Affiliations: Mathematics Department, Faculty of Science and Arts, Khulais, King Abdulaziz University (KAU), Jeddah, KSA | Mathematics Department, Faculty of Science, Al-Azhar University (Assiut Branch), Assiut, Egypt | Mathematics & Statistic Department, Faculty of Science, Taif University, Taif, Saudi Arabia | Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, Cairo, Egypt | Basic Science Department, Faculty of Engineering, The British University in Egypt, Al-Shorouk City, Cairo, Egypt
Note:  Corresponding author: Y. Abd Elmaboud, Tel.: +966538239670; E-mail: email@example.com
Abstract: Peristaltic motion of an incompressible Newtonian fluid with variable viscosity induced by periodic sinusoidal traveling wave propagating along the walls of a finite-length tube has been investigated. A perturbation method of solution is sought. The viscosity parameter α (α << 1) is chosen as a perturbation parameter and the governing equations are developed up to the first-order in the viscosity parameter (α). The analytical solution has been derived for the radial velocity at the tube wall, the axial pressure gradient across the length of the tube, and the wall shear stress under the assumption of low Reynolds number and long wavelength approximation. The impacts of physical parameters such as the viscosity and the parameter determining the shape of the constriction on the pressure distribution and on the wall shear stress for integral and non-integral number of waves are illustrated. The main conclusion that can be drawn out of this study is that the peaks of pressure fluctuate with time and attain different values with non-integral numbers of peristaltic waves. The considered problem is very applicable in study of biological flow and industrial flow.
Keywords: Peristalsis, finite tube, variable viscosity, lubrication theory