Unsteady peristaltic transport of Maxwell fluid through finite length tube: application to oesophageal swallowing

Abstract

This paper analytically investigates the unsteady peristaltic transport of the Maxwell fluid in a finite tube. The walls of the tube are subjected to the contraction waves that do not cross the stationary boundaries. The analysis is carried out by a long wavelength approximation in the non-dimensional form. The expressions for the axial and radial velocities are derived. The pressures across the wavelength and the tubelength are also estimated. The reflux phenomenon is discussed, which culminates into the determination of the reflux limit. Mathematical formulations are physically interpreted for the flow of masticated food materials such as bread and white eggs in the oesophagus. It is revealed that the Maxwell fluids are favorable to flow in the oesophagus as compared with the Newtonian fluids. This endorses the experimental finding of Takahashi et al. (Takahashi, T., Ogoshi, H., Miyamoto, K., and Yao, M. L. Viscoelastic properties of commercial plain yoghurts and trial foods for swallowing disorders. Rheology, 27, 169-172 (1999)). It is further revealed that the relaxation time does not affect the shear stress and the reflux limit. It is found that the pressure peaks are identical in the integral case while different in the non-integral case.

Magnetohydrodynamic Peristaltic Flow of a Pseudoplastic Fluid in a Curved Channel

“…After the experimental study of Latham [1], a number of investigations have been presented on peristalsis under different flow geometries, assumptions, and fluid models. Few recent representative studies in this direction are done by Tripathi [2 -5]; Pandey and Chaube [6]; Pandey and Tripathi [7]; Srinivas and Kothandapani [8]; Abd elmaboud and Mekheimer [9]; Hayat et al [10,11]; Mekheimer and Abd elmaboud [12]; Mekheimer et al [13]; Abd elmaboud and Mekheimer [14]; Gharsseldien et al [15]; Tripathi and Bég [16]; Tripathi et al [17 -19]; Bég [20] and many others.…”

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

“…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 wall does work on the fluid [Brasseur and Corssin, 1987;Naciri, 1981;Pandey and Tripathi, 2012;Shapiro et al, 1969;Tripathi et al, 2011].…”

Mathematical Modelling of Swallowing of Viscoelastic Nature Food Through the Oesophagus Affected by Hiatus Hernia

“…Further, Pandey and Chaube [12] discussed the peristaltic transport of viscoelastic fluid through an axisymmetric circular tube with varying cross sections. Pandey and Tripathi [13] also analyzed unsteady peristaltic transport of Maxwell fluid through a finite length tube. Sankad et al [14] studied the peristaltic transport of a Herschel-Bulkley fluid in a channel of the non-uniform cross section.…”