Peristaltic Flow of Giesekus Fluids through Curved Channels: an Approximate Solution

Peristaltic flow of a viscoelastic fluid is numerically studied in a plane channel. The fluid is assumed to obey the Giesekus model as its constitutive equation, and the flow is assumed to be occurring under incompressible, laminar, and two-dimensional conditions. To simplify the equations of motion, use is made of the long-wavelength assumption together with the creeping-flow assumption. It is shown that for this particular fluid model, the governing equations are reduced to a system of coupled nonlinear ODEs, which are solved numerically using finite difference method. Numerical results show that the elastic behavior of a fluid can significantly decrease the pressure rise of peristaltic pumps. On the other hand, a radially-imposed magnetic field is shown to increase the pressure rise of the pump when the flow rate is less than a certain value. The results are interpreted in terms of the extensional-flow behavior of the fluid as represented by the fluid's mobility (or, extensional) factor.