Abstract
With the development of medical science, non-Newtonian fluids have taken on added significance with a variety of applications in real life. The flow of non-Newtonian fluids in tubes and pipes plays a vital role in daily life. The examples of such applications are medical instruments, human body, machines, etc. The study of such mechanisms with the Newtonian fluids has not been found satisfactory due to nonlinear behavior of stress strain relationship. In the present analysis, the study of peristaltic flow in a tube has been carried out taking into account the non-Newtonian fluid : Rabinowitsch fluid model. Considering the significant terms in Navier-Stokes equations, solutions have been derived for fluid flow in axial direction in terms of pressure gradient. Using the continuity of flow, and exact solution has been derived for fluid pressure at wall. To establish the applicability of the solution, results for pressure rise at wall, pressure gradient and streamlines have been presented graphically.
Highlights
In last few decades, the analysis of the peristaltic flows has played very important role in the development of medical science, and received much attention of the bio-mechanics researchers, though, it has various applications engineering and industries too
It has been found that the use of high molecular weight polymer solutions can give rise to a non-Newtonian fluid with minimized sensitivity of change in shearing strain rate (Spikes, 1994)
The following stress-strain relation holds for Rabinowitsch fluid model for one dimensional fluid flow:
Summary
The analysis of the peristaltic flows has played very important role in the development of medical science, and received much attention of the bio-mechanics researchers, though, it has various applications engineering and industries too. It has been found that the use of high molecular weight polymer solutions (viscosity index improvers) can give rise to a non-Newtonian fluid with minimized sensitivity of change in shearing strain rate (Spikes, 1994). Rabinowitsch fluid model (Singh, Gupta and Kapur, 2011) is an established model (Wada and Hayashi, 1971) to analyse the non-Newtonian behaviour of the fluid.
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