Starting solutions for the motion of second grade fluids due to oscillating shear stresses

2015 ◽  
Vol 4 (2) ◽  
Author(s):  
Muhammad Jamil
Keyword(s):  
Analytic Solutions ◽  
Second Grade ◽  
Shear Stresses ◽  
Exact Analytic Solutions ◽  
Transient Solutions ◽  
Grade Fluid ◽  
Starting Solutions ◽  
Second Grade Fluids ◽  
Graphical Illustration ◽  
Special Case

AbstractExact analytic solutions for the motion of second grade fluid between two infinite coaxial cylinders are established. The motion is produced by the inner cylinder that at time t = 0+ applies torsional and longitudinal oscillating shear stresses to the fluid. The exact analytic solutions, obtained with the help of Laplace and finite Hankel transforms, and presented as a sum of the steady-state and transient solutions, satisfy both the governing equations and all associate initial and boundary conditions. In the special case when a1 to 0 they reduce to those for a Newtonian fluid. Finally, the effect of various parameters of interest on transient parts of velocity components, velocity profiles as well as comparison between second grade and Newtonian fluids is discussed through graphical illustration.

scholarly journals Starting solutions for some simple oscillating motions of second-grade fluids

2006 ◽  
Vol 2006 ◽  
pp. 1-9 ◽  
Author(s):  
C. Fetecau ◽  
Corina Fetecau
Keyword(s):  
Rectangular Cross Section ◽  
Navier Stokes ◽  
Second Grade ◽  
Governing Equations ◽  
Transient Solutions ◽  
Grade Fluid ◽  
Stokes Fluid ◽  
Starting Solutions ◽  
Second Grade Fluids ◽  
Special Case

The exact starting solutions corresponding to the motions of a second-grade fluid, due to the cosine and sine oscillations of an infinite edge and of an infinite duct of rectangular cross-section as well as those induced by an oscillating pressure gradient in such a duct, are determined by means of the double Fourier sine transforms. These solutions, presented as sum of the steady-state and transient solutions, satisfy both the governing equations and all associate initial and boundary conditions. In the special case whenα1→0, they reduce to those for a Navier-Stokes fluid.

On the Impulsive Motion of Flat Plate in a Generalized Second Grade Fluid

2004 ◽  
Vol 59 (11) ◽  
pp. 829-837 ◽  
Author(s):  
Moustafa El-Shahed
Keyword(s):  
Differential Equations ◽  
Flat Plate ◽  
Transverse Magnetic ◽  
Analytic Solutions ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Exact Analytic Solutions ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid ◽  
Fox’S H Function

We investigate the effect of a transverse magnetic field on the unsteady flow of a generalized second grade fluid through a porous medium past an infinite flat plate. Using fractional partial differential equations, we are able to describe the velocity and stress fields of the flow. We also obtain exact analytic solutions of these differential equations in terms of the Fox’s H-function

scholarly journals Analytical Solutions for the Flow of a Fractional Second Grade Fluid due to a Rotational Constantly Accelerating Shear

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
M. Kamran ◽  
M. Imran ◽  
M. Athar
Keyword(s):  
Fluid Motion ◽  
Analytic Solutions ◽  
Second Grade ◽  
Governing Equations ◽  
Second Grade Fluid ◽  
Coaxial Cylinders ◽  
Exact Analytic Solutions ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid ◽  
Similar Solutions

Exact analytic solutions are obtained for the flow of a generalized second grade fluid in an annular region between two infinite coaxial cylinders. The fractional calculus approach in the governing equations of a second grade fluid is used. The exact analytic solutions are constructed 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 constantly accelerating shear. The solutions that have been obtained satisfy both the governing equations and all imposed initial and boundary conditions. Moreover, they can be easily specialized to give similar solutions for second grade and Newtonian fluids. Finally, the influence of the pertinent parameters on the fluid motion, as well as a comparison between the three models, is underlined by graphical illustrations.

scholarly journals Three-Dimensional Couette Flow of a Second-Grade Fluid Along Periodic Injection/Suction

Coatings ◽  
2019 ◽  
Vol 9 (9) ◽  
pp. 553 ◽  
Author(s):  
Muhammad Afzal Rana ◽  
Yasar Ali ◽  
Babar Ahmad ◽  
Muhammad Touseef Afzal Rana
Keyword(s):  
Transverse Direction ◽  
Flow Direction ◽  
Three Dimensional ◽  
Analytic Solutions ◽  
Main Flow ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Suction Velocity ◽  
Grade Fluid ◽  
Main Flow Direction

This work explores the three-dimensional laminar flow of an incompressible second-grade fluid between two parallel infinite plates. The assumed suction velocity comprises a basic steady dispersal with a superimposed weak transversally fluctuating distribution. Because of variation of suction velocity in transverse direction on the wall, the problem turns out to be three-dimensional. Analytic solutions for velocity field, pressure and skin friction are presented and effects of dimensionless parameters emerging in the model are discussed. It is observed that the non-Newtonian parameter plays dynamic part to rheostat the velocity component along main flow direction.

scholarly journals Analytic solution of Stokes second problem for second-grade fluid

2006 ◽  
Vol 2006 ◽  
pp. 1-8 ◽  
Author(s):  
S. Asghar ◽  
S. Nadeem ◽  
K. Hanif ◽  
T. Hayat
Keyword(s):  
Analytical Solution ◽  
Laplace Transformation ◽  
Material Parameter ◽  
Analytic Solution ◽  
Second Grade ◽  
Perturbation Techniques ◽  
Second Grade Fluid ◽  
Transient Solutions ◽  
Grade Fluid ◽  
Stokes Second Problem

Using Laplace transformation and perturbation techniques, analytical solution is obtained for unsteady Stokes' second problem. Expressions for steady and transient solutions are explicitly determined. These solutions depend strongly upon the material parameter of second-grade fluid. It is shown that phase velocity decreases by increasing material parameter of second-grade fluid.

scholarly journals A note on “Taylor–Couette flow of a generalized second grade fluid due to a constant couple”

2010 ◽  
Vol 15 (2) ◽  
pp. 155-158 ◽  
Author(s):  
C. Fetecau ◽  
A. U. Awan ◽  
M. Athar
Keyword(s):  
Exact Solution ◽  
Steady State ◽  
Unsteady Flow ◽  
Couette Flow ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid ◽  
New Form ◽  
Second Grade Fluids

In this brief note, we show that the unsteady flow of a generalized second grade fluid due to a constant couple, as well as the similar flow of Newtonian and ordinary second grade fluids, ultimately becomes steady. For this, a new form of the exact solution for velocity is established. This solution is presented as a sum of the steady and transient components. The required time to reach the steady-state is obtained by graphical illustrations.

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.

scholarly journals Heat transfer analysis on rotating flow of a second-grade fluid past a porous plate with variable suction

2005 ◽  
Vol 2005 (5) ◽  
pp. 555-582 ◽  
Author(s):  
T. Hayat ◽  
Zaheer Abbas ◽  
S. Asghar
Keyword(s):  
Heat Transfer ◽  
Skin Friction ◽  
Porous Plate ◽  
Analytic Solutions ◽  
Heat Transfer Analysis ◽  
Second Grade ◽  
Rotating Flow ◽  
Momentum And Heat Transfer ◽  
Grade Fluid ◽  
Higher Temperature

We deal with the study of momentum and heat transfer characteristics in a second-grade rotating flow past a porous plate. The analysis is performed when the suction velocity normal to the plate, as well as the external flow velocity, varies periodically with time. The plate is assumed at a higher temperature than the fluid. Analytic solutions for velocity, skin friction, and temperature are derived. The effects of various parameters of physical interest on the velocity, skin friction, and temperature are shown and discussed in detail.

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