Non-Newtonian fluid flow induced by peristaltic waves in a curved channel

This paper is devoted to the study of peristaltic flow of a non-Newtonian fluid in a curved channel. The constitutive relationship between stress and shear rate for a non-Newtonian third grade fluid is used. The problem is governed by a set of two nonlinear partial differential equations. These equations are then transformed into a single nonlinear ordinary differential equation in the stream function under long wavelength and low Reynolds number assumptions. This nonlinear ordinary differential equation is solved for stream function by the shooting method using Mathematica. The important phenomenon of pumping and trapping is presented graphically and discussed in detail. It is found that for a non-Newtonian third grade fluid an increase in the curvature of the channel helps in reducing the pressure rise over one wavelength in pumping region. This result is in contrast to the previous result obtained for the pressure rise over one wavelength for a Newtonian fluid. For a Newtonian fluid, the pressure rise over one wavelength increases with an increase in the curvature. The trapping phenomenon is also altered with the presence of curvature and as a result the symmetry observed for a bolus of the trapped fluid in the case of a straight channel is destroyed and splits into two asymmetrical parts for the curved channel. The outer bolus suppresses the inner bolus towards the lower wall. It is also noted that an increase in size and circulation of boluses achieve a maximum for large values of the shear thickening parameter ββ. Moreover, the size of two boluses in a third grade fluid is larger in comparison with their counterparts in a Newtonian fluid. Further, the lower trapping limit of the flow rate ΘΘ is also changed in the curved channel. In fact the lower trapping limit of the curved channel exceeds that of the straight channel.