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Translational symmetries in variables <jats:italic>t<\/jats:italic> and <jats:italic>y<\/jats:italic> are employed to construct two different classes of closed\u2010form 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.<\/jats:p>","DOI":"10.1155\/2012\/931587","type":"journal-article","created":{"date-parts":[[2012,11,1]],"date-time":"2012-11-01T21:02:43Z","timestamp":1351803763000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Closed\u2010Form Solutions for a Nonlinear Partial Differential Equation Arising in the Study of a Fourth Grade Fluid Model"],"prefix":"10.1155","volume":"2012","author":[{"given":"Taha","family":"Aziz","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"F. 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