Steady laminar plume generated from a heated line in polymer solutions

Abstract

From the theoretical viewpoint, governing equations are derived for a steady laminar plume generated from a heated line in polymer solutions, in which similarity variables and the single polymer chain model are introduced. The resolved solutions imply that polymers promote the velocity in the centerline-near region but suppress that in the region far from the centerline. The equivalent effect of polymers is understood as producing two space-dependent source terms, which can explain the interaction between polymers and fluid flow from the viewpoint of energy transport. There exists a critical Weissenberg number (Wi) beyond which the promotion effect in the centerline-near region disappears, which results from the competition of stretching and relaxation of the polymer chain. Meanwhile, the corresponding modification of similarity velocity and heat transport are illustrated and validated numerically by single plume flow in polymer solutions. This work thus may contribute to the understanding of the polymer effect on single plume flow and further the heat transport enhancement mechanism in the bulk flow of turbulent Rayleigh-Bénard convection with polymers.