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.

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.

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 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 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 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 Critical Study on Rotational Flow of a Fractional Oldroyd-B Fluid Induced by a Circular Cylinder

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
M. Kamran ◽  
M. Athar ◽  
M. Imran
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Circular Cylinder ◽  
Second Grade ◽  
Critical Study ◽  
Convolution Product ◽  
Rotational Flow ◽  
General Solutions ◽  
Grade Fluid ◽  
Limiting Case

We considered the unsteady flow of a fractional Oldroyd-B fluid through an infinite circular cylinder with the help of infinite Hankel and Laplace transforms. The motion of the fluid is produced by the cylinder that, at time t=0+ is subject to a time-dependent angular velocity. The established solutions have been presented under series form in terms of the generalized G functions satisfy all imposed initial and boundary conditions. The corresponding solutions for ordinary Oldroyd-B, ordinary and fractional Maxwell, ordinary and fractional second-grade, and Newtonian fluids, performing the same motion, are acquired as limiting cases of general solutions. The keynote points regarding this work to mention are that (1) we extracted the expressions for velocity field and shear stress corresponding to the motion of fractional second-grade fluid as a limiting case of general solutions; (2) the expressions for velocity field and shear stress are in the most simplified form in contrast with the studies of Siddique and Sajid (2011), in which the expression for the velocity field involves the convolution product as well as the integral of the product of generalized G functions. Finally, numerical results are presented graphically and discussed in order to reveal some physical aspects of obtained results.

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.

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