04 Mar 2021-Applied Mathematics and Mechanics-english Edition (Springer Science and Business Media LLC)-Vol. 42, Iss: 4, pp 583-592

Abstract: The peristaltic flow of a heated Jeffrey fluid inside a duct with an elliptic cross-section is studied. A thorough heat transfer mechanism is interpreted by analyzing the viscous effects in the energy equation. The governing mathematical equations give dimensionless partial differential equations after simplification. The final simplified form of the mathematical equations is evaluated with respect to the relevant boundary conditions, and the exact solution is attained. The results are further illustrated by graphs, and the distinct aspects of peristaltic flow phenomena are discussed.

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Topics: Partial differential equation (54%), Boundary value problem (53%)

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5 results found

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Salman Akhtar^{1}, Luthais B. McCash^{2}, Sohail Nadeem^{1}, Salman Saleem^{3} +1 more•Institutions (4)

Abstract: A mathematical model is presented to analyse the flow characteristics and heat transfer aspects of a heated Newtonian viscous fluid with single wall carbon nanotubes inside a vertical duct having elliptic cross section and sinusoidally fluctuating walls. Exact mathematical computations are performed to get temperature, velocity and pressure gradient expressions. A polynomial solution technique is utilized to obtain these mathematical solutions. Finally, these computational results are presented graphically and different characteristics of peristaltic flow phenomenon are examined in detail through these graphs. The velocity declines as the volume fraction of carbon nanotubes increases in the base fluid. Since the velocity of fluid is dependent on its temperature in this study case and temperature decreases with increasing volumetric fraction of carbon nanotubes. Thus velocity also declines for increasing volumetric fraction of nanoparticles.

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Topics: Convective heat transfer (57%), Newtonian fluid (56%), Heat transfer (54%) ... show more

6 Citations

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Abstract: Peristaltic flow of hybrid nanofluid inside a duct having sinusoidally advancing boundaries and elliptic cross-section is mathematically investigated. The notable irreversibility effects are also examined in this mathematical research by considering a descriptive entropy analysis. In addition, this work provides a comparison analysis for two distinct nanofluid models: a hybrid model (Cu-Ag/water) and a phase flow model (Cu/water). A comprehensive graphical description is also provided to interpret the physical aspects of this mathematical analysis.

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Topics: Nanofluid (54%)

4 Citations

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Abstract: This novel investigation suggests the implementation of famous numerical technique namely Galerkin finite element technique for peristaltic study of non-Newtonian fluid confined by a porous tube. The rheological consequences for non-Newtonian materials are executed by using micropolar fluid. The problem is modeled in form of Navier–Stokes expressions. The flow simulations are carried by utilizing the impact of the magnetic field and uniform porous medium. Additionally, the role of inertial forces is also observed as a novelty for current analysis. Unlike typical investigations, the presumptions of lubrication theory are not implemented in the modeling which allows the participation of inertial forces in the governing equations and provided the results independent of wavelength. The solution of the modeled set of coupled non-linear partial differential equations is obtained by Galerkin finite element method with quadratic triangular elements. The verification of attained numerical results with available literature for low Reynolds number approximation is also presented and found in excellent agreement. It is observed that the peristaltic mixing enhances with increasing the inertial and Lorentz force while reverse observations are noticed with for the dense porous medium. An increase in pressure rise per wavelength is observed for micropolar fluid as compared to that of viscous fluid. It is further claimed that the peristaltic mixing is improved with increasing the Reynolds number and permeability of porous medium.

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Topics: Porous medium (56%), Lubrication theory (55%), Galerkin method (55%) ... show more

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09 Aug 2021-

Abstract: This study investigates the effects of viscous dissipation and a heat source or sink on the magneto-hydrodynamic laminar boundary layer flow of a Jeffrey fluid past a vertical plate. The governing boundary layer non-linear partial differential equations are reduced to non-linear ordinary differential equations using suitable similarity transformations. The resulting system of dimensionless differential equations is then solved numerically using the bivariate spectral quasi-linearisation method. The effects of some physical parameters that include the Schmidt number, Eckert number, radiation parameter, magnetic field parameter, heat generation parameter, and the ratio of relaxation to retardation times on the velocity, temperature, and concentration profiles are presented graphically. Additionally, the influence of some physical parameters on the skin friction coefficient, local Nusselt number, and the local Sherwood number are displayed in tabular form.

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Topics: Boundary layer (65%), Nusselt number (65%), Eckert number (63%) ... show more

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28 results found

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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.

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Topics: Reynolds number (55%), Wavelength (52%)

1,132 Citations

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01 Sep 1968-

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)

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Topics: Adverse pressure gradient (58%), Hele-Shaw flow (57%), Reynolds number (57%) ... show more

1,104 Citations

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Abstract: We have analyzed the mechanics of peristaltic pumping of a non-Newtonian fluid through an axisymmetric conduit. The material was represented by the constitutive equation for a second-order fluid. A perturbation series (to second order) in dimensionless wavenumber of an infinite harmonic traveling wave was used to obtain explicit forms for the velocity field and a relation between the flow rate and the pressure gradient, in terms of the Reynolds number, the dimensionless non-Newtonian parameters, and the occlusion. Results were compared with other studies, in both Newtonian and non-Newtonian cases. Also, we have shown that the flow of a Newtonian fluid through a rigid, axisymmetric tube with an axial, sinusoidal variation of radius is a special case of this analysis.

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Topics: Second-order fluid (66%), Generalized Newtonian fluid (66%), Fluid mechanics (62%) ... show more

164 Citations

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Abstract: The study is concerned with the analysis of two flow domains of peristaltic motion in tubes. In the first analysis the wall disturbance wavelength is much larger than the average tube radius. There is a simple algebraic relation between the average flow rate and pressure differential across a wavelength. In the second analysis the disturbance wavelength may be as small as the average radius. A numerical technique may be used to determine the relation between average flow rate and pressure differential across a wavelength.

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Topics: Radius (51%), Wavelength (51%)

126 Citations

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Abstract: Peristaltic pumping is investigated, generated by means of an infinite train of waves travelling along the wall of a cylindrical tube. The theory is based on the general second order integral constitutive equation for viscoelastic (simple) liquids. Analytical and closed form solutions are presented for the first order and the stationary part of the second order flow field approximations with respect to the amplitude ratio. It turns out that the zero—shear viscosity η 0 and the complex viscosity η*(ω) are the only relevant fluid properties.

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Topics: Viscosity (55%), Viscoelasticity (52%), Constitutive equation (50%)

111 Citations