Relative Influences of Inertia and Polymeric Viscoelastic Effects on Nusselt Numbers within Rotating Couette Flows

Abstract

In past investigations of elastic instabilities and elastic turbulence, almost no attention has been devoted to the effects and influences of inertial phenomena. Within the present investigation, Nusselt number data are provided to illustrate the relative influences of inertia and polymeric viscoelastic phenomena within a rotating Couette flow (RCF) environment. Data are provided from experimental measurements of local surface heat transfer characteristics for different flow passage heights, one radial position, and different values of disk rotational speed for polyacrylamide polymer concentrations ρ of 0 ppm, 100 ppm, 150 ppm, and 300 ppm. With this approach, data for a wide range of shear rate γ˙ values, Weissenberg numbers, and first normal stress difference values are provided. Nusselt number data are provided as dependent upon a newly developed P′ parameter, equal to ReEI/Re0.22, which collapse into a single distribution over the range of P′ values considered which range from 0 to about 182. Such characteristics indicate that the P′ parameter provides an appropriate means to simultaneously account for the relative influences of inertia and polymeric viscoelastic effects. The use of such a power law dependence for Re additionally gives P′ values which are dominated by ReEI values when the Weissenberg number Wi is greater than the elastic instability transition onset value. The experimental conditions associated with this value correspond to the change from inertia domination (with buoyance influences) to polymeric viscoelastic domination which occurs for shear rates in the vicinity of 11 to 12 s−1. For Weissenberg numbers greater than the onset value, Nusselt numbers associated with H = 5 mm are generally the highest values measured, with magnitudes that steadily increase with γ˙. Associated Nusselt numbers become as high as about 3.0, whereas zero-shear rate values (obtained with zero rotation) are in the vicinity of 1.0. At lower Weissenberg number magnitudes (below the transition onset value), Nusselt numbers cover a wide range of values as experimental conditions and configuration are varied, as a consequence of the complicated and simultaneous influences of inertia, buoyancy, and dilute polymer presence.