Table of Contents
ISRN Thermodynamics
Volume 2012 (2012), Article ID 181286, 6 pages
http://dx.doi.org/10.5402/2012/181286
Research Article

Effects of Viscous Dissipation on the Thermal Boundary Layer of Pseudoplastic Power-Law Non-Newtonian Fluids Using Discretization Method and the Boubaker Polynomials Expansion Scheme

1ESSTT, Université de Tunis, 63 Rue Sidi Jabeur, 5100 Mahdia, Tunisia
2Department of Mathematics and Mechanics, University of Science and Technology Beijing, Beijing 100083, China
3Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
4School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China

Received 6 January 2012; Accepted 31 January 2012

Academic Editors: S. Hashimoto and G. Polidori

Copyright © 2012 Karem Boubaker et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. W. R. Schowalter, “The application of boundary-layer theory to power-law pseudo plastic fluids: similar solutions,” AIChE Journal, vol. 6, pp. 24–28, 1960. View at Google Scholar
  2. A. Acrivos, M. J. Shah, and E. E. Petersen, “Momentum and heat transfer in laminar Boundary-Layer flows of non-Newtonian fluids past external surfaces,” AIChE Journal, vol. 6, pp. 312–317, 1960. View at Google Scholar
  3. T. Y. Wang, “Mixed convection from a vertical plate to non-Newtonian fluids with uniform surface heat flux,” International Communications in Heat and Mass Transfer, vol. 22, no. 3, pp. 369–380, 1995. View at Google Scholar · View at Scopus
  4. T. Y. Wang, “Mixed convection heat transfer from a vertical plate to non-Newtonian fluids,” International Journal of Heat and Fluid Flow, vol. 16, no. 1, pp. 56–61, 1995. View at Google Scholar · View at Scopus
  5. F. M. Hady, “Mixed convection Boundary-Layer flow of non-Newtonian fluids on a horizontal plate,” Applied Mathematics and Computation, vol. 68, no. 2-3, pp. 105–112, 1995. View at Google Scholar · View at Scopus
  6. K. Kumari, I. Pop, and H. S. Takhar, “Free convection in power-law fluids near a three-dimensional stagnation point,” International Journal of Heat and Fluid Flow, vol. 18, pp. 625–631, 1997. View at Google Scholar
  7. T. G. Howell, D. R. Jeng, and K. J. De Witt, “Momentum and heat transfer on a continuous moving surface in a power law fluid,” International Journal of Heat and Mass Transfer, vol. 40, no. 8, pp. 1853–1861, 1997. View at Google Scholar · View at Scopus
  8. J. H. Rao, D. R. Jeng, and K. J. De Witt, “Momentum and heat transfer in a power-law fluid with arbitrary injection/suction at a moving wall,” International Journal of Heat and Mass Transfer, vol. 42, no. 15, pp. 2837–3847, 1999. View at Google Scholar · View at Scopus
  9. I. A. Hassanien, A. A. Abdullah, and R. S. R. Gorla, “Flow and heat transfer in a power-law fluid over a nonisothermal stretching sheet,” Mathematical and Computer Modelling, vol. 28, no. 9, pp. 105–116, 1998. View at Publisher · View at Google Scholar · View at Scopus
  10. N. Luna, F. Méndez, and C. Treviño, “Conjugated heat transfer in circular ducts with a power-law laminar convection fluid flow,” International Journal of Heat and Mass Transfer, vol. 45, no. 3, pp. 655–666, 2002. View at Publisher · View at Google Scholar · View at Scopus
  11. A. Pinarbasi and M. Imal, “Viscous heating effects on the linear stability of Poiseuille flow of an inelastic fluid,” Journal of Non-Newtonian Fluid Mechanics, vol. 127, no. 2-3, pp. 67–71, 2005. View at Publisher · View at Google Scholar · View at Scopus
  12. C.-H. Chen, “Effect of viscous dissipation on heat transfer in a non-Newtonian liquid film over an unsteady stretching sheet,” Journal of Non-Newtonian Fluid Mechanics, vol. 135, no. 2-3, pp. 128–135, 2005. View at Publisher · View at Google Scholar · View at Scopus
  13. H. I. Andersson, K. H. Bech, and B. S. Dandapat, “Magnetohydrodynamic flow of a power-law fluid over a stretching sheet,” International Journal of Non-Linear Mechanics, vol. 27, no. 6, pp. 929–936, 1992. View at Google Scholar · View at Scopus
  14. R. Cortell, “A note on magnetohydrodynamic flow of a power-law fluid over a stretching sheet,” Applied Mathematics and Computation, vol. 168, no. 1, pp. 557–566, 2005. View at Publisher · View at Google Scholar · View at Scopus
  15. M. A. A. Mahmoud and M. A. E. Mahmoud, “Analytical solutions of hydromagnetic Boundary-Layer flow of a non-Newtonian power-law fluid past a continuously moving surface,” Acta Mechanica, vol. 181, no. 1-2, pp. 83–89, 2006. View at Publisher · View at Google Scholar · View at Scopus
  16. I. Pop, M. Rashidi, and R. S. R. Gorla, “Mixed convection to power-law type non-Newtonian fluids from a vertical wall,” Polymer-Plastics Technology and Engineering, vol. 30, no. 1, pp. 47–66, 1991. View at Google Scholar · View at Scopus
  17. I. Pop, “Boundary layer flow at a three-dimensional stagnation point in power-law non-Newtonian fluids,” International Journal of Heat and Fluid Flow, vol. 14, no. 4, pp. 408–412, 1993. View at Google Scholar · View at Scopus
  18. R. S. R. Gorla, I. Pop, and J. K. Lee, “Convective wall plume in power-law fluid: second-order correction for the adiabatic wall,” Warme-und Stoffubertragung, vol. 27, no. 8, pp. 473–479, 1992. View at Publisher · View at Google Scholar · View at Scopus
  19. M. C. Ece and E. Buyuk, “Similarity solutions for free convection to power-law fluids from a heated vertical plate,” Applied Mathematics Letters, vol. 33, no. 1, pp. 119–125, 1990. View at Google Scholar · View at Scopus
  20. L. Zheng, X. Zhang, and C. Lu, “Heat transfer for power law non-Newtonian fluids,” Chinese Physics Letters, vol. 23, no. 12, pp. 3301–3304, 2006. View at Publisher · View at Google Scholar · View at Scopus
  21. L. Zheng, X. Zhang, and L. Ma, “Fully developed convective heat transfer of power law fluids in a circular tube,” Chinese Physics Letters, vol. 25, no. 1, pp. 195–197, 2008. View at Publisher · View at Google Scholar · View at Scopus
  22. A. Belhadj, O. Onyango, and N. Rozibaeva, “Boubaker polynomials expansion scheme-related heat transfer investigation inside keyhole model,” Journal of Thermophysics and Heat Transfer, vol. 23, no. 3, pp. 639–640, 2009. View at Publisher · View at Google Scholar · View at Scopus
  23. A. S. Kumar, “An analytical solution to applied mathematics-related Love's equation using the Boubaker polynomials expansion scheme,” Journal of the Franklin Institute, vol. 347, no. 9, pp. 1755–1761, 2010. View at Publisher · View at Google Scholar · View at Scopus
  24. A. Belhadj, J. Bessrour, M. Bouhafs, and L. Barrallier, “Experimental and theoretical cooling velocity profile inside laser welded metals using keyhole approximation and Boubaker polynomials expansion,” Journal of Thermal Analysis and Calorimetry, vol. 97, no. 3, pp. 911–920, 2009. View at Publisher · View at Google Scholar · View at Scopus
  25. P. Barry and A. Hennessy, “Meixner-type results for Riordan arrays and associated integer sequences, section 6: the Boubaker polynomials,” Journal of Integer Sequences, vol. 13, pp. 1–34, 2010. View at Google Scholar
  26. M. Agida and A. S. Kumar, “A Boubaker polynomials expansion scheme solution to random Love's equation in the case of a rational Kernel,” Electronic Journal of Theoretical Physics, vol. 7, no. 24, pp. 319–326, 2010. View at Google Scholar · View at Scopus
  27. A. Yildirim, S. T. Mohyud-Din, and D. H. Zhang, “Analytical solutions to the pulsed Klein-Gordon equation using modified variational iteration method (MVIM) and Boubaker polynomials expansion scheme (BPES),” Computers and Mathematics with Applications, vol. 59, no. 8, pp. 2473–2477, 2010. View at Publisher · View at Google Scholar · View at Scopus
  28. J. Ghanouchi, H. Labiadh, and K. Boubaker, “An attempt to solve the heat transfer equation in a model of pyrolysis spray using 4q-order m-Boubaker polynomials,” International Journal of Heat and Technology, vol. 26, no. 1, pp. 49–53, 2008. View at Google Scholar · View at Scopus
  29. O. B. Awojoyogbe and K. Boubaker, “A solution to Bloch NMR flow equations for the analysis of hemodynamic functions of blood flow system using m-Boubaker polynomials,” Current Applied Physics, vol. 9, no. 1, pp. 278–288, 2009. View at Publisher · View at Google Scholar · View at Scopus
  30. S. Slama, J. Bessrour, and K. B. Ben Mahmoud, “Study of temperature 3D profile during weld heating phase using Boubaker polynomials expansion,” Thermochimica Acta, vol. 55, pp. 401–404, 2009. View at Publisher · View at Google Scholar · View at Scopus
  31. S. Slama, M. Bouhafs, and K. B. Ben Mahmoud, “A Boubaker polynomials solution to heat equation for monitoring A3 point evolution during resistance spot welding,” International Journal of Heat and Technology, vol. 26, no. 2, pp. 141–146, 2008. View at Google Scholar · View at Scopus
  32. S. Tabatabaei, T. Zhao, O. Awojoyogbe, and F. Moses, “Cut-off cooling velocity profiling inside a keyhole model using the Boubaker polynomials expansion scheme,” Heat and Mass Transfer/Waerme- und Stoffuebertragung, vol. 45, no. 10, pp. 1247–1251, 2009. View at Publisher · View at Google Scholar · View at Scopus
  33. S. Fridjine and M. Amlouk, “A new parameter: an ABACUS for optimizing PVT hybrid solar device functional materials using the Boubaker polynomials expansion scheme,” Modern Physics Letters B, vol. 23, no. 17, pp. 2179–2182, 2009. View at Publisher · View at Google Scholar · View at Scopus
  34. H. Rahmanov, “A solution to the non linear korteweg-de-vries equation in the particular case dispersion-adsorption problem in porous media using the spectral Boubaker polynomials expansion scheme (BPES),” Studies in Nonlinear Sciences, vol. 2, no. 1, pp. 46–49, 2011. View at Google Scholar
  35. A. Milgram, “The stability of the Boubaker polynomials expansion scheme (BPES)-based solution to Lotka-Volterra problem,” Journal of Theoretical Biology, vol. 271, no. 1, pp. 157–158, 2010. View at Publisher · View at Google Scholar · View at Scopus
  36. M. Benhaliliba, C. E. Benouis, K. Boubaker et al., “A new guide to thermally optimized doped oxides monolayer spray-grown solar cells: the amlouk-Boubaker optothermal expansivity ?ab,” in Solar Cells, L. A. Kosyachenko, Ed., pp. 27–41, InTech, 2011. View at Google Scholar
  37. M. Dada, M. A. Aweda, O. B. Awojoyogbe, and K. Boubaker, “A polynomial expression to the magnetic phase-shift induced in leon-vigmond model of the human heart,” Physical Journal of Mechanics in Medicine an Biology, vol. 12, no. 1, pp. 1–7, 2012. View at Google Scholar
  38. L. C. Zheng, X. X. Zhang, K. Boubaker, U. Yücel, E. Gargouri-Ellouze, and A. Yıldırım, “Similarity and Boubaker polynomials expansion scheme BPES comparative solutions to the heat transfer equation for incompressible non-newtonian fluids: case of laminar boundary energy equation,” The European Physical Journal, vol. 55, no. 21102, 5 pages, 2011. View at Google Scholar