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.

Some Exact Solutions to Equations of Motion of an Incompressible Second Grade Fluid

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
Saif Ullah ◽  
Irsa Maqbool
Keyword(s):  
Exact Solutions ◽  
Equations Of Motion ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Complex Functions ◽  
Contour Plots ◽  
Stream Functions ◽  
Grade Fluid ◽  
Steady Plane ◽  
Physical Features

In this paper, we derive some exact solutions of the equations governing the steady plane motions of an incompressible second grade fluid. For this purpose, the vorticity and stream functions both are expressed in terms of complex variables and complex functions. The derived solutions represent the flows having streamlines as a family of ellipses, parabolas, concentric circles, and rectangular hyperbolas. Some physical features of the derived solutions are also illustrated by their contour plots.

scholarly journals Unsteady stagnation point flow of a non-Newtonian second-grade fluid

2003 ◽  
Vol 2003 (60) ◽  
pp. 3797-3807 ◽  
Author(s):  
F. Labropulu ◽  
X. Xu ◽  
M. Chinichian
Keyword(s):  
Finite Difference ◽  
Stagnation Point ◽  
Infinite Plate ◽  
Second Grade ◽  
Two Dimensional ◽  
Second Grade Fluid ◽  
Harmonic Oscillations ◽  
Finite Difference Technique ◽  
Two Dimensional Flow ◽  
Grade Fluid

The unsteady two-dimensional flow of a viscoelastic second-grade fluid impinging on an infinite plate is considered. The plate is making harmonic oscillations in its own plane. A finite difference technique is employed and solutions for small and large frequencies of the oscillations are obtained.

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.

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.

Peaceman-Rachford ADI Scheme for the Two-Dimensional Flow of a Second-Grade Fluid

2009 ◽  
Author(s):  
E. Momoniat ◽  
C. Harley ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Second Grade ◽  
Two Dimensional ◽  
Second Grade Fluid ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Grade Fluid ◽  
Adi Scheme

Influence of Thermal Radiation on Blasius Flow of a Second Grade Fluid

2009 ◽  
Vol 64 (12) ◽  
pp. 827-833 ◽  
Author(s):  
Tasawar Hayat ◽  
Meraj Mustafa ◽  
Muhammad Sajid
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Skin Friction Coefficient ◽  
Second Grade ◽  
Analysis Method ◽  
Second Grade Fluid ◽  
Flow And Heat Transfer ◽  
Homotopy Analysis ◽  
Two Dimensional Flow ◽  
Grade Fluid

This work describes the series solution of two-dimensional flow and heat transfer of a second grade fluid in the presence of radiation. The governing partial differential equations are reduced into ordinary differential equations by appropriate similarity tranformation. The series solutions of the resulting ordinary differential equations are obtained by using the homotopy analysis method (HAM). The convergence of the solution is discussed explicitly. The influence of pertinent parameters on the velocity and temperature is graphically displayed and discussed. Numerical values of the skin friction coefficient and the Nusselt number are also tabulated

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
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