A STUDY OF INFLUENCE OF NON-UNIFORM PARAMETER ON PERISTALTIC TRANSPORT OF CARREAU FLUID THROUGH A FINITE LENGTH CHANNEL: APPLICATION TO BILE FLOW

Abstract

The present manuscript is detailed here to analyze the impact of non uniform parameter on different types of tapered
duct which has a great similarity to bile flow through narrow or wider duct. For present analysis fluid is taken as non-Newtonian,
also Carreau fluid model is taken into interest to describe the flow characteristic of non-Newtonian bile. The wall geometry of duct is
described by the sinusoidal wave propagating along the axial direction. The governing equations of motion and continuity are simplified
with the analytical approach by considering long wavelength and low Reynolds number approximation. Analytical solutions have been
calculated for velocity, pressure gradient, shear stress and pressure rise also the impact of effecting parameters such as power index,
Weissenberg number, amplitude ratio and non-uniform parameter are discussed for different types of ducts (i.e., converging duct,
diverging duct and non-tapered duct) by plotting the graphs in MATLAB R2018b software. It is found that Bile velocity is captured
maximum in case of converging duct. Also, for Newtonian bile i.e., n = 1 or We = 0 bile reaches to its maximum velocity also When
bile is considered as Newtonian fluid (n = 1 or We = 0) less amount of wall shear stress S
rz is noticed.