Nasir Ali

Recently, Maraj and Nadeem (E. N. Maraj, S. Nadeem, Z. Naturforsch. A 70, 513 (2015)) discussed the application of Rabinowitsch fluid model for the mathematical analysis of peristaltic flow in a curved channel. The mathematical analysis presented by these authors is scrutinised in detail and certain subtle details are pointed out which affect the final results.

An attempt is made to investigate the peristaltic motion of a Giesekus fluid in a planar channel under long wavelength and low Reynolds number approximations. Under these assumptions, the flow problem is modelled as a second-order nonlinear ordinary differential equation. Both approximate and exact solution of this equation are presented. The validity of the approximate solution is examined by comparing it with the exact solution. A parametric study is performed to analyze the effects of non-dimensional parameters associated with the Giesekus fluid model (a and We) on flow velocity, pressure rise per wavelength, and trapping phenomenon. It is found that the behaviour of longitudinal velocity and pattern of streamlines for a Giesekus fluid deviate from their counterparts for a Newtonian fluid by changing the parameters a and We. In fact, the magnitude of the longitudinal velocity at the center of the channel for a Giesekus fluid is less than that for a Newtonian fluid. It is also observed that the pressure rise per wavelength decreases in going form Newtonian to Giesekus fluid. Moreover, the size of trapped bolus is large and it circulates faster for a Newtonian fluid in comparison to a Giesekus fluid.

Peristaltic flow of a third grade fluid in a circular cylindrical tube is undertaken when the no-slip condition at the tube wall is no longer valid. The governing nonlinear equation together with nonlinear boundary conditions is solved analytically by means of the perturbation method for small values of the non-Newtonian parameter, the Debroah number. A numerical solution is also obtained for which no restriction is imposed on the non-Newtonian parameter involved in the governing equation and the boundary conditions. A comparison of the series solution and the numerical solution is presented. Furthermore, the effects of slip and non-Newtonian parameters on the axial velocity and stream function are discussed in detail. The salient features of pumping and trapping are discussed with particular focus on the effects of slip and non-Newtonian parameters. It is observed that an increase in the slip parameter decreases the peristaltic pumping rate for a given pressure rise. On the contrary, the peristaltic pumping rate increases with an increase in the slip parameter for a given pressure drop (copumping). The size of the trapped bolus decreases and finally vanishes for large values of the slip parameter.

An analysis is carried out to study the peristaltic motion of an incompressible Oldroyd 4-constant fluid in a planar channel. The flow modeling is first developed in dimensionless form and the governing problem is then simplified by adopting a long w