Shock Wave Solutions for Some Nonlinear Flow Models Arising in the Study of a Non-Newtonian Third 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...

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Bibliographic Details
Published inMathematical problems in engineering Vol. 2013; no. 2013; pp. 1 - 6
Main Authors Mahomed, Fazal Mahmood, Fatima, A., Moitsheki, Raseelo Joel, Aziz, Taha
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Publishing Corporation 01.01.2013
Hindawi Limited
Subjects
Applied mathematics
Engineering
Enhanced oil recovery
Geometry
Lie groups
Mathematical models
Mathematical problems
Mechanics
Methods
Non-Newtonian fluids
Nonlinear differential equations
Nonlinear equations
Physical properties
Viscosity
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Summary: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.
ISSN:1024-123X
1563-5147
DOI:10.1155/2013/602902