Eur. Phys. J. Plus (2019) 134: 395
https://doi.org/10.1140/epjp/i2019-12717-8

Regular Article

Numerical study of Hall effects on the peristaltically induced motion of a viscous fluid through a non-uniform regime: An application to the medical science

¹ Department of Mathematics, Northern University, Nowshera, KPK, Pakistan
² Department of Mathematics & Statistics, International Islamic University, Islamabad, Pakistan

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

Received: 2 January 2019
Accepted: 29 April 2019
Published online: 22 August 2019

Abstract

Impacts of Hall current (potential) on the peristaltically induced motion of a magneto-hydrodynamics (MHD) viscous incompressible fluid is analysed in a curved geometry. This study is novel in term of integrating numerically the Hall effects with peristaltic propulsive phenomena bounded within the curved regime. The usage of these electro-kinetically controlled devices in the modern era of bio-medical industries makes this study relatively new and interesting. Firstly, the governing equations are modelled in a curvilinear coordinates system. Secondly, these equations are transformed into a dimensionless system of equations by using dimensionless variables under long-wavelength and low-Reynold-number assumptions. The numerical solution of these governing equations is obtained with the appropriate boundary conditions (BCs) by using the BVP4C technique. The significant influences of several embedded physical parameters such as the curvature parameter, Hartmann number, Hall parameter in the velocity profile, pumping and trapping phenomena's are argued expansively through graphs. It is visible that the effects of the Hall current are dominant over the boundary layer (BL) phenomena for large values of the Hall parameter. Moreover, comparison among the straight channel and the curved channel is also highlighted. Furthermore, the validation of the numerical code is given at some particular values of the curvature parameter through numeric tables.