International Journal of Heat and Mass Transfer, Vol.38, No.15, 2761-2770, 1995
Buoyant Turbulent-Flow Driven by Internal Energy Generation
Two thermal microscales for buoyancy driven turbulent flows are proposed. The first of these scales, arranged relative to viscous dissipation, is [GRAPHICS] which explicitly includes the limit for sigma --> infinity, and, arranged relative to inertial production, is [GRAPHICS] which explicitly includes the limit for sigma --> 0 infinity. Here sigma = v/a denotes the Prandtl number dagger and P-beta the production of buoyant turbulent energy. The limits of this scale for sigma similar to 1, and sigma --> 0, infinity are shown to be the celebrated Kolmogorov scale and its extensions known as the Oboukhov-Corrsin and Batchelor scales, respectively. The eta(theta) scale is independent of any integral (or geometric) effect. The second of these scales in terms of the limit for sigma --> infinity is [GRAPHICS] and in terms of the limit for sigma --> infinity 0 is [GRAPHICS] where l is an integral (or geometric) scale. When expressed in terms of buoyant force induced by internal energy generation, these scales relative to the integral scale become [GRAPHICS] where [GRAPHICS] and [GRAPHICS] is the appropriate Rayleigh number and Pr is the Prandtl number. Here Phi = mu(’)"/rho c(p), mu"’ being the rate of energy generation per unit volume. A two-layer heat transfer model for turbulent flow driven by internal energy generated between two horizontal plates is proposed. The model yields, in terms of the foregoing scales, [GRAPHICS] or, in terms of Pi(i) [GRAPHICS] where Nu denotes the Nusselt number. The special case of this relation for Pr > 1 is already known to correlate the experimental literature on electrolytically heated water.
Keywords:CONVECTION