Interaction of Pulsatile Flow With Peristaltic Transport of a Viscoelastic Fluid: Case of a Maxwell Fluid

Abstract

This article analytically investigates the interaction of pulsatile flow with peristaltic transport of a viscoelastic Maxwell fluid in a cylindrical tube. The flow is considered unsteady even in the wave frame analysis where we impose a periodic pressure gradient. This transport is studied under low Reynolds number and long wavelength approximations. The governing equations are developed up to the second-order in the Deborah number and the Womersley number. We first analyzed the impact of the pulsatile flow, of the occlusion and of the viscoelastic effects of fluid on the pressure rise and on the friction force. Physical behavior of different parameters of the problem has been graphically presented and the influence of these parameters on the mechanical efficiency has been analyzed.

Effects of Rheological Parameters of a Viscoplastic Fluid on Peristaltic Pumping in a Cylindrical Tube

“…The mechanical efficiency is defined as the ratio between the average rate per wavelength at which work is done by the moving fluid against a pressure head and the average rate at which the walls do work on the fluid [8]. The expression of E is found as follows [9,10]:…”

Peristaltic transport of a fractional Burgers’ fluid with variable viscosity through an inclined tube

“…The mechanical e ciency is de ned as the ratio between the average rate per wavelength at which work is done by the moving uid against a pressure head and the average rate at which the walls do work on the uid [9,29]. We nd the expression of the mechanical e ciency E as follows :…”

“…These uids play an important role in uid mechanics. For example, Maxwell, Oldroyd, Jeffrey, Johnson-Segalman, Thein-Tanner, Micropolar, Third and Fourth grade uids have all been the subject of work, such as [9][10][11][12][13][14][15][16] respectively. More recently in rheology, the study of viscoelastic uids ows with fractional derivatives play an important role.…”

Effects of Heat Transfer and an Endoscope on Peristaltic Flow of a Fractional Maxwell Fluid in a Vertical Tube

“…The peristaltic transport of a Newtonian fluid at long wavelengths at low Reynolds number has been studied with particles suspended by Kaimal [2] or without particles by Shapiro et al [3] and by Mishra and Rao [4]. The non-Newtonian effects of fluids on the peristaltic transport have been studied for a third-grade fluid by Ali et al [5], for a Jeffrey fluid by Abd-Alla et al [6], for a Maxwell model by Rachid and Ouazzani [7], for a Herschel-Bulkley fluid by Medhavi [8], or for a power-law fluid by Shukla and Gupta [9]. The effect of an endoscope on peristaltic flow for a Newtonian fluid through a nonuniform annulus has been analyzed by Mekheimer [10].…”