  21. A. Hirn, M. Lanzendorfer, and J. Stebel, Finite element approximation of flow of fluids with shear-rate-and pressuredependent viscosity, IMA J. Numer. Anal., 32, No. 4, 1604–1634 (2012).

    Article  MathSciNet  Google Scholar 

  22. Kostas D. Housiadas, An exact analytical solution for viscoelastic fluids with pressure-dependent viscosity, J. Non-Newtonian Fluid Mech., 223, 147–156 (2015).

    Article  MathSciNet  Google Scholar 

  23. A. Mahdavi Khatibi, M. Mirzazadeh, and F. Rashidi, Forced convection heat transfer of Giesekus viscoelastic fluid in pipes and channels, Heat Mass Transf., 46, 405–412 (2010).

    Article  Google Scholar 

  24. Hadi Mokarizadeh, Maedeh Asgharian, and Ahmadreza Raisi, Heat transfer in Couette–Poiseuille flow between parallel plates of the Giesekus viscoelastic fluid, J. Non-Newtonian Fluid Mech., 196, 95–101 (2013).

    Article  Google Scholar 

  25. N. V. Tyabin, O. Kh. Dakhin, and A. V. Baranov, Effect of temperature and pressure on rheological complex media flow in a plane channel, Teplofiz. Vys. Temp., 20, No. 1, 81–86 (1982).

    Google Scholar 

  26. N. V. Tyabin, O. Kh. Dakhin, and A. V. Baranov, Conjugated heat transfer in the flow of a non-Newtonian fluid with variable properties in a flat duct, J. Eng. Phys. Thermophys., 45, No. 3, 979–983 (1985).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. I. M. Gubkin Russian State University of Oil and Gas, 65 Lenin Ave, Moscow, 119296, Russia

    A. V. Baranov

Authors
  1. A. V. Baranov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. V. Baranov.

Additional information

Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 93, No. 5, pp. 1342–1348, September–October, 2020.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Baranov, A.V. Influence of Temperature and Pressure on Viscoelastic Fluid Flow in a Plane Channel. J Eng Phys Thermophy 93, 1296–1302 (2020). https://doi.org/10.1007/s10891-020-02234-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10891-020-02234-0

Keywords

Search

Navigation