Porous Lining and Inclination Effects on Peristaltic Flow in a Non-Uniform Tube

Abstract

The consequences of varying pressure drop on a Herschel-Bulkley fluid as it flows through two-dimensional non-uniform porous tube have been explored. The governing equations of the model were solved analytically under long wavelength and low Reynolds number to determine the behavior of the fluid within the given conditions. Exact solutions are derived for the velocity field, stream functions, and pressure gradient. The observations disclose that an increase in the porous thickening of the wall enhances the pressure rise. The rise in Darcy’s numbers reduces the pressure rise. This suggests an inverse relationship between Darcy’s number and pressure difference. Also, the impact of various parameters involved in the solutions is presented graphically. The article concludes with a discussion on the trapping phenomena for Herschel-Bulkley fluid.