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.

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.

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.

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.

scholarly journals Taylor–Couette flow of a fractional second grade fluid in an annulus due to a time-dependent couple

2011 ◽  
Vol 16 (1) ◽  
pp. 47-58 ◽  
Author(s):  
M. Imran ◽  
M. Kamran ◽  
M. Athar ◽  
A. A. Zafar
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Exact Solutions ◽  
Unit Length ◽  
Time Dependent ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Coaxial Cylinders ◽  
Grade Fluid ◽  
Second Grade Fluids

Exact solutions for the velocity field and the associated shear stress, corresponding to the flow of a fractional second grade fluid between two infinite coaxial cylinders, are determined by means of Laplace and finite Hankel transforms. The motion is produced by the inner cylinder which is rotating about its axis due to a time-dependent torque per unit length 2πR1ft2. The solutions that have been obtained satisfy all imposed initial and boundary conditions. For β → 1, respectively β → 1 and α1 → 0, the corresponding solutions for ordinary second grade fluids and Newtonian fluids, performing the same motion, are obtained as limiting cases.

scholarly journals Analysis of dynamics variation against thixotropic parameter’s preferential range

2018 ◽  
Vol 45 (2) ◽  
pp. 231-251
Author(s):  
Nazish Shahid
Keyword(s):  
Shear Stress ◽  
Pressure Gradient ◽  
Flow Rate ◽  
Axial Velocity ◽  
Fluid Model ◽  
Current Model ◽  
Velocity Shear ◽  
Structural Parameter ◽  
Velocity Flow ◽  
Analysis Of Dynamics

Variation in the dynamics of a steady-state blood flow through a stenosed tapered artery has been investigated corresponding to changes in thixotropic parameter ? over the range [0,1]. To probe the role of parameter ? and differentiate the current model from other known non-Newtonian models, expressions of axial velocity, shear stress, wall shear stress and flow rate have been calculated depending upon this parameter and pressure gradient. Also, pressure gradient has been deduced uniquely with the help of the continuity equation. Our choice of calculating pressure gradient has led to obtaining shear stress such that its dependence on the structural parameter of our model, unlike most available results, motivates for further investigation. The simultaneous effects of varying yield stress and parameter ? on axial velocity, flow resistance and flow rate have been studied such that the differences between the Herschel?Bulkley fluid model and our current model can be pointed out. To validate the suitability of our model and some results in history, we have also obtained limiting results for particular values of ?.

Taylor-Couette Flow of an Oldroyd-B Fluid in an Annulus Due to a Time-Dependent Couple

2011 ◽  
Vol 66 (1-2) ◽  
pp. 40-46 ◽  
Author(s):  
Corina Fetecau ◽  
Muhammad Imran ◽  
Constantin Fetecau
Keyword(s):  
Exact Solutions ◽  
Couette Flow ◽  
Bessel Functions ◽  
Time Dependent ◽  
Second Grade ◽  
Governing Equations ◽  
Material Parameters ◽  
Taylor Couette ◽  
Similar Solutions ◽  
Taylor Couette Flow

Taylor-Couette flow in an annulus due to a time-dependent torque suddenly applied to one of the cylinders is studied by means of finite Hankel transforms. The exact solutions, presented under series form in terms of usual Bessel functions, satisfy both the governing equations and all imposed initial and boundary conditions. They can easily be reduced to give similar solutions for Maxwell, second grade, and Newtonian fluids performing the same motion. Finally, some characteristics of the motion, as well as the influence of the material parameters on the behaviour of the fluid, are emphasized by graphical illustrations.

Axial Couette flow of a generalized Oldroyd-B fluid due to a longitudinal time-dependent shear stress

2010 ◽  
Vol 33 (4) ◽  
pp. 429-441 ◽  
Author(s):  
A. U. Awan ◽  
Corina Fetecau ◽  
Qammar Rubbab
Keyword(s):  
Shear Stress ◽  
Couette Flow ◽  
Time Dependent

scholarly journals Flow of a second grade fluid with fractional derivatives due to a quadratic time dependent shear stress

2018 ◽  
Vol 57 (3) ◽  
pp. 1963-1969 ◽  
Author(s):  
Nauman Raza ◽  
M. Abdullah ◽  
Asma Rashid Butt ◽  
Aziz Ullah Awan ◽  
Ehsan Ul Haque
Keyword(s):  
Shear Stress ◽  
Fractional Derivatives ◽  
Time Dependent ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Grade Fluid

scholarly journals Connection between Classical Solutions of Stokes first Problem and those of Simple Couette Flow. Applications

2020 ◽  
Vol 2 (3) ◽  
pp. 1-3
Author(s):  
Constantin Fetecau ◽  
◽  
Marneni Narahari ◽  
Keyword(s):  
Shear Stress ◽  
Exact Solutions ◽  
Couette Flow ◽  
Direct Consequence ◽  
Viscous Fluids ◽  
Classical Solutions ◽  
New Exact Solutions ◽  
Constant Shear ◽  
Constant Shear Stress

The classical solutions of the first problem of Stokes for viscous fluids, as it was to be expected, are obtained as limiting cases of those of the simple Couette flow. Something similar is valid for the motions of the fluids induced by a constant shear stress on the boundary. As a direct consequence, new exact solutions are immediately obtained for other two classes of motions of the same fluids.

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