International Scientific Journal


The present study concerns the numerical analysis of both hydrodynamic and thermal properties of a Herschel-Bulkley fluid flow in a pipe. The flow, which involves forced heat transfer convection, is steady and takes place within a pipe of circular cross section with uniform wall temperature. The Herschel-Bulkley model with the Papanastasiou regularization is used and flow index values of 1 and 1.5 are considered. The study focuses on the effect of neglecting both viscous dissipation and temperature dependence of the fluid consistency on its hydrodynamic and thermal properties. For that purpose, we investigate both wall heating (Br<0) and wall cooling (Br>0) as well as the exponential temperature dependence of the consistency. The results show that neglecting both of these parameters results in more than a 50% underestimation of the heat transfer due to the viscous nature of this kind of fluid.
PAPER REVISED: 2013-04-10
PAPER ACCEPTED: 2013-04-27
CITATION EXPORT: view in browser or download as text file
  1. Steffe, J.F., Rheological methods in food process engineering. 2nd Ed., Freeman Press, USA, 1992.
  2. Piau, J.M., Carbopol gels: Elastoviscoplastic and slippery glasses made of individual swollen sponges Meso- and macroscopic properties, constitutive equations and scaling laws. J Non-Newtonian Fluid Mech, 144 (2007), pp. 1-29.
  3. Khatyr, R., Ouldhadda, D., Il Idrissi, A., Approche analytique de la convection forcée des fluides de Bingham dans un tube. C R Mecanique, 330 (2002), pp. 69-75.
  4. Khatyr, R., Ouldhadda, D., Il Idrissi, A., Viscous dissipation effects on the asymptotic behaviour of laminar forced convection for Bingham plastics in circular ducts. Int J Heat Mass Transfer, 46 (2003), pp. 589-598.
  5. Soares, E.J., Naccache, M.F., Souza Mendes, P.R., Heat transfer to viscoplastic materials flowing axially through concentric annuli. Int J Heat Fluid Flow, 24 (2003), pp. 762-773.
  6. Nascimento, U.C.S., Macêdo, E.N., Quaresma, J.N.N., Thermal entry region analysis through the finite integral transform technique in laminar flow of Bingham fluids within concentric annular ducts. Int J Heat Mass Transfer, 45 (2002), pp. 923-929.
  7. Min, T., Choi, H.G., Yoo, .J.Y., Choi, H., Laminar convective heat transfer of a Bingham plastic in a circular pipe II. Numerical approach hydrodynamically developing flow and simultaneously developing flow. Int J Heat Mass Transfer 40 (1997), pp. 3689-3701.
  8. Hammad, K.J., Vradis, G.C., Viscous dissipation and heat transfer in pulsatile flows of a yield stress fluid. Int Comm Heat Mass Transfer , 23 (1996), pp. 599-612.
  9. Vradis, G.C., Dougher, J., Kumar, S., Entrance pipe flow and heat transfer for a Bingham plastic. J Heat Mass Transfer, 36 (1993), pp. 543-552.
  10. Duvaut, G., Lions, J.L. Transfert de chaleur dans un fluide de Bingham dont la viscosité dépend de la temperature. J Funct Anal, 11 (1972), pp. 93-110.
  11. Vinay, G., Wachs, A., Agassant, J.F., Numerical simulation of non-isothermal viscoplastic waxy crude oil flows. J Non-Newtonian Fluid Mech, 128 (2005), pp. 144-162.
  12. Soares, M., Naccache, M.F., Souza Mendes, P.R., Heat transfer to viscoplastic materials flowing laminarly in the entrance region of tubes. Int J Heat Fluid Flow, 20 (1999), pp. 60-67.
  13. Nouar, C., Thermal convection for a thermo-dependent yield stress fluid in an axisymmetric horizontal duct. Int J Heat Mass Transfer, 48 (2005), pp. 5520-5535.
  14. Peixinho, J., Desaubry, C., Lebouche, M., Heat transfer of a non-Newtonian fluid (Carbopol aqueous solution) in transitional pipe flow. Int J Heat Mass Transfer, 51 (2008), pp. 198-209.
  15. Salah El-Din, M.M., Laminar fully developed mixed convection with viscous dissipation in a uniformly heated vertical double-passage channel. Thermal Science, 11-1 (2007), pp. 27-41. |16] Sharma, P.R., Singh, G., Effects of Ohmic heating and viscous dissipation on steady MHD flow near a stagnation point on an isothermal stretching sheet. Thermal Science, 13 (2009), pp. 5-12.
  16. Etemad, S.G., Mujumdar, A.S., Effects of variable viscosity and viscous dissipation on laminar convection heat transfer of a power law fluid in the entrance region of a semicircular duct. Int J Heat Mass Transfer, 38 (1995), pp. 2225-2238.
  17. Jambal, O., Shigechi, T., Ganbat, D., Momoki, S., Effects of viscous dissipation and fluid axial heat conduction on heat transfer for non Newtonian fluids in ducts with uniform wall temperature-Part I: parallel and circular duct. Int J Heat Mass Transfer, 32 (2005), pp. 1165-1173.
  18. Yamaguchi, H., Engineering and fluid mechanics. Springer, Netherlands, 2008.
  19. Kay, J.M., Nedderman, R.M., Fluid mechanics and transfer process. Cambridge University Press, Great Britain, 1985.
  20. Chhabra, R.P., Richardson, J.F., Non-Newtonian flow in the process industries-Fundamentals and engineering Applications. Butterworth Heinemann, Great Britain, 1999.
  21. Mitsoulis, E., On creeping drag flow of a viscoplastic fluid past a circular cylinder: wall effects. Chem Eng Sci, 59 (2004), pp. 789-800.
  22. Mitsoulis, E., Galazoulas, S., Simulation of viscoplastic flow past cylinders in tubes. J Non-Newtonian Fluid Mech, 158 (2009), pp. 132-141.
  23. Papanastasiou, T.C., Flow of materials with yield. J Rheol, 31 (1987), pp. 385-404.
  24. Patankar, S.V., Numerical heat transfer and fluid flow. Hemisphere Publishing Co., New York, 1980.
  25. Nouar, C., Benaouda-Zouaoui, B., Desaubry, C., Laminar mixed convection in a horizontal annular duct. Case of thermodependent non-Newtonian fluid. Eur. J. Mech. B - Fluids, 19 (2000), pp. 423-452.
  26. Javaherdeh, K., Devienne, R., Transfert thermique pour l'écoulement en canalisation cylindrique de fluides à seuil : cas du refroidissement à coefficient d'échange constant. Int J Heat Mass Transfer, 42 (1999), pp. 3861-3871.
  27. Métivier, C., Nouar, C., Linear stability of the Rayleigh-Bénard Poiseuille flow for thermodependent viscoplastic fluids. J Non-Newtonian Fluid Mech, 163 (2009), pp. 1-8.
  28. Nouar, C., Devienne, R., Lebouché, M., Convection thermique pour un fluide de Herschel-Bulkley dans la région d'entrée d'une conduite. Int J Heat Mass Transfer, 37 (1994), pp. 1-12.
  29. Aydin, O., Effects of viscous dissipation on the heat transfer in forced pipe flow. Part 1: both hydrodynamically and thermally fully developed flow. Energ Convert and Manag, 46 (2005), pp. 757-769.
  30. Labsi, N., Benkahla, Y.K., Boutra, A., Hydrodynamic and thermal characterization of the flow of a Herschel-Bulkley fluid in a pipe. Book series Computer-Aided Chemical Engineering, ISBN 978-0-444-53569-6, 28 (2010), pp. 1411-1416, Ed. Elsevier.

© 2019 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence