Secondary flows in tubes of arbitrary shape

Abstract

Publisher Summary This chapter considers the simple fluid of multiple integral-type models with fading memory. Secondary flows are determined in the case of laminar longitudinal flows in approximately triangular and square conduits, when the flow is driven by small-amplitude oscillatory pressure gradients. The chapter presents the mathematical background and determining the velocity field of laminar Newtonian unsteady flow in non-circular pipes. This is followed by an analysis of the pulsating flow in circular pipes of a viscoelastic fading memory fluid of the multiple integral type. A mathematical expression for the axial velocity is developed for flow in non-circular pipes driven by a pressure gradient oscillating around a non-zero mean. The analytical steps that lead to the determination of the transversal velocity field are developed. Plots that depict the main features of axial and secondary flow fields are also presented. Fully developed Newtonian flows in pipes are rectilinear when they are driven by a longitudinal pressure gradient, properties are kept constant, no wall-suction is considered, and the pipe is a straight cylinder of arbitrary cross-section. No secondary flows are possible under these conditions. The linearity of the equations of motion makes it possible to use a wide variety of analytical methods that yield either exact closed-form, or approximate solutions.