scholarly journals First Problem of Stokes for Generalized Burgers' Fluids

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Muhammad Jamil
Keyword(s):  
Shear Stress ◽  
Steady State ◽  
Velocity Field ◽  
Integral Transforms ◽  
Newtonian Fluids ◽  
Rheological Parameters ◽  
Second Grade ◽  
Material Parameters ◽  
Transient Solutions ◽  
Similar Solutions

The velocity field and the adequate shear stress corresponding to the first problem of Stokes for generalized Burgers’ fluids are determined in simple forms by means of integral transforms. The solutions that have been obtained, presented as a sum of steady and transient solutions, satisfy all imposed initial and boundary conditions. They can be easily reduced to the similar solutions for Burgers, Oldroyd-B, Maxwell, and second-grade and Newtonian fluids. Furthermore, as a check of our calculi, for small values of the corresponding material parameters, their diagrams are almost identical to those corresponding to the known solutions for Newtonian and Oldroyd-B fluids. Finally, the influence of the rheological parameters on the fluid motions, as well as a comparison between models, is graphically illustrated. The non-Newtonian effects disappear in time, and the required time to reach steady-state is the lowest for Newtonian fluids.

First Exact Solutions for Flows of Rate Type Fluids in a Circular Duct that Applies a Constant Couple to the Fluid

2014 ◽  
Vol 69 (5-6) ◽  
pp. 232-238 ◽  
Author(s):  
Corina Fetecau ◽  
Mehwish Rana ◽  
Niat Nigar ◽  
Constantin Fetecau
Keyword(s):  
Shear Stress ◽  
Circular Cylinder ◽  
Integral Transforms ◽  
Second Grade ◽  
Rotational Flow ◽  
Stress Distributions ◽  
Circular Duct ◽  
Material Parameters ◽  
Similar Solutions ◽  
Rate Type

Rotational flow of an Oldroyd-B fluid induced by an infinite circular cylinder that applies a constant couple to the fluid is studied by means of integral transforms. Such a problem is not solved in the existing literature for rate type fluids and the present solutions are based on a simple but important remark regarding the governing equation for the non-trivial shear stress. The solutions that have been obtained satisfy all imposed initial and boundary conditions and can easy be reduced to the similar solutions corresponding to Maxwell, second-grade, and Newtonian fluids performing the same motion. Finally, the influence of material parameters on the velocity and shear stress distributions is graphically underlined.

AXIAL FLOW OF SEVERAL NON-NEWTONIAN FLUIDS THROUGH A CIRCULAR CYLINDER

2010 ◽  
Vol 02 (03) ◽  
pp. 543-556 ◽  
Author(s):  
D. VIERU ◽  
I. SIDDIQUE
Keyword(s):  
Velocity Field ◽  
Circular Cylinder ◽  
Axial Flow ◽  
Newtonian Fluids ◽  
Time Dependent ◽  
Second Grade ◽  
Material Parameters ◽  
Hankel Transforms ◽  
Dimensionless Variables ◽  
Similar Solutions

The velocity field, the longitudinal and the normal tensions corresponding to the axial flow of an Oldroyd-B fluid due to an infinite circular cylinder subject to a longitudinal time-dependent stress are determined by means of the Laplace and finite Hankel transforms. The similar solutions for Maxwell, second grade or Newtonian fluids have been obtained as particular cases of the solutions for Oldroyd-B fluids. Finally, by using dimensionless variables, some characteristics of the motion as well as the influence of the material parameters on the behavior of fluid are shown by graphical illustrations.

Effects of Side Walls on the Motion Induced by an Infinite Plate that Applies Shear Stresses to an Oldroyd-B Fluid

2013 ◽  
Vol 68 (12) ◽  
pp. 725-734 ◽  
Author(s):  
Mehwish Rana ◽  
Nazish Shahid ◽  
Azhar Ali Zafar
Keyword(s):  
Steady State ◽  
Exact Solutions ◽  
Fluid Motion ◽  
Infinite Plate ◽  
Integral Transforms ◽  
Second Grade ◽  
Shear Stresses ◽  
Transient Solutions ◽  
Side Walls ◽  
Similar Solutions

Unsteady motions of Oldroyd-B fluids between two parallel walls perpendicular to a plate that applies two types of shears to the fluid are studied using integral transforms. Exact solutions are obtained both for velocity and non-trivial shear stresses. They are presented in simple forms as sums of steady-state and transient solutions and can easily be particularized to give the similar solutions for Maxwell, second-grade and Newtonian fluids. Known solutions for the motion over an infinite plate, applying the same shears to the fluid, are recovered as limiting cases of general solutions. Finally, the influence of side walls on the fluid motion, the distance between walls for which their presence can be neglected, and the required time to reach the steady-state are graphically determined.

General Solutions for the Unsteady Flow of Second-Grade Fluids over an Infinite Plate that Applies Arbitrary Shear to the Fluid

2011 ◽  
Vol 66 (12) ◽  
pp. 753-759 ◽  
Author(s):  
Constantin Fetecau ◽  
Corina Fetecau ◽  
Mehwish Rana
Keyword(s):  
Shear Stress ◽  
Unsteady Flow ◽  
Infinite Plate ◽  
Unsteady Motion ◽  
Newtonian Fluids ◽  
Second Grade ◽  
Moving Plate ◽  
General Solutions ◽  
Similar Solutions ◽  
Second Grade Fluids

General solutions corresponding to the unsteady motion of second-grade fluids induced by an infinite plate that applies a shear stress ƒ (t) to the fluid are established. These solutions can immediately be reduced to the similar solutions for Newtonian fluids. They can be used to obtain known solutions from the literature or any other solution of this type by specifying the function ƒ (.). Furthermore, in view of a simple remark, general solutions for the flow due to a moving plate can be developed.

Some Unsteady Flows of a Jeffrey Fluid between Two Side Walls over a Plane Wall

2011 ◽  
Vol 66 (12) ◽  
pp. 745-752 ◽  
Author(s):  
Masood Khan ◽  
Faiza Iftikhar ◽  
Asia Anjum
Keyword(s):  
Infinite Plate ◽  
Unsteady Flows ◽  
Integral Transforms ◽  
Plane Wall ◽  
Second Grade ◽  
Jeffrey Fluid ◽  
Transient Solutions ◽  
Side Walls ◽  
Similar Solutions ◽  
Oscillating Plate

In this paper, some time-dependent flows of a non-Newtonian fluid between two side walls over a plane wall are investigated. The following three problems have been studied: (i) flow due to an oscillating plate, (ii) flow due to an accelerating plate, and (iii) flow due to applied constant stress. The explicit expressions for the velocity field are determined by using the integral transforms. The solutions that have been obtained, depending on the initial and boundary conditions, are written as sum of the steady state and transient solutions. The similar solutions for second-grade and Newtonian fluids can be deduced as limiting cases of our solutions. Furthermore, in absence of the side walls they reduce to the similar solutions over an infinite plate. The effects of some important parameters due to side walls on the flow field are investigated.

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.

scholarly journals Exact solutions for the unsteady rotational flow of a generalized second grade fluid through a circular cylinder

2010 ◽  
Vol 15 (4) ◽  
pp. 437-444 ◽  
Author(s):  
M. Kamran ◽  
M. Imran ◽  
M. Athar
Keyword(s):  
Velocity Field ◽  
Circular Cylinder ◽  
Time Dependent ◽  
Second Grade ◽  
Rotational Flow ◽  
Second Grade Fluid ◽  
Special Cases ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid ◽  
Similar Solutions

Here the velocity field and the associated tangential stress corresponding to the rotational flow of a generalized second grade fluid within an infinite circular cylinder are determined by means of the Laplace and finite Hankel transforms. At time t = 0 the fluid is at rest and the motion is produced by the rotation of the cylinder around its axis with a time dependent angular velocity Ωt. The solutions that have been obtained are presented under series form in terms of the generalized G-functions. The similar solutions for the ordinary second grade and Newtonian fluids, performing the same motion, are obtained as special cases of our general solution.

A Note on the Transient Solution of Stokes' Second Problem with Arbitrary Initial Phase

2006 ◽  
Vol 22 (4) ◽  
pp. 349-354 ◽  
Author(s):  
C.-M. Liu ◽  
I.-C. Liu
Keyword(s):  
Shear Stress ◽  
Steady State ◽  
Initial Phase ◽  
Transient State ◽  
Wall Stress ◽  
Transform Method ◽  
Transient Solutions ◽  
Stokes Second Problem ◽  
Oscillating Plate ◽  
Steady State Solutions

AbstractThe flow of a viscous fluid disturbed by an oscillating plate of arbitrary initial phase is studied in present note. The exact solutions of the velocity and the shear stress are solved using a Laplace transform method. The velocity is derived in terms of complementary error functions and the shear stress on the boundary is given in the form of Fresnel integrals. Since the steady-state solutions are well known, our discussions are focused on the transient solutions. The transient state will disappear faster for the wall stress than that for the velocity field. Comparing the results corresponding to different initial phases, the cosine case reaches to the steady state more rapidly than the sine case.

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 On analytical study of factional Oldroyd-B flow in annular region of two torsionally oscillating cylinders

2012 ◽  
Vol 16 (2) ◽  
pp. 411-421 ◽  
Author(s):  
A. Mahmood
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Analytical Study ◽  
Analytic Solutions ◽  
Circular Cylinders ◽  
Second Grade ◽  
General Solutions ◽  
Exact Analytic Solutions ◽  
Governing Differential Equation ◽  
R Functions

The velocity field and the associated shear stress corresponding to the torsional oscillatory flow of a fractional Oldroyd-B fluid, also called generalized Oldroyd-B fluid (GOF), between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. Initially, the fluid and cylinders are at rest and after some time both cylinders suddenly begin to oscillate around their common axis with different angular frequencies of their velocities. The exact analytic solutions of the velocity field and associated shear stress, that have been obtained, are presented under integral and series forms in terms of generalized G and R functions. Moreover, these solutions satisfy the governing differential equation and all imposed initial and boundary conditions. The respective solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for the similar flow of classical Oldroyd-B, generalized Maxwell, classical Maxwell, generalized second grade, classical second grade and Newtonian fluids are also obtained as limiting cases of our general solutions.

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