Superposition of longitudinal and plane flows of a non-Newtonian fluid between eccentric cylinders

Abstract

Results obtained in previous papers on the flow of an incompressible non-Newtonian fluid, satisfying the second-order Rivlin—Ericksen constitutive equation, in the annular region between infinite circular cylinders with parallel axes, which results from the longitudinal steady motion of the inner cylinder, or the existence of a longitudinal pressure gradient, or the steady rotation of the cylinders about their axes, are used to calculate the effect on the forces exerted by the fluid on the cylinders when certain of these flows are superposed. As an asymptotic case, the forces exerted by the fluid on an infinite cylinder immersed in a half-space of the fluid bounder by a plane rigid wall are obtained when the cylinder moves parallel to the wall with a constant velocity inclined at an arbitrary angle to its length.