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Advances in Mathematical Physics
Volume 2017, Article ID 9724381, 10 pages
https://doi.org/10.1155/2017/9724381
Research Article

Unsteady Helical Flows of a Size-Dependent Couple-Stress Fluid

1Department of Computer Sciences, Air University Multan Campus, Multan, Pakistan
2Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan
3Department of Mathematics, University of Management and Technology, Sialkot Campus, Pakistan
4Department of Management Sciences, Air University Multan Campus, Multan, Pakistan

Correspondence should be addressed to Qammar Rubbab; moc.liamg@rammaqbabur

Received 1 December 2016; Accepted 15 January 2017; Published 8 February 2017

Academic Editor: John D. Clayton

Copyright © 2017 Qammar Rubbab 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. A. R. Hadjesfandiari, G. F. Dargush, and A. Hajesfandiari, “Consistent skew-symmetric couple stress theory for size-dependent creeping flow,” Journal of Non-Newtonian Fluid Mechanics, vol. 196, pp. 83–94, 2013. View at Publisher · View at Google Scholar · View at Scopus
  2. E. Cosserat and F. Cosserat, Theorie des Corps Deformables, A. Hermann et fils, Paris, France, 1909.
  3. R. A. Toupin, “Elastic materials with couple-stresses,” Archive for Rational Mechanics and Analysis, vol. 11, pp. 385–414, 1962. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  4. R. D. Mindlin and H. F. Tiersten, “Effects of couple-stresses in linear elasticity,” Archive for Rational Mechanics and Analysis, vol. 11, pp. 415–448, 1962. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  5. W. T. Koiter, “Couple-stresses in the theory of elasticity I and II,” Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, Series B, Physical Sciences, vol. 67, pp. 17–44, 1967. View at Google Scholar
  6. V. K. Stokes, “Couple stresses in fluids,” Physics of Fluids, vol. 9, no. 9, pp. 1709–1715, 1966. View at Publisher · View at Google Scholar · View at Scopus
  7. A. R. Hadjesfandiari and G. F. Dargush, “Couple stress theory for solids,” International Journal of Solids and Structures, vol. 48, no. 18, pp. 2496–2510, 2011. View at Publisher · View at Google Scholar · View at Scopus
  8. A. R. Hadjesfandiari, A. Hajesfandiari, and G. F. Dargush, “Skew-symmetric couple-stress fluid mechanics,” Acta Mechanica, vol. 226, no. 3, pp. 871–895, 2015. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  9. H. Bakhti and L. Azrar, “Steady flow of couple-stress fluid in constricted tapered artery: effects of transverse magnetic field, moving catheter, and slip velocity,” Journal of Applied Mathematics, vol. 2016, Article ID 9289684, 11 pages, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. R. N. Pralhad and D. H. Schultz, “Modeling of arterial stenosis and its applications to blood diseases,” Mathematical Biosciences, vol. 190, no. 2, pp. 203–220, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  11. V. K. Verma, M. P. Singh, and V. K. Katiyar, “Mathematical modeling of blood flow through stenosed tube,” Journal of Mechanics in Medicine and Biology, vol. 8, no. 1, pp. 27–32, 2008. View at Publisher · View at Google Scholar · View at Scopus
  12. B. S. Shenoy and R. Pai, “Effect of turbulence on the static performance of a misaligned externally adjustable fluid film bearing lubricated with couple stress fluids,” Tribology International, vol. 44, no. 12, pp. 1774–1781, 2011. View at Publisher · View at Google Scholar · View at Scopus
  13. N. B. Naduvinamani and S. B. Patil, “Numerical solution of finite modified Reynolds equation for couple stress squeeze film lubrication of porous journal bearings,” Computers and Structures, vol. 87, no. 21-22, pp. 1287–1295, 2009. View at Publisher · View at Google Scholar · View at Scopus
  14. T. Hayat, M. Awais, A. Safdar, and A. A. Hendi, “Unsteady three dimensional flow of couple stress fluid over a stretching surface with chemical reaction,” Nonlinear Analysis: Modelling and Control, vol. 17, no. 1, pp. 47–59, 2012. View at Google Scholar · View at MathSciNet
  15. M. Devakar and T. K. V. Iyengar, “Generalized Stokes' problems for an incompressible couple stress fluid,” International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, vol. 8, no. 1, pp. 113–116, 2014. View at Google Scholar
  16. N. Yokoi and A. Yoshizawa, “Statistical analysis of the effects of helicity in inhomogeneous turbulence,” Physics of Fluids A, vol. 5, no. 2, pp. 464–477, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  17. N. Yokoi and A. Brandenburg, “Large-scale flow generation by inhomogeneous helicity,” Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, vol. 93, no. 3, Article ID 033125, 2016. View at Publisher · View at Google Scholar · View at Scopus
  18. F. Awad, N. A. H. Haroun, P. Sibanda, and M. Khumalo, “On couple stress effects on unsteady nanofluid flow over stretching surfaces with vanishing nanoparticle flux at the wall,” Journal of Applied Fluid Mechanics, vol. 9, no. 4, pp. 1937–1944, 2016. View at Google Scholar · View at Scopus
  19. S. Ahmed, O. Anwar Bég, and S. K. Ghosh, “A couple stress fluid modeling on free convection oscillatory hydromagnetic flow in an inclined rotating channel,” Ain Shams Engineering Journal, vol. 5, no. 4, pp. 1249–1265, 2014. View at Publisher · View at Google Scholar · View at Scopus
  20. Y. Kwon, “Incompressible limit for the compressible flows of nematic liquid crystals in the whole space,” Advances in Mathematical Physics, vol. 2015, Article ID 427865, 7 pages, 2015. View at Publisher · View at Google Scholar
  21. B. Panicaud and E. Rouhaud, “Derivation of Cosserat's medium equations using different multi-dimensional frameworks,” Acta Mechanica, vol. 227, no. 2, pp. 367–385, 2016. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  22. Y. A. Brychkov, Handbook of Special Functions. Derivatives, Integrals, Series and Other Formulas, Chapman and Hall/CRC, Boca Raton, Fla, USA, 2008.
  23. W. Magnus, F. Oberhettinger, and R. P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics, Springer, New York, NY, USA, 1966. View at MathSciNet
  24. L. Debnath and D. Bhatta, Integral Transforms and Their Applications, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2nd edition, 2007. View at Publisher · View at Google Scholar
  25. J. Kang, Y. Liu, and T. Xia, “Unsteady flows of a generalized fractional Burgers' fluid between two side walls perpendicular to a plate,” Advances in Mathematical Physics, vol. 2015, Article ID 521069, 9 pages, 2015. View at Publisher · View at Google Scholar · View at MathSciNet