Eur. Phys. J. Plus (2020) 135: 49
https://doi.org/10.1140/epjp/s13360-019-00029-8

Regular Article

A numerical simulation of the creeping flow of hybrid-nano-fluid through a curved configuration due to metachronal waves propulsion of beating cilia

¹ Department of Mathematics, Northern University, Nowshera, KPK, Pakistan
² Department of Mathematics and Statistics, International Islamic University Islamabad (IIUI), Islamabad, Pakistan

^* e-mail: khurram.phdma12@iiu.edu.pk

Received: 7 August 2019
Accepted: 23 September 2019
Published online: 13 January 2020

Abstract

In the current era, the transportation of the nanofluids and the hybrid nanofluids due to the natural propulsive like contraction and relaxation of the flexible walls and the cilia movement has momentous applications in various embryonic technologies. Motivated by the multi-disciplinary evolution and research in this direction, a mathematical model is proposed to study the numerical simulation of the hybrid nanofluid through a curved domain due to the metachronal wave-propulsion of the beating cilia under the creeping flow phenomena. Furthermore, the flow characteristics of a non-Newtonian fluid model (Powell–Eyring fluid model) is discussed in details. The governing equations are obtained in terms of the curvilinear coordinates in the laboratory frame. Transform this system of equations from the fixed frame to the wave frame by introducing a linear relation between these two frames. The numerical solution of the non-dimensional-zed equations is obtained by using an explicit finite difference technique through FORTRAN. It is found that the visco-elastic parameter (Weissenberg number) overcomes the effects of curvature. The amplitude of the cilia has a massive role in fluid transportation through a confined curved channel. The hybrid fluid played an important role in the enhancement of the heat phenomena. A comparison between the straight and curved channels is also highlighted. This research study is very productive to the biological fluid propulsion of the medical micro-machines in the drug delivery.