Exact solutions for the Poiseuille flow of a generalized Maxwell fluid induced by time-dependent shear stress

2011 ◽  
Vol 51 ◽  
pp. 416
Author(s):  
Waseem Akhtar ◽  
Corina Fetecau ◽  
A. U. Awan
Keyword(s):  
Shear Stress ◽  
Exact Solutions ◽  
Poiseuille Flow ◽  
Maxwell Fluid ◽  
Time Dependent ◽  
Generalized Maxwell Fluid

EXACT SOLUTIONS FOR THE POISEUILLE FLOW OF A GENERALIZED MAXWELL FLUID INDUCED BY TIME-DEPENDENT SHEAR STRESS

2010 ◽  
Vol 51 (4) ◽  
pp. 416-429 ◽  
Author(s):  
W. AKHTAR ◽  
CORINA FETECAU ◽  
A. U. AWAN
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Circular Cylinder ◽  
Poiseuille Flow ◽  
Fluid Motion ◽  
Maxwell Fluid ◽  
Time Dependent ◽  
Infinite Cylinder ◽  
Similar Solutions ◽  
Generalized Maxwell Fluid

AbstractThe Poiseuille flow of a generalized Maxwell fluid is discussed. The velocity field and shear stress corresponding to the flow in an infinite circular cylinder are obtained by means of the Laplace and Hankel transforms. The motion is caused by the infinite cylinder which is under the action of a longitudinal time-dependent shear stress. Both solutions are obtained in the form of infinite series. Similar solutions for ordinary Maxwell and Newtonian fluids are obtained as limiting cases. Finally, the influence of the material and fractional parameters on the fluid motion is brought to light.

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 Exact Solutions of Rayleigh-Stokes Problem for Heated Generalized Maxwell Fluid in a Porous Half-Space

2008 ◽  
Vol 2008 ◽  
pp. 1-10 ◽  
Author(s):  
Changfeng Xue ◽  
Junxiang Nie
Keyword(s):  
Exact Solutions ◽  
Half Space ◽  
Stokes Problem ◽  
Maxwell Fluid ◽  
Constitutive Relationship ◽  
Classical Solutions ◽  
Maxwell Fluids ◽  
Fourier Sine Transform ◽  
Porous Half Space ◽  
Generalized Maxwell Fluid

The Rayleigh-Stokes problem for a generalized Maxwell fluid in a porous half-space with a heated flat plate is investigated. For the description of such a viscoelastic fluid, a fractional calculus approach in the constitutive relationship model is used. By using the Fourier sine transform and the fractional Laplace transform, exact solutions of the velocity and the temperature are obtained. Some classical results can be regarded as particular cases of our results, such as the classical solutions of the first problem of Stokes for Newtonian viscous fluids, Maxwell fluids, and Maxwell fluids in a porous half-space.

Exact Solutions for the Fractional Time-Dependent Oldroyd-B Fluid Model Subject to a Constantly Accelerated Shear Stress

2014 ◽  
Vol 518 ◽  
pp. 114-119 ◽  
Author(s):  
Chun Rui Li ◽  
Lian Cun Zheng
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Pressure Gradient ◽  
Exact Solutions ◽  
Couette Flow ◽  
Fractional Derivatives ◽  
Fluid Model ◽  
Time Dependent ◽  
Infinite Cylinder ◽  
Model Subject

In this paper, based on the fractional model, we present an investigation on the couette flow of a generalized Oldroyd-B fluid within an infinite cylinder subject to a time-dependent shear stress which is affected by the internal constantly decelerated pressure gradient. By using the fractional derivatives Laplace and finite Hankel transforms, the obtained solutions for the velocity field and shear stress, written in terms of generalized R function, are presented the similar characteristics with Newtonian and non-Newtonian fluids. Moreover, the effects of various parameters are systematically analyzed.

scholarly journals Exact Solutions for the Axial Couette Flow of a Fractional Maxwell Fluid in an Annulus

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
M. Imran ◽  
A. U. Awan ◽  
Mehwish Rana ◽  
M. Athar ◽  
M. Kamran
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Exact Solutions ◽  
Couette Flow ◽  
Maxwell Fluid ◽  
Circular Cylinders ◽  
Rotational Flow ◽  
Material Parameters

The velocity field and the adequate shear stress corresponding to the rotational flow of a fractional Maxwell fluid, between two infinite coaxial circular cylinders, are determined by applying the Laplace and finite Hankel transforms. The solutions that have been obtained are presented in terms of generalized Ga,b,c(·,t) and Ra,b(·,t) functions. Moreover, these solutions satisfy both the governing differential equations and all imposed initial and boundary conditions. The corresponding solutions for ordinary Maxwell and Newtonian fluids are obtained as limiting cases of our general solutions. Finally, the influence of the material parameters on the velocity and shear stress of the fluid is analyzed by graphical illustrations.

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