Blood Flow in Multi-Sinusoidal Curved Passages with Biomimetic Rheology: An Application of Blood Pumping

Gamal Hassan Sewify, Khurram Javid, Muhammad Adeel, Aamar Abbasi, Sami Ullah Khan, Mohamed Omri and Lioua Kolsi
Additional contact information
Gamal Hassan Sewify: Deanship of Scientific Research, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Khurram Javid: Department of Mathematics, Northern University, Wattar-Wali Road, Nowshera 24110, Pakistan
Muhammad Adeel: Department of Mathematics, Northern University, Wattar-Wali Road, Nowshera 24110, Pakistan
Aamar Abbasi: Department of Mathematics, University of Azad Jammu & Kashmir, Muzaffarabad 13100, Pakistan
Sami Ullah Khan: Department of Mathematics, COMSATS University Islamabad, Sahiwal 57000, Pakistan
Mohamed Omri: Deanship of Scientific Research, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Lioua Kolsi: Department of Mechanical Engineering, College of Engineering, Ha’il University, Ha’il City 81451, Saudi Arabia

Mathematics, 2022, vol. 10, issue 9, 1-19

Abstract: The unsteady flow of biological liquid through non-uniform pumps under porosity impacts is considered. The Jeffrey fluid is used as blood in the current study, which is also characterized as viscoelastic fluid because of its dual characteristics: on the one hand, its viscosity in nature; on the other hand, its elastic effect. Rheological equations are framed in a curvilinear coordinates system, and porosity influences are simulated with the body force term in momentum equations. The flow system has been transformed from fixed to wave frame using a linear–mathematical transformation between these two frames. In the next mathematical steps, these transformed equations are given in non-dimensional form using physical variables. The system of PDE is reduced to an ODE under lubrication theory and long wavelength approximation. Solutions to reduced ordinary differential equations are obtained numerically in MATLAB software via a BVP4C scheme. The physical impacts of the involved parameters on flow features, such as curvature, porosity (Darcy’s number), non-uniformity, and viscoelastic parameters, have been visualized graphically. Multi-sinusoidal waves are used in the boundary wall of the curved pump for peristaltic pumping. The magnitude of velocity profile for a saw-tooth wave (trapezoidal wave) is larger (smaller) than all other natures of peristaltic waves. The larger intensity of Darcy’s number has a dynamic role in the reduction of peristaltic pumping, whereas the opposite behavior is noticed when increasing the non-uniform nature of a channel. A comparison between all multi-sinusoidal waves is also addressed. The results of the present research shall be very productive for the manufacture of peristaltic pumps for drug delivery and bio-medical systems.

Keywords: blood flow; pumping phenomenon; Jeffrey fluid; multi-sinusoidal waves; numerical scheme (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/9/1579/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/9/1579/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:9:p:1579-:d:810374

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().