Browsing by Author "Demiray, Hilmi"

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    The effect of a bump in an elastic tube on wave propagation in a viscous fluid of variable viscosity
    (Elsevier Science, 2007) Demiray, Hilmi
    In the present work treating the arteries as a thin walled prestressed elastic tube with a bump and the blood as a Newtonian fluid of variable viscosity we have studied the propagation of weakly nonlinear waves in such a medium by employing the reductive perturbation method in the longwave approximation. Korteweg-deVries-Burgers equation with variable coefficients is obtained as the evolution equation. Seeking a progressive wave type of solution to this evolution equation it is observed that the wave speed is variable. The numerical calculations show that the wave speed reaches to its maximum value at the center of the bump but it gets smaller and smaller as we go away from the center of the bump. Such a result seems to be reasonable from physical considerations. © 2006 Elsevier Inc. All rights reserved.
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    The effects of higher-order approximations in a fluid-filled elastic tube with stenosis
    (Verlag der Zeitschrift fur Naturforschung, 2006) Demiray, Hilmi
    Treating arteries as thin-walled prestressed elastic tubes with a narrowing (stenosis) and blood as an inviscid fluid we study the propagation of weakly nonlinear waves in such a fluid-filled elastic tube by employing the reductive perturbation method in the long wave approximation. It is shown that the evolution equation of the first-order term in the perturbation expansion may be described by the conventional Korteweg-de Vries (KdV) equation. The evolution equation for the second-order term is found to be the linearized KdV equation with a nonhomogeneous term which contains the contribution of the stenosis. A progressive wave type solution is sought for the evolution equation and it is observed that the wave speed is variable which results from the stenosis. We study the variation of the wave speed with the distance parameter ? for various amplitude values of the stenosis. It is observed that near the center of the stenosis the wave speed decreases with increasing stenosis amplitude. However sufficiently far from the center of the stenosis stenosis amplitude becomes negligibly small. © 2006 Verlag der Zeitschrift für Naturforschung.