# Explicit solution for some generalized fluids in laminar flow with slip boundary conditions

Volume 18, Issue 3, pp 272--281 Publication Date: April 13, 2018       Article History
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### Authors

Mourad Chamekh - Mathematics Department, Colleges of Science and Arts, AlKamel, University of Jeddah, KSA $\&$ University of Tunis El Manar, National Engineering School at Tunis, LAMSIN, 1002, Tunis, Tunisia Tarig. M. Elzaki - Mathematics Department, Colleges of Science and Arts, AlKamel, University of Jeddah, KSA

### Abstract

In this study, we present a new approximation method to give an explicit solution of a laminar flow using a Sisko model. This is a problem of a generalized Newtonian fluid with slip boundary conditions. The proposed method is based on the variational iteration method (VIM) combined with an approximation step. This method is validated where the exact solution is available. In addition, in order to enrich the discussion, a numerical method is presented. The results illustrate that the VIM may be more effective that the finite difference method for a dilatant fluid. However, the VIM will be inappropriate for pseudoplastic fluid cases.

### Keywords

• Sisko model
• variational iteration method
• dilatant fluid
• pseudoplastic fluid

•  47E05
•  35F30

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