An Exact Solution of Non-Newtonian Peristaltic Flow in a Tube : Rabinowitsch Fluid Model

Singh, Udaya P.

doi:10.4038/josuk.v10i0.7991

Cited by 10 publications

(21 citation statements)

References 13 publications

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“…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]. Singh [9] examined the exact solution of Rabinowitsch peristaltic flow in a tube, and found that the pseudoplastic and dilatant fluids counted on the instantaneous flow rate.…”

Section: Introductionmentioning

confidence: 99%

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

Mostapha

2021

Journal of Mathematics

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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.

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Section: Introductionmentioning

confidence: 99%

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

Mostapha

2021

Journal of Mathematics

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“…Over the most recent couple of years, some researchers have explored peristaltic transport for the Rabinowitsch fluid model. Singh and Singh (2014) investigated peristaltic flow in a tube using Rabinowitsch fluid model. Akbar and Nadeem (2014) studied Rabinowitsch fluid model in peristalsis.…”

Section: Introductionmentioning

confidence: 99%

Theoretical Study of Heat Transfer on Peristaltic Transport of Non-Newtonian Fluid Flowing in a Channel: Rabinowitsch Fluid Model

Singh¹,

Medhavi

Gupta

et al. 2018

Int J Math, Eng, Manag Sci

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The present investigation is concerned with the problem of heat transfer and peristaltic flow of non-Newtonian fluid using Rabinowitsch fluid model through a channel under long wavelength and low Reynolds number approximation. Expressions for velocity, pressure gradient, pressure rise, friction force and temperature have been obtained. The effect of different parameters on velocity, pressure gradient, pressure rise, streamlines, friction force and temperature have been discussed through graphs.

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“…The above model fluid model converts into a pseudoplastic fluid model for

(γ > 0)

, Newtonian fluid model when

(γ = 0)

, and Dilatant fluid model when

(γ < 0)

. The Rabinowitsch model has been confirmed by the investigational results that are obtained by Wada et al 35 Singh et al 36–38 investigated the non‐Newtonian Rabinowitsch fluid model for velocity and pressure gradient relation. Akbar et al 39 discussed the mechanical properties and thermal conductivity effect for the Rabinowitsch fluid model.…”

Section: Introductionmentioning

confidence: 70%

Heat transfer analysis for particle–fluid suspension thermomagnetohydrodynamic peristaltic flow with Darcy–Forchheimer medium

et al. 2020

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This theoretical analysis explores the effect of heat and mass transfer on particle–fluid suspension for the Rabinowitsch fluid model with the stiffness and dynamic damping effects through Darcy–Brinkman–Forchheimer porous medium. In this study, we also incorporate slip and transverse magnetic field effects. Using low Reynolds number, to neglect inertial forces and to keep the pressure constant during the flow, channel height is used largely as compared with the ratio of length of the wave. A numerical technique is used to solve flow governing system of differential equations. Particular attention is paid to viscous damping force parameter, stiffness parameter, and rigidity parameter; also, the numerical data for thermal profile, momentum, and concentration distribution are presented graphically. Outcomes are deliberated in detail for different fluid models (thinning, thickening, and viscous models). It is found that velocity profile increases for greater values of viscous damping effect and stiffness and rigidity parameter for shear thinning, but conflicting comportment is showed for thickening nature model. Viscous dissipation effects increases the thermal profile for all cases of fluid models. The scope of the present article is valuable in explaining the blood transport dynamics in small vessels while considering the important wall features with chemical reaction characteristics. The current analysis has extensive applications in biomedical engineering field, that is, peristaltic pumps.

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An Exact Solution of Non-Newtonian Peristaltic Flow in a Tube : Rabinowitsch Fluid Model

Cited by 10 publications

References 13 publications

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

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

Theoretical Study of Heat Transfer on Peristaltic Transport of Non-Newtonian Fluid Flowing in a Channel: Rabinowitsch Fluid Model

Heat transfer analysis for particle–fluid suspension thermomagnetohydrodynamic peristaltic flow with Darcy–Forchheimer medium

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