scholarly journals Exact analytical solutions for axial flow of a fractional second grade fluid between two coaxial cylinders

2011 ◽  
Vol 1 (2) ◽  
pp. 022002
Author(s):  
M. Imran ◽  
M. Kamran ◽  
M. Athar
Keyword(s):  
Analytical Solutions ◽  
Axial Flow ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Exact Analytical Solutions ◽  
Coaxial Cylinders ◽  
Grade Fluid

Some Exact Analytical Solutions for Two-Dimensional Flow of an Incompressible Second Grade Fluid

2015 ◽  
Vol 137 (10) ◽  
Author(s):  
Saif Ullah
Keyword(s):  
Analytical Solutions ◽  
Separation Of Variables ◽  
Point Of View ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Exact Analytical Solutions ◽  
Contour Plots ◽  
Two Dimensional Flow ◽  
Grade Fluid ◽  
Physical Features

This investigation deals with some exact analytical solutions of the incompressible second grade fluid by using the method based on the separation of variables. In many cases, this method can derive exact analytical solutions easier than other methods. A family of solutions is derived in this paper, which governs scientific and engineering experimentations. The derived solutions represent the flows having streamlines as a family of ellipses, parabolas, concentric circles, and rectangular hyperbolas. From practical point of view, these flows have applications in many manufacturing processes in industry. Some physical features of the derived solutions are also illustrated by their contour plots.

scholarly journals On semi-inverse solutions for the time-dependent flows of a second-grade fluid

2006 ◽  
Vol 2006 ◽  
pp. 1-22 ◽  
Author(s):  
Muhammad R. Mohyuddin ◽  
S. Asghar ◽  
T. Hayat ◽  
A. M. Siddiqui
Keyword(s):  
Stream Function ◽  
Analytical Solutions ◽  
Time Dependent ◽  
Polar Coordinates ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Inverse Solutions ◽  
Grade Fluid

This paper deals with analytical solutions for the time-dependent equations arising in a second-grade fluid. The solutions have been developed by assuming certain forms of the stream function. Expressions for velocity components are obtained for flows in plane polar, axisymmetric cylindrical, and axisymmetric spherical polar coordinates. The obtained solutions are compared with existing results.

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 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.

Effect of Magnetic Field with Parabolic Motion on Fractional Second Grade Fluid

2021 ◽  
Vol 5 (4) ◽  
pp. 163
Author(s):  
Nazish Iftikhar ◽  
Muhammad Bilal Riaz ◽  
Jan Awrejcewicz ◽  
Ali Akgül
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Analytical Solutions ◽  
Differential Operators ◽  
Fluid Velocity ◽  
Rate Of Change ◽  
Second Grade ◽  
Dynamical Process ◽  
Second Grade Fluid ◽  
Grade Fluid

This paper is an analysis of the flow of magnetohydrodynamics (MHD) second grade fluid (SGF) under the influence of chemical reaction, heat generation/absorption, ramped temperature and concentration and thermodiffusion. The fluid was made to flow through a porous medium. It has been proven in many already-published articles that heat and mass transfer do not always follow the classical mechanics process that is known as memoryless process. Therefore, the model using classical differentiation based on the rate of change cannot really replicate such a dynamical process very accurately; thus, a different concept of differentiation is needed to capture such a process. Very recently, new classes of differential operators were introduced and have been recognized to be efficient in capturing processes following the power law, the decay law and the crossover behaviors. For the study of heat and mass transfer, we applied the newly introduced differential operators to model such flow. The equations for heat, mass and momentum are established in the terms of Caputo (C), Caputo–Fabrizio (CF) and Atangana–Baleanu in Caputo sense (ABC) fractional derivatives. The Laplace transform, inversion algorithm and convolution theorem were used to derive the exact and semi-analytical solutions for all cases. The obtained analytical solutions were plotted for different values of existing parameters. It is concluded that the fluid velocity shows increasing behavior for κ, Gr and Gm, while velocity decreases for Pr and M. For Kr, both velocity and concentration curves show decreasing behavior. Fluid flow accelerates under the influence of Sr and R. Temperature and concentration profiles increase for Sr and R. Moreover, the ABC fractional operator presents a larger memory effect than C and CF fractional operators.

SECOND‐GRADE FLUID FLOW WITH POWER‐LAW HEAT FLUX AND A HEAT SOURCE

2013 ◽  
Vol 44 (8) ◽  
pp. 687-702 ◽  
Author(s):  
Tasawar Hayat ◽  
Sabir A. Shehzad ◽  
Muhammad Qasim ◽  
F. Alsaadi ◽  
Ahmed Alsaedi
Keyword(s):  
Heat Flux ◽  
Fluid Flow ◽  
Heat Source ◽  
Power Law ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Grade Fluid ◽  
Power Law Heat Flux

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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