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.

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 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 hydromagnetic flow through porous medium near an accelerating plate in the presence of magnetic field

2018 ◽  
Vol 25 (3) ◽  
pp. 409-418 ◽  
Author(s):  
Amir Khan ◽  
Gul Zaman
Keyword(s):  
Shear Stress ◽  
Second Grade ◽  
Porous Space ◽  
Second Grade Fluid ◽  
New Exact Solutions ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid ◽  
Similar Solutions

AbstractNew exact solutions are obtained for unsteady magnetohydrodynamic (MHD) flows of a generalized second-grade fluid near a uniform accelerating plate. The generalized second-grade fluid saturates the porous space. A fractional derivative is used in the governing equation. Analytical expressions for the velocity and shear stress fields are obtained by using the Laplace transform technique for fractional calculus. The obtained solutions are expressed in the series form in terms of Fox H-functions. Similar solutions for an ordinary second-grade fluid passing through a porous space are also derived. Moreover, several graphs are constructed for the pertinent parameters to analyze the characteristics of the velocity and shear stress field.

scholarly journals Taylor–Couette flow of a generalized second grade fluid due to a constant couple

2010 ◽  
Vol 15 (1) ◽  
pp. 3-13 ◽  
Author(s):  
M. Athar ◽  
M. Kamran ◽  
C. Fetecau
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Boundary Conditions ◽  
Unit Length ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Coaxial Cylinders ◽  
Constant Torque ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid

The velocity field and the adequate shear stress, corresponding to the flow of a generalized second grade fluid in an annular region 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 constant torque f per unit length. The solutions that have been obtained satisfy all imposed initial and boundary conditions. For β → 1 or β → 1 and α1 → 0, the corresponding solutions for an ordinary second grade fluid, respectively, for the Newtonian fluid, performing the same motion, are obtained as limiting cases.

scholarly journals Flows with Slip of Oldroyd-B Fluids over a Moving Plate

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Abdul Shakeel ◽  
Sohail Ahmad ◽  
Hamid Khan ◽  
Nehad Ali Shah ◽  
Sami Ul Haq
Keyword(s):  
Integral Transform ◽  
Fluid Velocity ◽  
Translational Motion ◽  
Fluid Motion ◽  
Maxwell Fluid ◽  
Analytic Solutions ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Moving Plate ◽  
Grade Fluid

A general investigation has been made and analytic solutions are provided corresponding to the flows of an Oldroyd-B fluid, under the consideration of slip condition at the boundary. The fluid motion is generated by the flat plate which has a translational motion in its plane with a time-dependent velocity. The adequate integral transform approach is employed to find analytic solutions for the velocity field. Solutions for the flows corresponding to Maxwell fluid, second-grade fluid, and Newtonian fluid are also determined in both cases, namely, flows with slip on the boundary and flows with no slip on the boundary, respectively. Some of our results were compared with other results from the literature. The effects of several emerging dimensionless and pertinent parameters on the fluid velocity have been studied theoretically as well as graphically in the paper.

scholarly journals A new fourth-order explicit group method in the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Muhammad Asim Khan ◽  
Norhashidah Hj. Mohd Ali ◽  
Nur Nadiah Abd Hamid
Keyword(s):  
Finite Difference ◽  
Stokes Problem ◽  
Stability And Convergence ◽  
Second Grade ◽  
Group Method ◽  
Two Dimensional ◽  
Second Grade Fluid ◽  
The Matrix ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid

Abstract In this article, a new explicit group iterative scheme is developed for the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid. The proposed scheme is based on the high-order compact Crank–Nicolson finite difference method. The resulting scheme consists of three-level finite difference approximations. The stability and convergence of the proposed method are studied using the matrix energy method. Finally, some numerical examples are provided to show the accuracy of the proposed method.

Transient Free Convection Mass Transfer of Second-grade Fluid Flow with Wall Transpiration

CFD Letters ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 35-52
Author(s):  
Mohamad Alif Ismail ◽  
Mohamad Hidayad Ahmad Kamal ◽  
Lim Yeou Jiann ◽  
Anati Ali ◽  
Sharidan Shafie
Keyword(s):  
Mass Transfer ◽  
Schmidt Number ◽  
Second Grade ◽  
Concentration Profiles ◽  
Governing Equations ◽  
Second Grade Fluid ◽  
Wall Suction ◽  
Viscoelastic Parameter ◽  
Grade Fluid ◽  
Wall Injection

The study of mass transfer in the non-Newtonian fluid is essential in understanding the engine lubrication, the cooling system of electronic devices, and the manufacturing process of the chemical industry. Optimal performance of the practical applications requires the appropriate conditions. The unsteady transient free convective flow of second-grade fluid with mass transfer and wall transpiration is concerned in the present communication. The behavior of the second-grade fluid under the influence of injection or suction is discussed. Suitable non-dimensional variables are utilized to transform the governing equations into non-dimensional governing equations. A Maple solver “pdsolve” that is using the centered implicit scheme of a finite difference method is utilized to solve the dimensionless governing equations numerically. The effects of wall injection or suction parameter, second-grade fluid viscoelastic parameter, Schmidt number, and modified Grashof number on the velocity and concentration profiles are graphically displayed and analyzed. The results show that with increasing wall suction, viscoelastic parameter, and Schmidt number, the velocity and concentration profiles decrease. Whereas, the velocity profiles show an opposite tendency in situations of wall injection. The wall suction has increased the skin friction and also the rate of mass diffusion in the second-grade fluid.

Flows of a generalized second grade fluid in a cylinder due to a velocity shock

2019 ◽  
Vol 60 ◽  
pp. 720-730 ◽  
Author(s):  
Itrat Abbas Mirza ◽  
Muhammad Saeed Akram ◽  
Imran Siddique
Keyword(s):  
Second Grade ◽  
Second Grade Fluid ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid
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