# Hall effects on peristaltic flow of couple stress fluid in a vertical asymmetric channel

VIT University

^{1}01 Nov 2017-Vol. 263, Iss: 6, pp 062021

TL;DR: In this article, the influence of Hall effect on peristaltic transport of a couple stress fluid in a vertical asymmetric channel is examined under the assumptions of low Reynolds number and long wavelength.

Abstract: The influence of Hall effect on peristaltic transport of a couple stress fluid in a vertical asymmetric channel is examined. The problem is solved under the assumptions of low Reynolds number and long wavelength. The velocity, temperature and concentration are obtained by using analytical solutions. Effect of Hall parameter, couple stress fluid parameter, Froude number, Hartmann number and the phase difference on the pumping characteristics, temperature and concentration are discussed graphically.

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TL;DR: In this paper, the peristaltic transport of an incompressible micropolar non-Newtonian nanofluid following the Sutterby model is investigated.

Abstract: The current study investigates the peristaltic transport of an incompressible micropolar non—Newtonian nanofluid following the Sutterby model. The heat and mass transfer inside the two-dimensional symmetric vertical channel is considered. The system is affected by a strong magnetic field together with thermal radiation, couple stress, chemical reaction, Joule heating, heat generation, Dufour, Soret and Hall current effects. The governing equations of motion are analytically solved by utilizing the long wavelength and low Reynolds number approximations. Furthermore, the resulted boundary—value problem is solved by means of the Homotopy perturbation method (HPM). An illustration of the influence of the various physical parameters in the foreign distributions; such as Hall currents, magnetic field, Sutterby, couple stress, Brownian motion, thermophoresis and slip parameters is obtained throughout a set of graphs and tables. It is observed that the axial velocity enhances with the increase in the Sutterby parameter. Furthermore, the temperature decreases with the larger values of a heat transfer Biot number. While, the concentration enlarges with the increase in the values of mass transfer Biot numbers. Moreover, the trapping phenomenon is discussed throughout a set of figures. This depicts the variation of the streamlines under the impact of couple stress, amplitude ratio, and magnetic field parameters. It is noticed that the size of the trapped bolus increases with the increase in the foregoing three parameters.

11 citations

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TL;DR: In this article, the authors present the mathematical modeling for peristaltic transport of nanofluid with applications of double-diffusive convection and Hall features, and the flow has been induced by a converg...

Abstract: Current analysis presents the mathematical modeling for peristaltic transport of nanofluid with applications of double-diffusive convection and Hall features. The flow has been induced by a converg...

9 citations

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TL;DR: The peristaltic flow of Carreau nanofluid with heat and mass transfer through porous medium inside a symmetric horizontal channel with flexible walls is investigated in this paper, the problem is modulated mathematically by a system of non-linear PDE which describe the motion, heat and nanoparticles phenomenon of the fluid.

Abstract: The peristaltic flow of Carreau nanofluid with heat and mass transfer through porous medium inside a symmetric horizontal channel with flexible walls is investigated. The Hall currents with viscous dissipation, heat absorption and chemical reaction are considered, the system is stressed by a uniform strong magnetic field. The problem is modulated mathematically by a system of non-linear PDE which describe the motion, heat and nanoparticles phenomenon of the fluid. These equations with subjected boundary conditions are transferred to a dimensionless form and simplified under the assumptions of long wavelength and low Reynolds number, then solved analytically by using perturbation technique for small Weissen-berg number. In other word these equations are solved also numerically by using Runge-Kutta-Merson method with Newton iteration in a shooting and matching technique. The effects of the emerging physical parameters of the problem on the velocity, temperature, and nanoparticles phenomena are discussed numerically for both techniques used for solutions and illustrated graphically through a set of figures. It is found that this problem plays a dramatic role in controlling the solutions. A comparison between the obtained solutions from both methods is made.

2 citations

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TL;DR: In this article, the authors investigated the effect of peristaltic wave propagation on the flow of fluid in a tube and showed that the theoretical pressure rise per wavelength decreases linearly with increasing time-mean flow and that the percentage of reflux flow can be very high.

Abstract: Pumping by means of an infinite train of peristaltic waves is investigated under conditions for which the relevant Reynolds number is small enough for inertial effects to be negligible and the wavelength to diameter ratio is large enough for the pressure to be considered uniform over the cross-section. Theoretical results are presented for both plane and axisymmetric geometries, and for amplitude ratios ranging from zero to full occlusion. For a given amplitude ratio, the theoretical pressure rise per wavelength decreases linearly with increasing time-mean flow. An experiment with a quasi-two-dimensional apparatus confirmed the theoretical values.Calculations of the detailed fluid motions reveal that under many conditions of operation the net time-mean flow is the algebraic difference between a forward time-mean flow in the core of the tube and a backward (‘reflux’) time-mean flow near the periphery. The percentage of reflux flow can be very high. This reflux phenomenon is probably of physiologic significance in the functioning of the ureter and the gastro-intestinal system. A second fluid-mechanical peculiarity with physiological implications is that of ‘trapping’: under certain conditions an internally circulating bolus of fluid, lying about the axis, is transported with the wave speed as though it were trapped by the wave.

1,298 citations

01 Sep 1968

TL;DR: In this paper, the authors investigated the effect of peristaltic wave propagation on the flow of fluid in the tube and showed that the theoretical pressure rise per wavelength decreases linearly with increasing time-mean flow, and that the percentage of reflux flow can be very high.

Abstract: : Pumping by means of an infinite train of peristaltic waves is investigated under conditions for which (1) the relevant Reynolds number is small enough for inertial effects to be negligible and (2) the wavelength-diameter ratio is large enough for the pressure to be considered uniform over the cross-section. Theoretical results are presented for both plane and axi-symmetric geometries, and for amplitude ratios ranging from zero to full occlusion. For a given amplitude ratio, the theoretical pressure rise per wavelength decreases linearly with increasing time-mean flow. An experiment with a quasi-two-dimensional apparatus confirmed the theoretical values. Calculations of the detailed fluid motions reveal that under many conditions of operation the net time-mean flow is the algebraic difference between a forward time-mean flow in the core of the tube and a backward ('reflux') time-mean flow near the periphery. The percentage of reflux flow can be very high. This reflux phenomenon is probably of physiologic significance in the functioning of the ureter and the gastro-intestinal system. A second fluid mechanical peculiarity with physiological implications is that of 'trapping': under certain conditions an internally-circulating bolus of fluid, lying about the axis, is transported with the wave speed as though it were trapped by the wave. (Author)

1,104 citations

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TL;DR: The effects of couple stresses in fluids are considered in this paper, where a series of boundary value problems are solved to indicate the effects of the couple stresses as well as for experiments measuring the various material constants.

Abstract: The effects of couple stresses in fluids are considered. Linearized constitutive equations are proposed for force and couple stresses. A series of boundary‐value problems are solved to indicate the effects of couple stresses as well as for experiments measuring the various material constants. It is found that a size effect comes in which is not present in the nonpolar case (couple stresses absent).

860 citations

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TL;DR: In this paper, the peristaltic transport of an incompressible, electrically conducting Maxwell fluid in a planar channel is considered, where the flow in the porous space is due to a sinusoidal wave traveling on the channel walls.

182 citations

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VIT University

^{1}TL;DR: The analytical solution has been obtained in the form of temperature from which an axial velocity, stream function and pressure gradient have been derived.

132 citations