Modeling of Nonlinear Variable Viscosity on Peristaltic Transport of Fluid with Slip Boundary Conditions: Application to Bile Flow in Duct

Abstract

The present article deals with variable viscosity on the peristaltic transport of bile in an inclined duct under the action of slip boundary conditions. The wall geometry is described by the sinusoidal wave propagating in the axial direction with different amplitude and with constant speed. The flow of fluid is examined in a wave frame of reference, moving with the velocity of the wave.  Mathematical modeling of the problem includes equations of motion and continuity. The fluid flow is investigated by converting the equations into a non-dimensionalized form simplified considering long wavelength and low Reynolds number approximation. The analytic expressions for axial velocity, pressure gradient, and pressure rise over a single wavelength cycle are obtained. The impact of various parameters such as slip parameter, viscosity parameter, angle of inclination, gravity parameter and amplitude ratio on axial velocity, pressure gradient and pressure rise are discussed in detail by plotting graphs in MATLAB R2018b software. In this article, a comparison of linear and nonlinear variation of viscosity of bile has been made. It is concluded that velocity and pressure rise is more in case linear variation of viscosity, whereas more pressure gradient is required in case of nonlinear variation of viscosity.