Similarity Solutions Of The Boundary Layer Equations For A Nonlinearly Stretching Sheet

Consideration is given to a class of nonlinear third-order differential equations arising in fluid flow over a nonlinearly stretching sheet. Existence of a solution of the nonlinear third-order differential equation over 0\u3cη\u3c∞ is established in this paper, answering the open question of Vajravelu and Cannon (Appl. Math. Comput. 2006; 181:609-618). That is, we prove with estimates independent of R for solutions of the third-order differential equation on [0,R]. The existence of a solution on 0\u3cη\u3c∞ follows from the Ascoli-Arzela Theorem. Furthermore, numerical solutions are obtained and presented through graphs, and the influence of the physical parameter on the flow characteristics is discussed. Copyright © 2009 John Wiley & Sons, Ltd