Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
권호 표지
DOI QR코드

DOI QR Code

EXACT SOLUTION FOR STEADY PAINT FILM FLOW OF A PSEUDO PLASTIC FLUID DOWN A VERTICAL WALL BY GRAVITY

  • Alam, M.K. (NATIONAL UNIVERSITY OF COMPUTER & EMERGING SCIENCES) ;
  • Rahim, M.T. (NATIONAL UNIVERSITY OF COMPUTER & EMERGING SCIENCES) ;
  • Islam, S. (DEPARTMENT OF MATHEMATICS, ABDUL WALI KHAN UNIVERSITY) ;
  • Siddiqui, A.M. (PENNSYLVANIA STATE UNIVERSITY, YORK CAMPUS)
  • Received : 2012.03.30
  • Accepted : 2012.09.14
  • Published : 2012.09.25
Download PDF
⟨ Previous Next ⟩

Abstract

Here in this paper, the steady paint film flow on a vertical wall of a non-Newtonian pseudo plastic fluid for drainage problem has been investigated. The exact solution of the nonlinear problem is obtained for the velocity profile. Also the average velocity, volume flux, shear stress on the wall, force to hold the wall in position and normal stress difference have been derived. We retrieve Newtonian case, when material constant ${\mu}_1$ and relaxation time ${\lambda}_1$ equal zero. The results for co-rotational Maxwell fluid is also obtained by taking material constant ${\mu}_1$ = 0. The effect of the zero shear viscosity ${\eta}_0$, the material constant ${\mu}_1$, the relaxation time ${\lambda}_1$ and gravitational force on the velocity profile for drainage problem are discussed and plotted.

Keywords

References

  1. Siddiqui, A.M., Islam, S. and Ghori, Q. K., Two-Dimensional Viscous Incompressible flows in a Porous Medium, J. of Porous Media, (2006), vol. 9(6), pp. 591-596. https://doi.org/10.1615/JPorMedia.v9.i6.70
  2. Islam, S. and Zhou, C.Y.(b), Exact Solutions of a Second Grade Fluid in a Porous Medium, Proc. NSC, Beijing, (2006).
  3. Islam, S. and Zhou, C.Y.(b), Certain inverse solutions of a second grade MHD aligned fluid flows in a porous medium, Journal of Porous Media, vol. 10(4), 401-408, (2007). https://doi.org/10.1615/JPorMedia.v10.i4.60
  4. Islam, S., Mohyuddin, M. R., and Zhou C. Y, Few exact solutions of non-Newtonian fluid in Porous Medium with Hall effects, Journal of porous Media, vol. 11(7), pp. 669-680, https://doi.org/10.1615/JPorMedia.v11.i7.50
  5. A. M. Siddiqui, M. KamranAlam, S. Islam, M. T. Rahim, Manzoor Elahi, A class of exact solutions of second grade fluid, Int. J. Phy. Sci. 6(24)5601-5608, 16 October, (2011).
  6. G. Astarita, G. Marrucci, Principle of non-Newtonian fluid mechanics, McGraw-Hill, London, (1974).
  7. R. B. Bird, R.C. Armstrong, O. Hassager, Dynamics of polymeric liquids, Fluid Mechanics, Wiley, New York, (1987).
  8. M. Moradi, Laminar flow heat transfer of a pseudoplastic fluid through a double pipe heat exchanger, Iranian Journal of Chemical Engineering, Vol. 3, No. 2, (2006); pp. 13-19.
  9. A.M. Siddiqui, R. Mahmood, Q.K. Ghori. Homotopy perturbation method for thin film flow of a third grade fluid down an inclined plane. Chaos, Solitons and Fractals 35 (2008) 140-147. https://doi.org/10.1016/j.chaos.2006.05.026
  10. A.M. Siddiqui, R. Mahmood, Q.K. Ghori. Some exact solutions for the thin film flow of a PTT fluid. Physics Letters A 356 (2006) 353-356. https://doi.org/10.1016/j.physleta.2006.03.071
  11. A.M. Siddiqui, R. Mahmood, Q.K. Ghori. Thin film flow of non-Newtonian fluids on a moving belt. Chaos, Solitons and Fractals 33 (2007) 1006-1016. https://doi.org/10.1016/j.chaos.2006.01.101
  12. A. M. Siddiqui, R. Mahmood and Q. K. Ghori, Homotopy Perturbation Method for Thin Film Flow of a Fourth Grade Fluid down a Vertical Cylinder, Physical Letters A, Vol. 352, 2006, pp. 404-410. doi:10.1016/j.physleta.2005.12.033.
  13. J. A. Deiber, A. S. M. Santa Cruz, On non-Newtonian fluid flow through a tube of circular cross section, Lat. AM. J. Chem. Eng. Appl. Chem., Vol. 14, (1984); pp. 19-38.