Exact solutions of nonlinear differential equations arising in third grade fluid flows

2004 ◽  
Vol 39 (10) ◽  
pp. 1571-1578 ◽  
Author(s):  
F.Talay Akyildiz ◽  
Hamid Bellout ◽  
K Vajravelu
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Nonlinear Differential Equations ◽  
Fluid Flows ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Grade Fluid

scholarly journals A Note on the Solutions of Some Nonlinear Equations Arising in Third-Grade Fluid Flows: An Exact Approach

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Taha Aziz ◽  
F. M. Mahomed
Keyword(s):  
Differential Equations ◽  
Numerical Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Fluid Flows ◽  
Third Grade ◽  
Physical Parameters ◽  
Third Grade Fluid ◽  
Grade Fluid ◽  
Physical Boundary ◽  
Steady State Solutions

In this communication, we utilize some basic symmetry reductions to transform the governing nonlinear partial differential equations arising in the study of third-grade fluid flows into ordinary differential equations. We obtain some simple closed-form steady-state solutions of these reduced equations. Our solutions are valid for the whole domain [0,∞) and also satisfy the physical boundary conditions. We also present the numerical solutions for some of the underlying equations. The graphs corresponding to the essential physical parameters of the flow are presented and discussed.

Generalized Couette Flow of a Third-Grade Fluid with Slip: The Exact Solutions

2010 ◽  
Vol 65 (12) ◽  
pp. 1071-1076 ◽  
Author(s):  
Rahmat Ellahi ◽  
Tasawar Hayat ◽  
Fazal Mahmood Mahomed
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Closed Form ◽  
Analytical Solutions ◽  
Present Note ◽  
Nonlinear Problems ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Flow Problems ◽  
Grade Fluid

The present note investigates the influence of slip on the generalized Couette flows of a third-grade fluid. Two flow problems are considered. The resulting equations and the boundary conditions are nonlinear. Analytical solutions of the governing nonlinear problems are found in closed form.

Thin Film Flow of a Third Grade Fluid with Variable Viscosity

2009 ◽  
Vol 64 (9-10) ◽  
pp. 553-558 ◽  
Author(s):  
Sohail Nadeem
Keyword(s):  
Thin Film ◽  
Film Flow ◽  
Variable Viscosity ◽  
Nonlinear Differential Equations ◽  
Third Grade ◽  
Outer Side ◽  
Physical Parameters ◽  
Third Grade Fluid ◽  
Thin Film Flow ◽  
Grade Fluid

The effects of variable viscosity on the flow and heat transfer in a thin film flow for a third grade fluid has been discussed. The thin film is considered on the outer side of an infinitely long vertical cylinder. The governing nonlinear differential equations of momentum and energy are solved analytically by using homotopy analysis method. The expression for the viscous dissipation and entropy generation are also defined. The graphical results are presented for various physical parameters appearing in the problem

scholarly journals Some Exact Solutions to Equations of Motion of an Incompressible Third Grade Fluid

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Saif Ullah
Keyword(s):  
Exact Solutions ◽  
Equations Of Motion ◽  
Third Grade ◽  
Solutions To Equations ◽  
Steady Flows ◽  
Third Grade Fluid ◽  
Complex Functions ◽  
Grade Fluid ◽  
Steady Plane ◽  
Transformation Methods

This investigation deals with some exact solutions of the equations governing the steady plane motions of an incompressible third grade fluid by using complex variables and complex functions. Some of the solutions admit, as particular cases, all the solutions of Moro et al. [1990, “Steady Flows of a Third Grade Fluid by Transformation Methods,” ZAMM, 70(3), pp. 189–198]

Exact solutions of a third grade fluid flow on a porous plate

2008 ◽  
Vol 202 (1) ◽  
pp. 376-382 ◽  
Author(s):  
K. Fakhar ◽  
Zhenli Xu ◽  
Cheng Yi
Keyword(s):  
Fluid Flow ◽  
Exact Solutions ◽  
Porous Plate ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Grade Fluid

Couette - Poiseuille Two-Layer Flow of a Third Grade Fluid

2013 ◽  
Vol 390 ◽  
pp. 103-110
Author(s):  
Ali R. Ansari ◽  
Maya K. Mitkova ◽  
Abdul M. Siddiqui
Keyword(s):  
Nonlinear Differential Equations ◽  
Material Constant ◽  
Immiscible Fluids ◽  
Third Grade ◽  
Third Grade Fluid ◽  
The Third ◽  
Grade Fluid ◽  
Layer Flow ◽  
Grade Material ◽  
Different Thickness

The two-layer Couette-Poiseuille flow of a third grade fluid is examined. The problem is reduced to solving nonlinear differential equations governing the motion of the two immiscible fluids in case of different thickness of layers. The solutions are used to study the effect of the third grade material parameter on the velocity profiles. The investigation focuses especially on the location of the velocity maximum as function of the viscosity and third grade material constant.

scholarly journals Shock Wave Solutions for Some Nonlinear Flow Models Arising in the Study of a Non-Newtonian Third Grade Fluid

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Taha Aziz ◽  
R. J. Moitsheki ◽  
A. Fatima ◽  
F. M. Mahomed
Keyword(s):  
Shock Wave ◽  
Differential Equations ◽  
Fluid Model ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Flow ◽  
Third Grade ◽  
Physical Parameters ◽  
Third Grade Fluid ◽  
Wave Solutions ◽  
Grade Fluid

This study is based upon constructing a new class of closed-form shock wave solutions for some nonlinear problems arising in the study of a third grade fluid model. The Lie symmetry reduction technique has been employed to reduce the governing nonlinear partial differential equations into nonlinear ordinary differential equations. The reduced equations are then solved analytically, and the shock wave solutions are constructed. The conditions on the physical parameters of the flow problems also fall out naturally in the process of the derivation of the solutions.

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