Eur. Phys. J. Spec. Top. (2022) 231: 545-555
https://doi.org/10.1140/epjs/s11734-021-00421-5

Regular Article

Mathematical modeling and analytical examination of peristaltic transport in flow of Rabinowitsch fluid with Darcy’s law: two-dimensional curved plane geometry

¹ School of Continuing Equation, Huzhou Vocational & Technical College, 313000, Huzhou, P. R. China
² Department of Mathematics, Division of Science and Technology, University of Education, 54770, Lahore, Pakistan
³ Department of Mathematics, Symbiosis Institute of Technology, Symbiosis International (Deemed University), 412115, Pune, India
⁴ Department of Mathematics, COMSATS University Islamabad, 57000, Sahiwal, Pakistan
⁵ Department of Mathematics and Statistics, Riphah International University I-14, 44000, Islamabad, Pakistan
⁶ Division of Computational Science, Faculty of Science, Prince of Songkla University, 90110, Hat Yai, Songkhla, Thailand
⁷ Department of Mathematics, College of Sciences, King Khalid University, 61413, Abha, Saudi Arabia

^e mikhan@math.qau.edu.pk

Received: 18 March 2021
Accepted: 16 December 2021
Published online: 4 January 2022

Abstract

In this paper, the authors presented the effects of space voids and electrical conductivity on the flow of a pseudoplastic (Rabinowitsch) fluid analyzed in a curved two-dimensional plane geometry. The walls of the channel are considered to develop the peristaltic waves along its length. The problem is manipulated under the observations of long wavelength and low Reynolds number approximations. The motion is assumed to be steady by transforming it in a wave frame traveling with the speed of wave. Analytical hybrid perturbation techniques have been incorporated to handle the complicated coupled differential equations. It is found that the results are well in agreement with the existing literature as a special case, evocating the validity of the study. Expressions of velocity, pressure gradient, and stream function have been invoked graphically. It is concluded from the results that porous medium and magnetic field suggest opposite variations of velocity and trapping circulating contours are stretching with magnetic field and contracting with increasing voids.