Peristaltic motion of third grade fluid in curved channel

Abstract

Analysis is performed to study the slip effects on the peristaltic flow of non-Newtonian fluid in a curved channel with wall properties. The resulting nonlinear partial differential equations are transformed to a single ordinary differential equation in a stream function by using the assumptions of long wavelength and low Reynolds number. This differential equation is solved numerically by employing the built-in routine for solving nonlinear boundary value problems (BVPs) through the software Mathematica. In addition, the analytic solutions for small Deborah number are computed with a regular perturbation technique. It is noticed that the symmetry of bolus is destroyed in a curved channel. An intensification in the slip effect results in a larger magnitude of axial velocity. Further, the size and circulation of the trapped boluses increase with an increase in the slip parameter. Different from the case of planar channel, the axial velocity profiles are tilted towards the lower part of the channel. A comparative study between analytic and numerical solutions shows excellent agreement.