## 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

**Permanent link to this document**

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