Axial MHD Flow of a Generalized Oldroyd-B Fluid Due to Two Oscillating Cylinders

2011 ◽  
Vol 354-355 ◽  
pp. 83-86
Author(s):  
Ya Qing Liu ◽  
Lian Cun Zheng ◽  
Jun Tie
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Fractional Calculus ◽  
Laplace Transform ◽  
Fluid Velocity ◽  
Mhd Flow ◽  
Hankel Transform ◽  
Constitutive Relationship ◽  
Relationship Of ◽  
Fluid Velocity Field

Axial magnetohydrodynamic (MHD) flows for Oldroyd-B fluid are investigated between two cylinders. The motion of the fluid is produced by the two oscillating cylinders. The fractional calculus approach is introduced to establish the constitutive relationship of a viscolastic fluid. Velocity field and shear stress of the motion are determined in terms of Bessel function and generalized Mittag-Leffler function by using Laplace transform and Hankel transform. The influence of pertinent parameters on the flows is delineated and appropriate conclusions are drawn.

The MHD Flows for a Heated Generalized Oldroyd-B Fluid With Fractional Derivative

2010 ◽  
Author(s):  
Yaqing Liu ◽  
Liancun Zheng ◽  
Xinxin Zhang ◽  
Fenglei Zong
Keyword(s):  
Fractional Calculus ◽  
Viscoelastic Fluid ◽  
Mhd Flow ◽  
Hankel Transform ◽  
Constitutive Relationship ◽  
Temperature Fields ◽  
Fractional Partial Differential Equations ◽  
Relation Model ◽  
Velocity And Temperature Fields ◽  
Relationship Of

In this paper, we present a circular motion of magnetohydrodynamic (MHD) flow for a heated generalized Oldroyd-B fluid. The fractional calculus approach is introduced to establish the constitutive relationship of a viscoelastic fluid. The velocity and temperature fields of the flow are described by fractional partial differential equations. Exact analytical solutions of velocity and temperature fields are obtained by using Hankel transform and Laplace transform for fractional calculus. Results for ordinary viscous flow are deduced by making the fractional order of differential tend to one and zero. It is shown that the fractional constitutive relation model is more useful than the conventional model for describing the properties of viscoelastic fluid.

scholarly journals Influence of MHD on Some Oscillating Motions of a Fractional Burgers' Fluid

2015 ◽  
Vol 12 (1) ◽  
pp. 221-237
Author(s):  
Baghdad Science Journal
Keyword(s):  
Exact Solution ◽  
Shear Stress ◽  
Velocity Field ◽  
Fractional Calculus ◽  
Integral Transforms ◽  
Constitutive Relationship ◽  
Oscillating Flows ◽  
Flow Parameters ◽  
Relationship Model ◽  
Burgers Fluid

This paper presents a study for the influence of magnetohydrodynamic (MHD) on the oscillating flows of fractional Burgers’ fluid. The fractional calculus approach in the constitutive relationship model is introduced and a fractional Burgers’ model is built. The exact solution of the oscillating motions of a fractional Burgers’ fluid due to cosine and sine oscillations of an infinite flat plate are established with the help of integral transforms (Fourier sine and Laplace transforms). The expressions for the velocity field and the resulting shear stress that have been obtained, presented under integral and series form in terms of the generalized Mittag-Leffler function, satisfy all imposed initial and boundary conditions. Finally, the obtained solutions are graphically analyzed for variations of interesting flow parameters. While the MATHEMATICA package is used to draw the figures velocity components in the plane.

Numerical study of the flow of a mixture of reacting gases in an inhomogeneous catalyst layer

2003 ◽  
Vol 3 ◽  
pp. 246-254
Author(s):  
C.I. Mikhaylenko ◽  
S.F. Urmancheev
Keyword(s):  
Velocity Field ◽  
Chemical Reactions ◽  
Porous Layer ◽  
Computational Experiment ◽  
Numerical Study ◽  
Fluid Velocity ◽  
Catalyst Layer ◽  
Granular Catalyst ◽  
Fluid Velocity Field

The behavior of a liquid flowing through a fixed bulk porous layer of a granular catalyst is considered. The effects of the nonuniformity of the fluid velocity field, which arise when the surface of the layer is curved, and the effect of the resulting inhomogeneity on the speed and nature of the course of chemical reactions are investigated by the methods of a computational experiment.

Wave Motion of a Compressible Viscous Fluid Contained in a Cylindrical Shell

1993 ◽  
Vol 115 (3) ◽  
pp. 302-312 ◽  
Author(s):  
J. H. Terhune ◽  
K. Karim-Panahi
Keyword(s):  
Velocity Field ◽  
Viscous Fluid ◽  
Imaginary Part ◽  
Fluid Velocity ◽  
Wave Number ◽  
Mode Shapes ◽  
Infinite Length ◽  
Complex Frequency ◽  
Compressible Viscous Fluid ◽  
Fluid Velocity Field

The free vibration of cylindrical shells filled with a compressible viscous fluid has been studied by numerous workers using the linearized Navier-Stokes equations, the fluid continuity equation, and Flu¨gge ’s equations of motion for thin shells. It happens that solutions can be obtained for which the interface conditions at the shell surface are satisfied. Formally, a characteristic equation for the system eigenvalues can be written down, and solutions are usually obtained numerically providing some insight into the physical mechanisms. In this paper, we modify the usual approach to this problem, use a more rigorous mathematical solution and limit the discussion to a single thin shell of infinite length and finite radius, totally filled with a viscous, compressible fluid. It is shown that separable solutions are obtained only in a particular gage, defined by the divergence of the fluid velocity vector potential, and the solutions are unique to that gage. The complex frequency dependence for the transverse component of the fluid velocity field is shown to be a result of surface interaction between the compressional and vortex motions in the fluid and that this motion is confined to the boundary layer near the surface. Numerical results are obtained for the first few wave modes of a large shell, which illustrate the general approach to the solution. The axial wave number is complex for wave propagation, the imaginary part being the spatial attenuation coefficient. The frequency is also complex, the imaginary part of which is the temporal damping coefficient. The wave phase velocity is related to the real part of the axial wave number and turns out to be independent of frequency, with numerical value lying between the sonic velocities in the fluid and the shell. The frequency dependencies of these parameters and fluid velocity field mode shapes are computed for a typical case and displayed in non-dimensional graphs.

scholarly journals Viscosity Landscape of Phase-Separated Lipid Membrane Estimated from Fluid Velocity Field

2020 ◽  
Vol 118 (7) ◽  
pp. 1576-1587 ◽  
Author(s):  
Yuka Sakuma ◽  
Toshihiro Kawakatsu ◽  
Takashi Taniguchi ◽  
Masayuki Imai
Keyword(s):  
Velocity Field ◽  
Lipid Membrane ◽  
Fluid Velocity ◽  
Fluid Velocity Field

Couette Flow of a Generalized Oldroyd-B Fluid due to Constantly Accelerated Shear Stress Coupled with the Pressure Gradient

2011 ◽  
Vol 354-355 ◽  
pp. 179-182
Author(s):  
Chun Rui Li ◽  
Lian Cun Zheng ◽  
Xin Xin Zhang ◽  
Jia Jia Niu
Keyword(s):  
Shear Stress ◽  
Laplace Transform ◽  
Pressure Gradient ◽  
Exact Solutions ◽  
Couette Flow ◽  
Fractional Derivatives ◽  
Hankel Transform ◽  
Time Dependent ◽  
Infinite Cylinder ◽  
Finite Hankel Transform

This paper presented an analysis for the couette flow of a generalized Oldroyd-B fluid within an infinite cylinder subject to a time-dependent shear stress with the influence of the internal constantly decelerated pressure gradient. The exact solutions are established by means of the combine of the sequential fractional derivatives Laplace transform and finite Hankel transform and presented by integral and series form in terms of the Mittag-Leffler function. Moreover, the effects of various parameters are analyzed in detail by graphical illustrations.

scholarly journals Axisymmetric stagnation-point flow and heat transfer of nanofluid impinging on a cylinder with constant wall heat flux

2019 ◽  
Vol 23 (5 Part B) ◽  
pp. 3153-3164 ◽  
Author(s):  
Hamid Mohammadiun ◽  
Vahid Amerian ◽  
Mohammad Mohammadiun ◽  
Iman Khazaee ◽  
Mohsen Darabi ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Velocity Field ◽  
Stagnation Point ◽  
Base Fluid ◽  
Fluid Velocity ◽  
Wall Heat Flux ◽  
Flow And Heat Transfer ◽  
Constant Wall Heat Flux ◽  
Fluid Velocity Field

The steady-state, viscous flow and heat transfer of nanofluid in the vicinity of an axisymmetric stagnation point of a stationary cylinder with constant wall heat flux is investigated. The impinging free-stream is steady and with a constant strain rate, k ?. Exact solution of the Navier-Stokes equations and energy equation are derived in this problem. A reduction of these equations is obtained by use of appropriate transformations introduced in this research. The general self-similar solution is obtained when the wall heat flux of the cylinder is constant. All the previous solutions are presented for Reynolds number Re = k ?a2/2n f ranging from 0.1 to 1000, selected values of heat flux and selected values of particle fractions where a is cylinder radius and n f is kinematic viscosity of the base fluid. For all Reynolds numbers, as the particle fraction increases, the depth of diffusion of the fluid velocity field in radial direction, the depth of the diffusion of the fluid velocity field in z-direction, shear-stresses and pressure function decreases. However, the depth of diffusion of the thermal boundary-layer increases. It is clear by adding nanoparticles to the base fluid there is a significant enhancement in Nusselt number and heat transfer.

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