Nonlinear waves in an elastic tube with variable prestretch filled with a fluid of variable viscosity
Yükleniyor...
Dosyalar
Tarih
2008-10
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Pergamon-Elsevier Science Ltd
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
In the present work, by employing the reductive perturbation method to the nonlinear equations of an incompressible, prestressed, homogeneous and isotropic thin elastic tube and to the exact equations of an incompressible Newtonian fluid of variable viscosity, we have studied weakly nonlinear waves in such a medium and obtained the variable coefficient Korteweg-deVries-Burgers (KdV-B) equation as the evolution equation. For this purpose, we treated the artery as an incompressible, homogeneous and isotropic elastic material subjected to variable stretches both in the axial and circumferential directions initially, and the blood as an incompressible Newtonian fluid whose viscosity changes with the radial coordinate. By seeking a travelling wave solution to this evolution equation, we observed that the wave front is not a plane anymore, it is rather a curved surface. This is the result of the variable radius of the tube. The numerical calculations indicate that the wave speed is variable in the axial coordinate and it decreases for increasing circumferential stretch (or radius). Such a result seems to be plausible from physical considerations, like Bernoulli's law. We further observed that, the amplitude of the Burgers shock gets smaller and smaller with increasing time parameter along the tube axis. This is again due to the variable radius, but the effect of it is quite small.
Açıklama
This work was supported by the Turkish Academy of Sciences.
Anahtar Kelimeler
Pressure waves, Solitary waves, Inviscid fluid, Arteries, Equation, Variable initial stretches, Elastic tubes, Variable coefficient KdV-B equation, Korteweg-de Vries equation, Solitons, Water waves, Differential equations, Fluid dynamics, Fluid mechanics, Hydrodynamics, Liquids, Newtonian liquids, Numerical analysis, Tubes (components), Viscosity, Waves, Evolution equations, Incompressible Newtonian fluid, Nonlinear equations
Kaynak
International Journal of Engineering Science
WoS Q Değeri
Q1
Scopus Q Değeri
Q1
Cilt
46
Sayı
10
Künye
Demiray, H. (2008). Nonlinear waves in an elastic tube with variable prestretch filled with a fluid of variable viscosity. International Journal of Engineering Science, 46(10), 949-957. doi:10.1016/j.ijengsci.2008.04.001
