Comments on “Peristaltic flow of a Williamson fluid in an asymmetric channel” (Commun. Nonlinear Sci. Numer. Simul. 15, 1705–1716)

✍ Scribed by Konstantin Koshel

• Publisher: Elsevier Science
• Year: 2012
• Tongue: English
• Weight: 141 KB
• Volume: 17
• Category: Article
• ISSN: 1007-5704
• DOI: 10.1016/j.cnsns.2011.03.036

✦ Synopsis

This comment provides an exact solution of general ODE, when authors of original paper [1] use the perturbation methods. It is important to use the most rigorous methods of results proof. I see it will be useful to indicate the simple method of such equations solution for future use for study of non-Newtonian fluids and for similar problem of nonlinear physics. Also important discussion of analogous problem was given in [2].

In the work [1], was presented a peristaltic flow of a Williamson model in an asymmetric channel. A regular perturbation expansion method is used to obtain the analytical solution of the non-linear problem. The trapped effect was obtained. But the exact solution of non-linear problem can be obtained. Let us consider the statement from [1]: ''Since, Eq. ( 17) is non-linear equation, its exact solution may be not possible, therefore, we employ the regular perturbation to find the solution.'' Let us see Eq. ( 17) from [1]