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,A Karthik

doi:10.32861/ajams.67.126.135

T S L Radhika, T Raja Rani + Show 1 more

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https://doi.org/10.32861/ajams.67.126.135

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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.

Highlights

Data with large observations, depending on the nature and depth of the inquiry, are often generated in all areas of human endeavor such as business, sports, academic institutions, research institutions, internet services etc [1,2,3,4]
Understanding of many instructors of introductory statistics classes are: mean cannot be graphically determined and numerical approach is more precise than geometrical technique
We make known that mathematical formulas for mean, median and mode were derived geometrically

Summary

Introduction

Data with large observations, depending on the nature and depth of the inquiry, are often generated in all areas of human endeavor such as business, sports, academic institutions, research institutions, internet services etc [1,2,3,4]. Representative in the sense that, the single number wholly summarizes or mirrors with relatively high precision, the characteristics of interest in the entire observations. Such representative number could be a central value for all the observations. Measures of central tendency is the study of dataset cluster around the central value popularly called average [7, 8]

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