Peristaltic Pumping of a Generalized Newtonian Fluid in an Elastic Tube

The paper investigates the peristaltic pumping of an incompressible non-Newtonian fluid in an elastic tube with long wavelengths and low Reynolds number approximations. Carreau fluid model is considered for present study to describe the peristaltic flow characteristics of non- Newtonian fluid in an elastic tube. Carreau fluid is a generalized Newtonian fluid which exhibits Newtonian behaviour for and it resembles as a power-law model at higher shear rates. For it exhibits shear-thinning property, i.e., the apparent viscosity reduces with increasing shear rate. The equations governing the fluid flow are solved with usual perturbation expansion by taking Weissenberg number as a perturbation parameter. The expressions for axial velocity, stream function and volume flow rate as function of pressure difference are derived. The effects of various pertinent parameters on variation of flux for a Carreau fluid flow through an elastic tube along with peristalsis are calculated and interpreted through graphs. The pressure rise per wavelength and shear stress distribution for different values of physical parameters are calculated and presented. Trapping phenomenon is presented graphically to understand the physical behaviour of various parameters. The difference in flux variation is examined by two different models of Rubinow and Keller (۱۹۷۲) and Mazumdar (۱۹۹۲). It is observed that in elastic tubes, the flux of Carreau fluid with peristalsis is more when the tension relation is a fifth degree polynomial as compared to exponential curve. When the power-law index or Weissenberg number and without peristalsis, the present results are similar to the observations of Rubinow and Keller (۱۹۷۲). Further, the relation between the function and radius of the elastic tube for both Newtonian, non-Newtonian cases are discussed graphically and these findings are identical with the investigations of Mazumdar (۱۹۹۲). The results observed for the present flow characteristics reports several interesting behaviours that warrant further study of physiological fluids in elastic tubes with peristalsis.

Keywords:

Peristaltic flow , Elastic tube , Non , Weissenberg number , law index , Newtonian fluid , Power