Peristaltic flow of Sisko fluid in a uniform inclined tube

We have analyzed an incompressible Sisko fluid through an axisymmetric uniform tube with a sinusoidal wave propagating down its walls. The present analysis of non-Newtonian fluid is investigated under the considerations of long wavelength and low Reynolds number approximation. The analytic solution is obtained using (i) the regular perturbation method (ii) the Homotopy analysis method (HAM). The comparison of both the solutions is presented graphically. The results for the pressure rise, frictional force and pressure gradient have been calculated numerically and the results are studied for various values of the physical parameters of interest, such as α (angle of inclination), b* (Sisko fluid parameter), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\phi}$$\end{document} (amplitude ratio) and n (power law index). Trapping phenomena is discussed at the end of the article.