Mechanics of heated Rabinowitsch fluid in elliptic vertical duct: Peristalsis and analytical study

Abstract

This work consists of the analytical study of the peristaltic flow of heated non-Newtonian fluid flow through an elliptical duct. The flow characteristics of Pseudoplastic and Dilatant fluids are analyzed in a vertically held elliptic duct by considering the Rabinowitsch fluid model. The mathematical model is processed to a dimensionless analysis by employing adequate nondimensional variables and extended wavelength approximation. The resulting PDEs are solved analytically in the elliptic domain using the explicit boundary condition form. A simpler second-degree polynomial is presented to get the solution of temperature. These analytical solutions are examined in detail by graphical analysis. It is found that the flow velocity of Pseudoplastic fluid is more prominent than Dilatant fluid in the vicinity of the centerline. The earlier and later fluids have a maximum axial speed at the channel’s mean and close to the peristaltic boundary. The greater buoyancy force (Grashof number) enhances the Pseudoplastic fluid’s velocity but diminishes the flow velocity of Dilatant fluid. Moreover, it is noticed that the aspect ratio has less impact, and the Grashof number has an effective influence on pressure rise. The streamlines of Rabinowitsch fluid break into vortices near the deformed wall. The vortices are comparatively less in the count for Dilatant fluid than Pseudoplastic fluid for quick flow and a more significant Grashof number.