Effects of fluid shear-thinning and yield stress on free convection in concentric and eccentric cylindrical annuli

Abstract

Laminar free convection in yield-pseudoplastic fluids (the Herschel-Bulkley model) for concentric and eccentric cylindrical annuli has been studied numerically. The combined effects of shear-thinning viscosity and yield stress on the heat transfer characteristics have been examined for the following ranges of parameters: Rayleigh number, Ra (103 to 106), Oldroyd number, Od (0 to Odmax), power-law index, n (0.2–1), Prandtl number, Pr (10–100), eccentricity, ε (0–1.18) and angular position of the inner cylinder, ϕ (0° to 180°). The results are interpreted in terms of the yield surfaces, fraction of yielded fluid, streamlines, isotherms, local Nusselt number and average Nusselt number. Overall, the eccentric positioning of the heated cylinder along the vertical centreline fosters convective transport with reference to that for the case of the concentric annulus. It is possible to achieve augmentation of up to 30% in heat transfer for the case of ε = 1.18, ϕ = 0° with respect to the concentric case at Ra = 105, Pr = 10. This is ascribed to the greater fraction of the annular area occupied by the yielded fluid-like regions. Conversely, horizontal shifting of the inner cylinder to an off-centre position has an adverse effect on heat transfer. Limited transient simulations have also been run to identify the conditions for the loss of steady flow behaviour. A predictive correlation has been developed for the average Nusselt number for its estimation in new applications.