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Time-Dependent Flow of a Couple Stress Fluid in an Elastic Circular Cylinder with Application to the Human Circulatory System

T. S. L. Radhika*, T. Raja Rani and A. Karthik
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T. S. L. Radhika*: BITS Pilani- Hyderabad Campus, Hyderabad, India
T. Raja Rani: Military Technological College, Muscat, Oman
A. Karthik: BITS Pilani- Hyderabad Campus, Hyderabad, India

Academic Journal of Applied Mathematical Sciences, 2020, vol. 6, issue 7, 126-135

Abstract: In this paper, we developed a mathematical model for blood flow in the human circulatory system. This model presumes blood to be a couple stress fluid, its flow to be pulsatile, and the artery an elastic circular pipe whose radius is assumed to vary with transmural pressure. The governing differential equation for the flow velocity is time-dependent and has been solved using the homotopy perturbation method. This velocity has been used to estimate the elastic modulus E of the artery, which is a measure of its stiffness and an important metric used by clinical practitioners to understand the state of the cardiovascular system. In this work, the radial artery has been considered and a limited set of experimental data, available for four cases, has been taken from the published literature to validate the model. While the experimental values of elastic modulus reported in literature lie in the range 2.68 1.81 MPa.s, those estimated through the proposed model range from 3.05 to 5.98 MPa.s, appearing to be in close agreement.

Keywords: Couple stress fluid; Elastic tube; Pulsatile flow; Circulatory system; Transmural pressure; Homotopy perturbation method (search for similar items in EconPapers)
Date: 2020
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DOI: 10.32861/ajams.67.126.135

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