Microscales of turbulence and heat transfer correlations

Abstract

The small-scale structure of forced, turbulent flows developed after Taylor and Kolmogorov is extended to that of buoyancy-driven flows. A thermal microscale is proposed. Here Pr = v/a denotes the Prandtl number and [Weierstrass p]B the production of buoyant, turbulent energy. Three limits of this scale are the Kolmogorov, Oboukhov-Corrsin and Batchelor scales, respectively. When expressed in terms of the buoyancy force rather than that of the buoyant production (energy), the proposed scale becomes or, relative to a length scale l characteristic for geometry [eta][theta]/l~PN-1/3 where is the fundamental dimensionless number for buoyancy-driven flows and Ra is the Rayleigh number. A heat transfer model based on this dimensionless number explains why the well-known correlation for natural convection, Nu~Ran, leads to an exponent less than 1/3 when it is considered for the buoyancy-driven flow between two horizontal plates.