Affiliations: Chair of Fluid Dynamics, Department of Mechanical Engineering, Darmstadt University of Technology, 64289 Darmstadt, Germany | Department of Mathematics, Faculty of Basic & Applied Sciences, IIU, Islamabad, Pakistan | Department of Mathematics, Quaid-i-Azam University, 4000 Islamabad, Pakistan
Note: [] Address for correspondence: Dr. N. Ali, Department of Mathematics, Faculty of Basic & Applied Sciences, International Islamic University (IIU), Islamabad, Pakistan. E-mail: [email protected].
Abstract: 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 wavelength assumption. It is found that unlike Oldroyd 3-constant fluid, the governing problem of an Oldroyd 4-constant fluid under a long wavelength approximation contains the rheological parameters. The resulting non-linear problem has been solved numerically using a combination of the finite difference scheme and the iterative method. In addition, an analytical solution is presented for the domain near the channel center. The effect of material parameters on the pumping and trapping is discussed. A comparison with the corresponding results for a viscous Newtonian fluid is also made.
