Peristaltic Flow of Viscoelastic Giesekus Fluid through Concentric Annuli with Heat Transfer

Abstract

The flow of non-Newtonian Giesekus fluid through a peristaltic annulus is presented. The interaction between the flow velocity and the heat transfer distributions is obtained due to the viscous dissipation in the energy equation. Due to the slow motion of the Giesekus fluid (Polymer solution), the small value of the Reynolds number is assumed. A modified longwave approximation, due to a series of the wavenumber, is applied to determine the zero as well as the first order distributions for the stress components, the velocity, and temperature. Also, the pressure rise, the radial position of the zero shear rates, and the rate of the heat flux are obtained numerically. The rheological properties of the non-Newtonian Giesekus fluid are discussed due to the mobility parameter and the time relaxation parameter. The graphical results illustrate that the mobility parameter and the time relaxation parameter enhance the flow. Meanwhile, the flow increases due to the peristaltic motion. According to the viscous dissipation effect, the temperature rises with the time relaxation parameter. Also, the contours of the streamlines are presented and the results illustrate that the trapping bolus disappears for the fluids with small-time relaxation and for the flow through a fixed channel without the peristalsis.