## Journal of Applied Mathematics

• J. Appl. Math.
• Volume 2012, Special Issue (2012), Article ID 931587, 16 pages.

### Closed-Form Solutions for a Nonlinear Partial Differential Equation Arising in the Study of a Fourth Grade Fluid Model

#### Abstract

The unsteady unidirectional flow of an incompressible fourth grade fluid bounded by a suddenly moved rigid plate is studied. The governing nonlinear higher order partial differential equation for this flow in a semiinfinite domain is modelled. Translational symmetries in variables $t$ and $y$ are employed to construct two different classes of closed-form travelling wave solutions of the model equation. A conditional symmetry solution of the model equation is also obtained. The physical behavior and the properties of various interesting flow parameters on the structure of the velocity are presented and discussed. In particular, the significance of the rheological effects are mentioned.

#### Article information

Source
J. Appl. Math., Volume 2012, Special Issue (2012), Article ID 931587, 16 pages.

Dates
First available in Project Euclid: 3 January 2013

https://projecteuclid.org/euclid.jam/1357180200

Digital Object Identifier
doi:10.1155/2012/931587

Mathematical Reviews number (MathSciNet)
MR2991604

Zentralblatt MATH identifier
1308.35044

#### Citation

Aziz, Taha; Mahomed, F. M. Closed-Form Solutions for a Nonlinear Partial Differential Equation Arising in the Study of a Fourth Grade Fluid Model. J. Appl. Math. 2012, Special Issue (2012), Article ID 931587, 16 pages. doi:10.1155/2012/931587. https://projecteuclid.org/euclid.jam/1357180200

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