Table of Contents
ISRN Mathematical Physics
Volume 2012, Article ID 732675, 31 pages
http://dx.doi.org/10.5402/2012/732675
Research Article

Effect of Wind Stress on the Dynamics and Stability of Nonisothermal Power-Law Film down an Inclined Plane

Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104, USA

Received 11 August 2011; Accepted 25 September 2011

Academic Editor: J. Frauendiener

Copyright © 2012 B. Uma. 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. C.-S. Yih, “Stability of parallel laminar flow with a free surface,” in Proceedings of the 2nd U.S. National Congress on Applied Mechanics, pp. 623–628, ASME, 1955.
  2. T. B. Benjamin, “Wave formation in laminar flow down an inclined plane,” Journal of Fluid Mechanics, vol. 2, no. 06, pp. 554–573, 1957. View at Google Scholar
  3. C.-S. Yih, “Stability of liquid flow down an inclined plane,” Physics of Fluids, vol. 6, no. 3, pp. 321–334, 1963. View at Google Scholar
  4. J. Benney, “Long waves on liquid films,” Journal of Mathematical Physics, vol. 45, pp. 150–155, 1966. View at Google Scholar
  5. H.-C. Chang and E. A. Demekhin, Complex Wave Dynamics on Thin Films, Elsevier Science, 2002.
  6. W. Nusselt, “Die oberflachen kondensation des wasserdamfes,” Z. VDI, vol. 50, pp. 541–546, 1916. View at Google Scholar
  7. S. G. Bankoff, “Stability of liquid flow down a heated inclined plane,” International Journal of Heat and Mass Transfer, vol. 14, no. 3, pp. 377–385, 1971. View at Google Scholar · View at Scopus
  8. E. Marschall and C. Y. Lee, “Stability of condensate flow down a vertical wall,” International Journal of Heat and Mass Transfer, vol. 16, no. 1, pp. 41–48, 1973. View at Google Scholar · View at Scopus
  9. S. P. Lin, “Stability of liquid flow down a heated inclined plane,” Letters in Heat and Mass Transfer, vol. 2, no. 5, pp. 361–369, 1975. View at Google Scholar · View at Scopus
  10. J. P. Burelbach, S. G. Bankoff, and S. H. Davis, “Nonlinear stability of evaporating/condensing liquid films,” Journal of Fluid Mechanics, vol. 195, pp. 463–494, 1988. View at Google Scholar
  11. S. G. Bankoff, “Significant questions in thin liquid film heat transfer,” Journal of Heat Transfer, vol. 116, no. 1, pp. 10–16, 1994. View at Google Scholar · View at Scopus
  12. S. G. Bankoff, “Dynamics and stability of thin heated liquid films,” Journal of Heat Transfer, vol. 112, no. 3, pp. 538–546, 1987. View at Google Scholar · View at Scopus
  13. S. W. Joo, S. H. Davis, and S. G. Bankoff, “Long-wave instabilities of heated falling films. Two-dimensional theory of uniform layers,” Journal of Fluid Mechanics, vol. 230, pp. 117–146, 1991. View at Google Scholar · View at Scopus
  14. B. Spindler, J. N. Solesio, and J. M. Delhaye, “On the equations describing the instabilities of liquid films with interfacial phase change,” Two-Phase Momenum Heat and Mass Transfer in Chemical Process and Energy Engineering Systems, vol. 1, pp. 339–344, 1978. View at Google Scholar · View at Scopus
  15. M. Ünsal and W. C. Thomas, “Linear stability analysis of film condensation,” The ASME Journal of Heat Transfer, vol. 100, no. 4, pp. 629–634, 1978. View at Google Scholar · View at Scopus
  16. B. Spindler, “Linear stability of liquid films with interfacial phase change,” International Journal of Heat and Mass Transfer, vol. 25, no. 2, pp. 161–173, 1982. View at Google Scholar · View at Scopus
  17. M. Ünsal and W. C. Thomas, “Nonlinear stability of film condensation,” Journal of Heat Transfer, vol. 102, no. 3, pp. 483–488, 1980. View at Google Scholar · View at Scopus
  18. C. C. Hwang and C. I. Weng, “Finite-amplitude stability analysis of liquid films down a vertical wall with and without interfacial phase change,” International Journal of Multiphase Flow, vol. 13, no. 6, pp. 803–814, 1987. View at Google Scholar · View at Scopus
  19. A. S. Gupta, “Stability of a visco-elastic liquid film flowing down an inclined plane,” Journal of Fluid Mechanics, vol. 28, no. 1, pp. 17–28, 1967. View at Google Scholar
  20. W. Lai, “Stability of an elastico-viscous liquid film flowing down an inclined plane,” Physics of Fluids, vol. 10, no. 4, pp. 844–847, 1967. View at Google Scholar · View at Scopus
  21. E. S. G. Shaqfeh, R. G. Larson, and G. H. Fredrickson, “The stability of gravity driven viscoelastic film-flow at low to moderate reynolds number,” Journal of Non-Newtonian Fluid Mechanics, vol. 31, no. 1, pp. 87–113, 1989. View at Google Scholar · View at Scopus
  22. K. Chen, “The onset of elastically driven wavy motion in the flow of two viscoelastic liquid films down an inclined plane,” Journal of Non-Newtonian Fluid Mechanics, vol. 45, no. 1, pp. 21–45, 1992. View at Google Scholar · View at Scopus
  23. H. I. Andersson and E. N. Dahl, “Gravity-driven flow of a viscoelastic liquid film along a vertical wall,” Journal of Physics D, vol. 32, no. 14, pp. 1557–1562, 1999. View at Publisher · View at Google Scholar · View at Scopus
  24. J. S. Lin and C. C. Hwang, “Finite amplitude long-wave instability of power-law liquid films,” International Journal of Non-Linear Mechanics, vol. 35, no. 5, pp. 769–777, 2000. View at Publisher · View at Google Scholar · View at Scopus
  25. P. J. Cheng, H. Y. Lai, and C. K. Chen, “Stability analysis of thin viscoelastic liquid film flowing down on a vertical wall,” Journal of Physics D, vol. 33, no. 14, pp. 1674–1682, 2000. View at Publisher · View at Google Scholar · View at Scopus
  26. C. T. Huang and B. Khomami, “The instability mechanism of single and multilayer Newtonian and viscoelastic flows down an inclined plane,” Rheologica Acta, vol. 40, no. 5, pp. 467–484, 2001. View at Publisher · View at Google Scholar · View at Scopus
  27. B. Uma and R. Usha, “Dynamics of a thin viscoelastic film on an inclined plane,” International Journal of Engineering Science, vol. 44, no. 20, pp. 1449–1481, 2006. View at Publisher · View at Google Scholar · View at Scopus
  28. H. I. Andersson and F. Irgens, “Gravity-driven laminar film flow of power-law fluids along vertical walls,” Journal of Non-Newtonian Fluid Mechanics, vol. 27, no. 2, pp. 153–172, 1988. View at Google Scholar · View at Scopus
  29. F. L. Ko and C. C. Mei, “Slow spreading of a sheet of Bingham fluid on an inclined plane,” Journal of Fluid Mechanics, vol. 207, pp. 505–529, 1989. View at Google Scholar · View at Scopus
  30. C. C. Hwang, J. L. Chen, J. S. Wang, and J. S. Lin, “Linear stability of power law liquid film flows down an inclined plane,” Journal of Physics D, vol. 27, no. 11, pp. 2297–2301, 1994. View at Google Scholar · View at Scopus
  31. S. Miladinova, G. Lebon, and E. Toshev, “Thin-film flow of a power-law liquid falling down an inclined plate,” Journal of Non-Newtonian Fluid Mechanics, vol. 122, no. 1–3, pp. 69–78, 2004. View at Publisher · View at Google Scholar · View at Scopus
  32. F. Rousset, S. Millet, V. Botton, and H. Ben Hadid, “Temporal stability of carreau fluid flow down an incline,” Journal of Fluids Engineering, Transactions of the ASME, vol. 129, no. 7, pp. 913–920, 2007. View at Publisher · View at Google Scholar · View at Scopus
  33. P. J. Cheng and H. Y. Lai, “Finite-amplitude long-wave instability of Bingham liquid films,” Nonlinear Analysis: Real World Applications, vol. 10, no. 3, pp. 1500–1513, 2009. View at Publisher · View at Google Scholar · View at Scopus
  34. R. Usha and B. Uma, “Weakly Nonlinear Stability Analysis of Condensate/Evaporating Power-Law Liquid Film Down an Inclined Plane,” Journal of Applied Mechanics, Transactions ASME, vol. 70, no. 6, pp. 915–923, 2003. View at Publisher · View at Google Scholar · View at Scopus
  35. R. S. R. Gorla, “Rupture of thin power-law liquid film on a cylinder,” Journal of Applied Mechanics, Transactions ASME, vol. 68, no. 2, pp. 294–297, 2001. View at Google Scholar · View at Scopus
  36. J. P. Pascal and S. J. D. D'Alessio, “Instability of power-law fluid flows down an incline subjected to wind stress,” Applied Mathematical Modelling, vol. 31, no. 7, pp. 1229–1248, 2007. View at Publisher · View at Google Scholar · View at Scopus
  37. M. Sheintuch and A. E. Dukler, “Phase plane and bifurcation analysis of thin wavy films under shear,” AIChE Journal, vol. 35, no. 2, pp. 177–186, 1989. View at Google Scholar · View at Scopus
  38. J. P. Pascal, “A two-layer model for a non-Newtonian gravity current subjected to wind shear,” Acta Mechanica, vol. 162, no. 1–4, pp. 83–98, 2003. View at Publisher · View at Google Scholar · View at Scopus
  39. C. Y. Lee and E. Marschall, “Laminar stability analysis of condensate film flow,” Wärme- und Stoffübertragung, vol. 7, no. 1, pp. 14–21, 1974. View at Publisher · View at Google Scholar · View at Scopus
  40. M. Ünsal, Stability of a condensate film flowing down a vertical plane, Ph.D. thesis, Polytechnic Institute and State University, Blacksburg, Va, USA, 1975.
  41. C. I. Hung, C. K. Chen, and J. S. Tsai, “Weakly nonlinear stability analysis of condensate film flow down a vertical cylinder,” International Journal of Heat and Mass Transfer, vol. 39, no. 13, pp. 2821–2829, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  42. J. S. Tsai, C. I. Hung, and C. K. Chen, “Nonlinear hydromagnetic stability analysis of condensation film flow down a vertical plate,” Acta Mechanica, vol. 118, pp. 197–212, 1996. View at Google Scholar · View at Scopus
  43. A. H. Nayfeh and D. T. Mook, Nonlinear Oscillations, Wiley, 1979.
  44. G. D. Smith, Numerical Solution of Partial Differential Equations: Finite Difference Methods, Clarendon Press, 1998.
  45. S. V. Alekseenko, V. E. Nakoryakov, and B. G. Pokusaev, Wave Flow in Liquid Films, Begell House, New York, NY, USA, 3rd edition, 1994.
  46. J. Liu, J. D. Paul, and J. P. Gollub, “Measurements of the primary instabilities of film flows,” Journal of Fluid Mechanics, vol. 250, pp. 69–101, 1993. View at Google Scholar · View at Scopus