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

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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.

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Acknowledgements

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University, Abha 61413, Saudi Arabia for funding this work through research groups program under Grant No. R.G.P-2/88/41.

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Authors and Affiliations

  1. School of Continuing Equation, Huzhou Vocational & Technical College, Huzhou, 313000, P. R. China

    Wei-Mao Qian

  2. Department of Mathematics, Division of Science and Technology, University of Education, Lahore, 54770, Pakistan

    Arshad Riaz

  3. Department of Mathematics, Symbiosis Institute of Technology, Symbiosis International (Deemed University), Pune, 412115, India

    Katta Ramesh

  4. Department of Mathematics, COMSATS University Islamabad, Sahiwal, 57000, Pakistan

    Sami Ullah Khan

  5. Department of Mathematics and Statistics, Riphah International University I-14, Islamabad, 44000, Pakistan

    M. Ijaz Khan

  6. Division of Computational Science, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla, 90110, Thailand

    Ronnason Chinram

  7. Department of Mathematics, College of Sciences, King Khalid University, Abha, 61413, Saudi Arabia

    M. Kbiri Alaoui

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  1. Wei-Mao Qian
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Correspondence to M. Ijaz Khan.

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Qian, WM., Riaz, A., Ramesh, K. et al. Mathematical modeling and analytical examination of peristaltic transport in flow of Rabinowitsch fluid with Darcy’s law: two-dimensional curved plane geometry. Eur. Phys. J. Spec. Top. 231, 545–555 (2022). https://doi.org/10.1140/epjs/s11734-021-00421-5

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