Representative velocity scale of Rayleigh‐Bénard convection with shear‐thinning fluids

Abstract

Although natural convection is frequently encountered in various chemical processes, Rayleigh number (Ra) cannot be defined fully in shear‐thinning fluid systems. In particular, the velocity scale, which is necessary to estimate the effective viscosity of the system, should be discussed carefully. Thus, in this study, the representative velocity scale of Rayleigh‐Bénard (RB) convection, which is a typical example of natural convection, with shear‐thinning fluids was investigated based on the velocity fields obtained using computational fluid dynamics. Numerical simulations revealed that the critical temperature difference at which RB convection starts to fully develop decreases with an increase in the shear‐thinning property. The shear‐thinning property also induced subcritical bifurcation. In addition, the velocity scale of convection increases with an increase in the shear‐thinning property. Thus, the shear‐thinning property is considered to accelerate convection. Compared with several types of velocity scales used by other researchers, significant deviations from the actual scale were observed. Therefore, a new type of velocity scale, including the buoyant to viscous force ratio, arbitrary parameter, and thermal diffusivity, was proposed. The proposed velocity scale allowed an approximate estimation of the actual velocity scale. Although further investigation of the validity is necessary with varying geometries and rheological parameters, this velocity scale will be useful for controlling RB convection with Newtonian/shear‐thinning fluids.