Series Solutions of Magnetohydrodynamic Peristaltic Flow of a Jeffrey Fluid in Eccentric Cylinders
TL;DR: In this article, the mathematical modelling on magnetohydrodynamic peristaltic flow of Jeffrey fluid in the gap between two eccentric tubes has been discussed in the presence of applied magnetic fi eld.
Abstract: In this article, the mathematical modelling on magnetohydrodynamic peristaltic flow of Jeffrey fluid in the gap between two eccentric tubes has been discussed in the presence of applied magnetic fi eld. Geometrically, we considered two eccentric tubes in which the inner tube is rigid while the tube at the outer side has a sinusoidal wave pro pagating along the wall. The governing equations for Jeffrey fluid in a cylindrical coordinates for three dimensional flow are given. The approximations of low Reynolds number and long wavelength have been employed to reduce the highly nonlinear partial differential equations. The problem has been solved with the help of homotopy perturbation method alongwith eigen function expansion method. The graphs of pressure rise, pressure gradient and velocity (for two and three dimensional flow) have been drawn. The stre amlines have also been presented to discuss the trapping bolus discipline.
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TL;DR: In this paper, the dimensionless velocities and shear stresses are obtained in two lateral directions past a porous linear stretching sheet, and self-similar solutions are obtained and compared with the available data for special cases.
Abstract: In this paper, magnetohydrodynamic (MHD) Casson fluid flow in two lateral directions past a porous linear stretching sheet is investigated. Self-similar solutions are obtained and compared with the available data for special cases. It is found that the present results are in an excellent agreement with the available data. The dimensionless velocities and shear stresses are obtained in both directions. Pertinent results are presented graphically and discussed quantitatively with respect to variation in Casson flow parameter as well as other fluid flow parameters.
296 citations
TL;DR: In this article, the effect of spatially variable magnetic field on ferrofluid flow and heat transfer is investigated and the combined effects of ferrohydrodynamic and magnetohydrodynamic have been taken into account.
Abstract: Effect of spatially variable magnetic field on ferrofluid flow and heat transfer is investigated. The enclosure is filled with Fe3O4–water nanofluid. Control volume based finite element method (CVFEM) is applied to solve the governing equations. The combined effects of ferrohydrodynamic and magnetohydrodynamic have been taken into account. The influences of Magnetic number, Hartmann number, Rayleigh number and nanoparticle volume fraction on the flow and heat transfer characteristics have been examined. Results show that enhancement in heat transfer decrease with increase of Rayleigh number while for two other active parameters different behavior is observed. Also it can be concluded that Nusselt number is an increasing function of Magnetic number, Rayleigh number and nanoparticle volume fraction while it is a decreasing function of Hartmann number.
240 citations
TL;DR: In this paper, the influence of heat and mass transfer on peristaltic flow in a non-uniform rectangular duct is studied under the consideration of long wavelength ( 0 ≪ λ → ∞ ) and low Reynolds number ( Re → 0 ).
142 citations
TL;DR: In this article, the peristaltic flow of Jeffrey fluid in a non-uniform rectangular duct under the effects of Hall and ion slip was theoretically studied, where an incompressible and magnetohydrodynamics fluid was also taken into account.
Abstract: Purpose – The purpose of this paper is to theoretically study the problem of the peristaltic flow of Jeffrey fluid in a non-uniform rectangular duct under the effects of Hall and ion slip. An incompressible and magnetohydrodynamics fluid is also taken into account. The governing equations are modelled under the constraints of low Reynolds number and long wave length. Recent development in biomedical engineering has enabled the use of the periastic flow in modern drug delivery systems with great utility. Design/methodology/approach – Numerical integration is used to analyse the novel features of volumetric flow rate, average volume flow rate, instantaneous flux and the pressure gradient. The impact of physical parameters is depicted with the help of graphs. The trapping phenomenon is presented through stream lines. Findings – The results of Newtonian fluid model can be obtained by taking out the effects of Jeffrey parameter from this model. No-slip case is a special case of the present work. The results ob...
126 citations
TL;DR: In this paper, the effect of heat transfer with the blood flow (non-Newtonian model) containing gold nanoparticles in a gap between two coaxial tubes, the outer tube has a sinusoidal wave traveling down its wall and the inner tube is rigid.
124 citations
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TL;DR: Wazwaz et al. as mentioned in this paper applied homotopy perturbation method to nonlinear boundary value problems and compared the result obtained by the present method with that obtained by Adomian method.
1,112 citations
Additional excerpts
...r ∂u ∂ r + 1 r2 ∂ 2u ∂θ 2 − N2 r2 u, (16)...
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TL;DR: In this paper, the peristaltic flow of Jeffrey fluid in an asymmetric channel is studied under long wavelength and low Reynolds number assumptions, where the fluid is electrically conducting by a transverse magnetic field.
Abstract: The peristaltic flow of a Jeffrey fluid in an asymmetric channel is studied under long wavelength and low Reynolds number assumptions. The fluid is electrically conducting by a transverse magnetic field. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phase. The flow is investigated in a wave frame of reference moving with the velocity of the wave. The expressions for stream function, axial velocity and axial pressure gradient have been obtained. The effects of various emerging parameters on the flow characteristics are shown and discussed with the help of graphs. The pumping characteristics, axial pressure gradient and trapping phenomenon have been studied. Comparison of various wave forms (namely sinusoidal, triangular, square and trapezoidal) on the flow is discussed.
285 citations
"Series Solutions of Magnetohydrodyn..." refers background in this paper
...Note that considering the cylindrical coordinates system for the velocity fieldV = (v,w,u) and in the absence of body force, equations(1) and (2) correspondingly take the following form...
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TL;DR: The effect of a magnetic field on peristaltic transport of blood in a non-uniform two-dimensional channels has been investigated under zero Reynolds number with long wavelength approximation and it is found that the pressure rise decreases as the couple-stress fluid parameter @c increases and increases as the Hartmann number M increases.
248 citations
"Series Solutions of Magnetohydrodyn..." refers background in this paper
...According to the flow geometry, the boundary conditions are defined as u = 0, at r = r2, (7)...
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TL;DR: A comprehensive analysis of peristaltic transport resulting from symmetric and asymmetric contractions is presented for various displacement waves on the channel walls and provides information on the flow field and possible trajectories by which an embryo may be transported before implantation at the uterine wall.
230 citations
Additional excerpts
...ρ [ ∂ v ∂ t +u ∂v ∂ z + v ∂ v ∂ r + w r ∂v ∂θ − w2 r ] =− ∂ p ∂ r + 1 r ∂ ∂ r (rSrr)+ 1 r ∂ ∂θ (Srθ )+ ∂ ∂ z (Srz)− Sθθ r , (4)...
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TL;DR: In this paper, the influence of an endoscope on the peristaltic flow of a couple stress fluid in an annulus under a zero Reynolds number and long wavelength approximation is discussed.
Abstract: This paper discusses the influence of an endoscope on the peristaltic flow of a couple stress fluid in an annulus under a zero Reynolds number and long wavelength approximation. The inner tube is uniform, rigid, while the outer tube has a sinusoidal wave traveling down its wall. Analytical expressions for the axial velocity, stream function and axial pressure gradient are established. The flow is investigated in a wave frame of reference moving with the velocity of the wave. Numerical calculations are carried out for the pressure rise, frictional forces and trapping. The features of the flow characteristics are analyzed by plotting graphs and discussed in detail.
192 citations