Open Access

ARTICLE

Two-Phase Flow of Blood with Magnetic Dusty Particles in Cylindrical Region: A Caputo Fabrizio Fractional Model

Anees Imitaz¹, Aamina Aamina¹, Farhad Ali^2,3,*, Ilyas Khan⁴, Kottakkaran Sooppy Nisar⁵

1 Department of Mathematics, City University of Science and Information Technology, Peshawar, 25000, Pakistan
2 Computational Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam
3 Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
4 Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah, 11952, Saudi Arabia
5 Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser, 11991, Saudi Arabia

* Corresponding Author: Farhad Ali. Email:

Computers, Materials & Continua 2021, 66(3), 2253-2264. https://doi.org/10.32604/cmc.2021.012470

Received 01 July 2020; Accepted 25 September 2020; Issue published 28 December 2020

Abstract

The present study is focused on the unsteady two-phase flow of blood in a cylindrical region. Blood is taken as a counter-example of Brinkman type fluid containing magnetic (dust) particles. The oscillating pressure gradient has been considered because for blood flow it is necessary to investigate in the form of a diastolic and systolic pressure. The transverse magnetic field has been applied externally to the cylindrical tube to study its impact on both fluids as well as particles. The system of derived governing equations based on Navier Stoke’s, Maxwell and heat equations has been generalized using the well-known Caputo–Fabrizio (C–F) fractional derivative. The considered fractional model has been solved analytically using the joint Laplace and Hankel (L&H) transformations. The effect of various physical parameters such as fractional parameter, Gr, M and γ on blood and magnetic particles has been shown graphically using the Mathcad software. The fluid behaviour is thinner in fractional order as compared to the classical one.

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Citations