Cover
Vol. 16 No. 2 (2025)

Published: December 15, 2025

Pages: 24-35

Research Paper

Influence of Inner Cylinder Rotation and Eccentricity on Convective Heat Transfer in Power-Law Non-Newtonian Flow within Annular Cylinders

Abstract

The annular geometry with inner cylinder eccentricity and rotation is significant in many thermal and engineering fields, particularly with non-Newtonian fluid flows. A numerical analysis examines the effects of rotation and eccentricity of the inner cylinder on the fluid flow and heat transfer characteristics of shear-thinning non-Newtonian fluids within annular geometry under developing steady laminar flow. The computational model simulates non-Newtonian annular flow using a power-law viscosity model for generalized Reynolds numbers ($100\le Re_{g}\le1000$), flow behavior index ($0.2\le n\le0.8$) and Taylor number $Ta=10^{4}$ with radius ratio $r^{*}=0.5$. The simulation employs hydraulic and thermal boundary conditions, including an adiabatic outer cylinder and a constant temperature at the inner rotating cylinder, while the outer cylinder remains stationary. Results show that axial flow at $n=0.2$ exhibits lower flow resistance and enhances convective transport compared to higher $n=0.8,$ especially for the concentric case $(\epsilon=0)$. However, increasing eccentricity from $\epsilon=0.2$ to $\epsilon=0.6$ alters the heat transfer behavior, with $n=0.8$ yielding the highest Nusselt numbers at $\epsilon=0.6$, due to the strong secondary flows and intensified local acceleration in the narrow gap. These outcomes reveal that heat transfer enhancement is not solely governed by flow resistance but is also influenced by secondary flows, boundary layer stability, and localized acceleration effects.

References

  1. F. A. Morrison, Understanding Rheology. 2001.
  2. J. F. R. R. P. Chhabra, Non-Newtonian Flow and Applied Rheology: Engineering Applications. 2011.
  3. H. A. Barnes, J. F. Hutton, and K. Walters, An Introduction to Rheology, no. vol. 3. in An Introduction to Rheology. Elsevier Science, 1989.
  4. O. H. R. Byron Bird, Robert C. Armstrong, Dynamics of polymeric liquids, 2nd ed. New York: Wiley, 1987.
  5. R. J. Poole, "Inelastic and flow-type parameter models for non-Newtonian fluids," J. Nonnewton. Fluid Mech., vol. 320, p. 105106, Oct. 2023, doi: 10.1016/j.jnnfm.2023.105106.
  6. P. J. Carreau, "Rheological Equations from Molecular Network Theories," Trans. Soc. Rheol., vol. 16, no. 1, pp. 99-127, Mar. 1972, doi: 10.1122/1.549276.
  7. M. M. Cross, "Rheology of non-Newtonian fluids: A new flow equation for pseudoplastic systems," J. Colloid Sci., vol. 20, no. 5, pp. 417-437, Jun. 1965, doi: 10.1016/0095-8522(65)90022-Χ.
  8. K. Yasuda, R. C. Armstrong, and R. E. Cohen, "Shear flow properties of concentrated solutions of linear and star branched polystyrenes," Rheol. Acta, vol. 20, no. 2, pp. 163-178, Mar. 1981, doi: 10.1007/BF01513059.
  9. M. P. Escudier, I. W. Gouldson, A. S. Pereira, F. T. Pinho, and R. J. Poole, "On the reproducibility of the rheology of shear-thinning liquids," J. Nonnewton. Fluid Mech., vol. 97, no. 2-3, pp. 99-124, Feb. 2001, doi: 10.1016/S0377-0257(00)00178-6.
  10. M. P. Escudier, P. J. Oliveira, and F. T. Pinho, "Fully developed laminar flow of purely viscous non-Newtonian liquids through annuli, including the effects of eccentricity and inner-cylinder rotation," Int. J. Heat Fluid Flow, vol. 23, no. 1, pp. 52-73, Feb. 2002, doi: 10.1016/S0142-727X(01)00135-7.
  11. S. H. Lin, "Heat transfer to generalized non-Newtonian Couette flow in annuli with moving outer cylinder," Int. J. Heat Mass Transf., vol. 35, no. 11, pp. 3069-3075, Nov. 1992, doi: 10.1016/0017-9310(92)90326-Ν.
  12. H. E. Ahmed and M. I. Ahmed, "Thermal performance of annulus with its applications; A review," Renew. Sustain. Energy Rev., vol. 71, no. December, pp. 170-190, 2017, doi: 10.1016/j.rser.2016.12.050.
  13. A. Davey, R. C. Di Prima, and J. T. Stuart, "On the instability of Taylor vortices," J. Fluid Mech., vol. 31, no. 01, p. 17, Jan. 1968, doi: 10.1017/S0022112068000029.
  14. K. S. Ball, B. Farouk, and V. C. Dixit, "An experimental study of heat transfer in a vertical annulus with a rotating inner cylinder," Int. J. Heat Mass Transf., vol. 32, no. 8, pp. 1517-1527, Aug. 1989, doi: 10.1016/0017-9310(89)90073-2.
  15. G. Zeng-Yuan and Z. Chao-Min, "Thermal drive in centrifugal fields-mixed convection in a vertical rotating cylinder," Int. J. Heat Mass Transf., vol. 35, no. 7, pp. 1635-1644, Jul. 1992, doi: 10.1016/0017-9310(92)90134-Ε.
  16. M. P. Escudier, I. W. Gouldson, P. J. Oliveira, and F. T. Pinho, "Effects of inner cylinder rotation on laminar flow of a Newtonian fluid through an eccentric annulus," Int. J. Heat Fluid Flow, vol. 21, no. 1, pp. 92-103, Feb. 2000, doi: 10.1016/S0142-727X(99)00059-4.
  17. W. M. Abed, A. Al-Damook, and W. H. Khalil, "Convective heat transfer in an annulus of concentric and eccentric cylinders with an inner rotating cylinder," Int. J. Heat Technol., vol. 39, no. 1, pp. 61-72, 2021, doi: 10.18280/ijht.390107.
  18. M. P. Escudier, I. W. Gouldson, and D. M. Jones, "Flow of shear-thinning fluids in a concentric annulus," Exp. Fluids, vol. 18, no. 4, pp. 225-238, Feb. 1995, doi: 10.1007/BF00195092.
  19. P. Escudier and I. W. Gouldson, "Configuration1 of Technical Report," no. 95, pp. 156-162, 1995.
  20. M. Escudier, P. Oliveira, F. Pinho, and S. Smith, "Fully developed laminar flow of non-Newtonian liquids through annuli: Comparison of numerical calculations with experiments," Exp. Fluids, vol. 33, no. 1, pp. 101-111, 2002, doi: 10.1007/s00348-002-0429-4.
  21. M. Sefid and E. Izadpanah, "Developing and fully developed non-newtonian fluid flow and heat transfer through concentric annuli," J. Heat Transfer, vol. 135, no. 7, pp. 1-8, 2013, doi: 10.1115/1.4023882.
  22. R. M. Manglik and P. Fang, "Thermal processing of viscous non-Newtonian fluids in annular ducts: effects of power-law rheology, duct eccentricity, and thermal boundary conditions," Int. J. Heat Mass Transf., vol. 45, no. 4, pp. 803-814, Feb. 2002, doi: 10.1016/S0017-9310(01)00186-7.
  23. R. M. Manglik and J. Prusa, "Viscous dissipation in non-Newtonian flows: Implications for the nusselt number," J. Thermophys. Heat Transf., vol. 9, no. 4, pp. 733-742, 1995, doi: 10.2514/3.732.
  24. V. Salubi, R. Mahon, and G. Oluyemi, "The combined effect of fluid rheology, inner pipe rotation and eccentricity on the flow of Newtonian and non-Newtonian fluid through the annuli," J. Pet. Sci. Eng., vol. 211, no. June 2021, p. 110018, 2022, doi: 10.1016/j.petrol.2021.110018.
  25. R. Ershadnia et al., "Non-Newtonian fluid flow dynamics in rotating annular media: Physics-based and data-driven modeling," J. Pet. Sci. Eng., vol. 185, no. November 2019, p. 106641, 2020, doi: 10.1016/j.petrol.2019.106641.
  26. L. Fusi, A. Farina, and K. R. Rajagopal, "Secondary flow of an elastic-viscoplastic fluid in an eccentric annulus," Int. J. Non. Linear. Mech., vol. 158, no. September 2023, p. 104564, 2024, doi: 10.1016/j.ijnonlinmec.2023.104564.
  27. B. Traore, C. Castelain, and T. Burghelea, "Efficient heat transfer in a regime of elastic turbulence," J. Nonnewton. Fluid Mech., vol. 223, pp. 62-76, 2015, doi: 10.1016/j.jnnfm.2015.05.005.
  28. G. Yao, J. Zhao, X. Shen, H. Yang, and D. Wen, "Effects of rheological properties on heat transfer enhancements by elastic instability in von-Karman swirling flow," Int. J. Heat Mass Transf., vol. 152, p. 119535, 2020, doi: 10.1016/j.ijheatmasstransfer.2020.119535.
  29. G. Yao, H. Yang, J. Zhao, and D. Wen, "Experimental study on flow and heat transfer enhancement by elastic instability in swirling flow," Int. J. Therm. Sci., vol. 157, no. May, p. 106504, 2020, doi: 10.1016/j.ijthermalsci.2020.106504.
  30. R. D. Whalley, W. M. Abed, D. J. C. Dennis, and R. J. Poole, "Enhancing heat transfer at the micro-scale using elastic turbulence," Theor. Appl. Mech. Lett., vol. 5, no. 3, pp. 103-106, 2015, doi: 10.1016/j.taml.2015.03.006.
  31. D. Y. Li, X. Bin Li, H. N. Zhang, F. C. Li, S. Z. Qian, and S. W. Joo, "Measuring heat transfer performance of viscoelastic fluid flow in curved microchannel using Ti-Pt film temperature sensor," Exp. Therm. Fluid Sci., vol. 77, pp. 226-233, 2016, doi: 10.1016/j.expthermflusci.2016.05.001.
  32. W. M. Abed, R. D. Whalley, D. J. C. Dennis, and R. J. Poole, "Experimental investigation of the impact of elastic turbulence on heat transfer in a serpentine channel," J. Nonnewton. Fluid Mech., vol. 231, pp. 68-78, 2016, doi: 10.1016/j.jnnfm.2016.03.003.
  33. A. B. Metzner and J. C. Reed, "Flow of Non-Newtonian Fluids-Correlation of the Laminar , Transition, and Turbulent-flow Regions," no. 4, 1955.
  34. W. Kozicki, C. H. Chou, and C. Tiu, "Non-Newtonian flow in ducts of arbitrary cross-sectional shape," Chem. Eng. Sci., vol. 21, no. 8, pp. 665-679, Aug. 1966, doi: 10.1016/0009-2509(66)80016-7.