Abstract
A theoretical investigation concerning the influence of externally imposed periodic body acceleration on the flow of blood through a time-dependent stenosed arterial segment by taking into account the slip velocity at the wall of the artery has been carried out. A mathematical model is developed by treating blood as a non-Newtonian fluid obeying the Casson fluid model. The pulsatile flow is analyzed by considering a periodic pressure gradient and the inertial effects as negligibly small. A suitable generalized geometry for time-dependent stenosis is taken into account. Perturbation method is used to solve the coupled implicit system of nonlinear differential equations that govern the flow of blood. Analytical expressions for the velocity profile, volumetric flow rate, and wall shear stress are obtained. A thorough quantitative analysis has been made through numerical computations of the variables involved in the analysis that are of special interest in this study. The computational results are presented graphically. The results for different values of the parameters involved in the problem under consideration presented here show that the flow is appreciably influenced by slip velocity in the presence of periodic body acceleration.
Highlights
There are number of evidences available in the scientific literatures that vascular fluid dynamics plays a major role in the development and progression of arterial diseases
Shit and Roy [21] examined the effect of externally imposed body acceleration and magnetic field on pulsatile flow of blood through an arterial segment having stenosis with noslip velocity condition
The motivation of this paper is to study the unsteady flow of blood through an arterial segment with time-dependent r d
Summary
There are number of evidences available in the scientific literatures that vascular fluid dynamics plays a major role in the development and progression of arterial diseases. Sud and Sekhon [18] analyzed the blood flow through a model of the human arterial system under the influence of periodic acceleration They observed that the body acceleration has an enhancing effect on the flow rate. Shit and Roy [21] examined the effect of externally imposed body acceleration and magnetic field on pulsatile flow of blood through an arterial segment having stenosis with noslip velocity condition. Ponalagusamy [26] and Biswas and Chakraborty [27, 28] have developed mathematical models for blood flow through stenosed arterial segment, by taking a velocity slip condition at the constricted wall. The effect of body acceleration on pulsatile flow of blood through an arterial segment having time-dependent stenosis in the presence velocity-slip has not been considered so far to the best of our knowledge.
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