Journal of Applied Science and Engineering

Published by Tamkang University Press

1.30

Impact Factor

1.60

CiteScore

M. E. Sayed-Ahmed This email address is being protected from spambots. You need JavaScript enabled to view it.1, A. Saif-Elyazal1 and L. Iskander2

1Department of Engineering Mathematics and Physics, Faculty of Engineering, Fayoum University, Fayoum-63111, Egypt
2Department of Engineering Mathematics and Physics, Faculty of Engineering, Cairo University, Giza-12163, Egypt


 

Received: November 29, 2006
Accepted: September 5, 2007
Publication Date: March 1, 2009

Download Citation: ||https://doi.org/10.6180/jase.2009.12.1.10  


ABSTRACT


Laminar fully developed flow and heat transfer of Herschel-Bulkley fluids through rectangular duct is investigated numerically. The non-linear momentum and energy equations are solved numerically using finite-element approximations. We consider two cases of thermal boundary conditions H1 and T thermal boundary conditions. The velocity, temperature profiles, product of friction factor-Reynolds number and Nusselt number for H1 and T thermal boundary conditions are computed for various values of the physical parameters of the Herschel-Bulkley fluids and aspect ratio of the duct. The present results have been compared with the known solution for Newtonian and power-law fluids and are found to be in good agreement.


Keywords: Numerical Analysis, Non-Newtonian Fluids, Heat Transfer, Rectangular Duct


REFERENCES


  1.  [1] Marco, S. M. and Han, L. S., “A Note on Limiting Nusselt Number in Duct with Constant Temperature Gradient by Analogy to Thin Plate Theory,” Trans. ASME, Vol. 77, pp. 625630 (1955).
  2. [2] Holmes, D. B. and Vermeulen, J. R., “Velocity Profile in Ducts with Rectangular Duct Cross-Sections,” Chem. Eng. Sci., Vol. 23, pp. 717722 (1968).
  3. [3] Munchkin, G. F., Solomonov, S. D. and Gordon, A. R., “Hydrodynamic Developed of a Laminar Velocity Field in Rectangular Channels,” J. Eng. Phys. (USSR), Vol. 25, pp. 12681271 (1973).
  4. [4] Natarajan, N. M. and Lakshmanan, S. M., “Laminar Flow in Rectangular Ducts: Prediction of the Velocity Profiles and Fraction Factors,” Indian J. Yechnol., Vol. 10, pp. 435438 (1972).
  5. [5] Shah, R. K. and London, A. L., “Laminar Flow Forced Convection in Ducts,” Advanced Heat Transfer (Suppl. 1) (1978).
  6. [6] Hartnett, J. P. and Kostic, M., “Heat Transfer to Newtonian and Non-Newtonian Fluids in Rectangular Duct,” Adv. Heat Transfer, Vol. 19, pp. 247356 (1989).
  7. [7] Schechter, R. S., “On the Steady Flow of a NonNewtonian Fluid in Cylinder Ducts,” AICHE J. Vol. 7, pp. 445448 (1961).
  8. [8] Whreeler, J. A. and Wissler, E. H., “The Friction Factor-Reynolds Number Relation for Steady Flow of Peseudoplastic Fluids through Rectangular Ducts,” AICHE J. Vol. 11, pp. 207216 (1965).
  9. [9] Kozicki, W., Chou, Ch and Tiu, C., “Non-Newtonian Fluid Inducts of Arbitrary Cross-Sectional Shape,” Chem. Eng. Sci, Vol. 21, pp. 562569 (1971).
  10. [10] Gao, S. X. and Hartnett, J. P., “Non-Newtonian Fluid Laminar Flow and Forced Convection Heat Transfer in Rectangular Ducts,” Int. J. Heat Mass Transfer, Vol. 35, pp. 28232836 (1992).
  11. [11] Seppo Syrjala, “Finite-Element Analysis of Fully Developed Laminar Flow of Power-Law Non-Newtonian Fluid in Rectangular Duct,” Int. Comm. Heat Mass Transfer, Vol. 22, pp. 549557 (1995).
  12. [12] Seppo Syrjala, “Further Finite-Element Analysis of Fully Developed Laminar Flow of Power-Law NonNewtonian Fluid in Rectangular Duct: Heat Transfer Prediction,” Int. Comm. Heat Mass Transfer, Vol. 23, pp. 799807 (1996).
  13. [13] Battra, R. L. and Eissa, M., “Heat Transfer of a Herschel-Bulkley Fluid in a Thermal Entrance Region of Parallel-Plate Channels with Viscous Dissipation Effects,” Proc. of the 19th National conf. on FMEP, Bombay (I.T.T., Powai), India, pp. A4-1A4-6 (1992).
  14. [14] Eissa, M., “Laminar Heat Transfer for Thermally Developing Flow of a Herschel-Bulkley Fluid in a Square Duct,” Int. Comm. Heat Mass Transfer, Vol. 27, pp. 10131024 (2000).
  15. [15] Sayed-Ahmed, M. E. and El-yazal, A. S., “Laminar Fully Developed Flow and Heat Transfer of Robertson-Stiff Fluids in a Rectangular Duct with Temperature Dependent Viscosity,” Int. Comm. Heat Mass Transfer, Vol. 30, pp. 851860 (2003).
  16. [16] Sayed-Ahmed, M. E. and El-yazal, A. S., “Laminar Fully Developed Flow and Heat Transfer of Robertson-Stiff Fluids in a Rectangular Duct,” Can. J. Phys. Vol. 83, pp. 165182 (2005).
  17. [17] Zienkiewicz, O. C. and Morgan, K., “Finite Elements and Approximation,” John Wiley & Sons, Inc. Canada, chapter (3) pp. 132139 (1983).