Exact solutions for n-layer concentric flow of PTT fluids through a cylindrical pipe

Abstract

Flows of multiple layers of fluids are encountered in many industrial and manufacturing processes. This paper investigates the concentric n-layer flow for Phan–Thien–Tanner (PTT) fluids through a cylindrical pipe. Finitely many immiscible non-Newtonian fluids are considered to be flowing concentrically in a tube. The flow is modelled using the exponential PTT fluid model and exact solutions for velocity fields and volume flow rates are computed. It has been shown that the corresponding results for linear PTT fluid model as well as Newtonian fluids can be deduced from the obtained expressions, and that they match with the present literature. It has also been observed that for such layered flow, the non-Newtonian parameters significantly affect the flow of fluids in adjacent layers. The effects of involved parameters on the velocity profiles are also shown graphically. We show that a unique velocity maximum exists along the axis of the pipe. Moreover, it is observed with the help of an example that layer thickness can be adjusted to obtain maximal flow rate with a given pressure gradient.