Advertisement

Travelling Waves In A Prestressed Elastic Tube Filled With A Fluid Of Variable Viscosity

  • Hilmi Demiray*Email author
  • Tay Kim Gaik
Part of the Springer Proceedings in Physics book series (SPPHY, volume 126)

In this work, treating the artery as a prestressed thin elastic tube with variable radius and the blood as an incompressible Newtonian fluid with variable viscosity, the propagation of nonlinear waves in such a composite medium is studied, in the long wave approximation, through the use of the reductive perturbation method and the Forced Korteweg-de Vries-Burgers (FKdVB) equation with variable coefficients is obtained as the evolution equation. A progressive wave type of solution is presented for this evolution equation and the result is discussed.

Keywords

prestressed elastic tube fluid of variable viscosity FKdVB equation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. S. Johnson, 1970. A non-linear equation incorporating damping and dispersion, Journal of Fluid Mechanics, 42, 49–60.zbMATHCrossRefADSMathSciNetGoogle Scholar
  2. 2.
    Y. Hashizume, 1985. Nonlinear Pressure Waves in a Fluid-Filled Elastic Tube, J. Phys. Soc.Japan, 54, 3305–3312.CrossRefADSGoogle Scholar
  3. 3.
    S. Yomosa, 1987. Solitary Waves in Large Blood Vessels, J. Phys. Soc. Japan, 56, 506–520.CrossRefADSMathSciNetGoogle Scholar
  4. 4.
    4 H. Demiray, 1996. Solitary waves in prestressed elastic tubes, Bull. Math. Biol, 58, 939–955.zbMATHCrossRefGoogle Scholar
  5. 5.
    H. Demiray, 1998. Slowly varying solitary waves in an elastic tube filled with a viscous fluid,ARI (formely, the Bulletin of Technical University of Istanbul), 51, 98–102.Google Scholar
  6. 6.
    6 H. Demiray, 2004. Solitary waves in a tapered prestressed fluid-filled elastic tube, Z. angew.Mat. Phys, 55, 282–294.zbMATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    N. Antar and H. Demiray, 2000. The Boundary layer approximation and nonlinear waves in elastic tubes, Int. J. Eng. Sci, 38, 1441–1457.CrossRefMathSciNetGoogle Scholar
  8. 8.
    H. Demiray, 2001. Solitary waves in elastic tubes filled with a layered fluid, Int. J. Eng. Sci,39, 629–640.CrossRefGoogle Scholar
  9. 9.
    A. Jeffrey and T. Kawahara, 1981. Asymptotitc methods in nonlinear wave theory, Pitman,Boston.Google Scholar
  10. 10.
    H. Demiray, 2003. A note on the travelling wave solution to the KdV-Burgers equation,Wave Motion, 38, 367–369;.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science + Business Media B.V 2008

Authors and Affiliations

  1. 1.Department of MathematicsIşk UniversityIstanbulTurkey
  2. 2.Science Study CenterUniversiti Teknologi Tun Hussein Onn MalaysiaJohorMalaysia

Personalised recommendations