The laminar flow of dilute polymer solutions around circular cylinders

Abstract

This paper describes the measurements of heat transfer and drag for the flow of dilute polymer solutions around very small cylinders. The thermal experiments were carried out at Reynolds numbers less than 50, and the results establish the dependence of the heat transfer on fluid velocity, cylinder diameter, solution concentration, and polymer molecular weight. The drag measurements were conducted with the same type of solutions and in the same Reynolds-number range. To complement the heat-transfer and drag measurements, the flows around a cylinder and through an orifice were examined visually. These flow-visualization studies showed that the streamline pattern with dilute polymer solutions can be significantly different from that with Newtonian fluids because of viscoelastic effects.An analysis of Rouse's theory of macromolecules shows that for low accelerations a dilute polymer solution behaves mechanically like a Maxwell model. The analysis thereby produces a relaxation time, a single parameter representing the elasticity of the fluid, which can be related to the properties of the solute and solvent. This relaxation time is contained in a new dimensionless group which governs dynamic similarity when induced elastic stresses dominate viscous stresses in the flow around a circular cylinder. The dimensionless group is shown to correlate the thermal data when the heat transfer does not depend on the free stream velocity.