Insight into the Significance of Hall Current and Joule Heating on the Dynamics of Darcy–Forchheimer Peristaltic Flow of Rabinowitsch Fluid

Ji-Huan He,Doaa R Mostapha

doi:10.1155/2021/3638807

Abstract

This paper aims to present the significance of the Hall current and Joule heating impacts on a peristaltic flow of a Rabinowitsch fluid through tapered tube. The Darcy–Forchheimer scheme is used for a porous medium; a mild stenosis is considered to study the impacts of radiative heat transfer and chemical reactions. Convective conditions are postulated for heat and mass transfer. In the meantime, the slip conditions are presumed for the velocity distribution. Soret and Dufour features bring the coupled differential systems. The hypotheses of a long wavelength and low Reynolds number are employed to approximate the governing equations of motion, and finally the homotopy perturbation method is adopted for numerical study. Pumping characteristics are revealed and the trapping procedure correlated with peristaltic transport is elucidated. The present study is very important in many medical applications, such as the gastric juice motion in the small intestine and the flow of blood in arteries. The mechanism of peristaltic transport with mild stenosis has been exploited for industrial applications like sanitary fluid transport and blood pumps in heart-lung machine. The influences of various physical parameters of the problem are debated and graphically drawn across a set of figures. It is noted that the axial velocity is reduced with the increase of the Hartmann number. However, enhancing both the Rabinowitsch parameter and the Forchheimer parameter gives rise to the fluid velocity. As well, it is debated that Rabinowitsch fluid produces a cubic term of pressure gradient. Therefore, the relation between mean flow rate and the pressure rise does not stay linear. It is recognized that the temperature rises with the enhancement of both Dufour number and Soret number. Furthermore, it is illustrated that the concentration impedes with the increase of the mass transfer Biot number. Also, it is revealed that the trapped bolus contracts in size by enlarging the maximum height of stenosis.

Highlights

Non-Newtonian fluids have a major role in the engineering, industrial systems, medical sciences, textile engineering, and materials science as well
Singh et al [3] determined a model of three major categories of fluids counting on different values of a nonlinear factor, and it can depict the behaviour of Newtonian fluids, shear thickening fluids, and shear thinning fluids. e Rabinowitsch model has many major implementations in the analysis of the squeeze film, annular disk, externally pressurized bearing, journal bearing, and pivoted curved slider bearings. e transit of fluid due to the symmetric contraction and expansion of flexible walls is recognized as a Journal of Mathematics peristaltic transport, and peristalsis has certainly determined the attention of physiologists, because the foremost mechanism for transporting fluids in many living organisms is the peristaltic transport; for illustration, see Burns and Parkes [4]
Shapiro et al [5] and Fung and Yih [7] scrutinized the peristaltic flows with some hypotheses, such as long wavelength approximation, low Reynolds number, and small amplitude ratio. e problem of peristaltic flow in a tube of Rabinowitsch fluid was scrutinized by Singh and Singh [8]

Summary

Introduction

Non-Newtonian fluids have a major role in the engineering, industrial systems, medical sciences, textile engineering, and materials science as well. E problem of peristaltic flow in a tube of Rabinowitsch fluid was scrutinized by Singh and Singh [8]. Hayat et al [31] scrutinized the impacts of Hall current and Joule heating on peristaltic flow under convective boundary conditions.

Results

Conclusion