Study on the turbulent thermal convection between two horizontal flat plates

Abstract

The buoyancy-driven fluid layer between a pair of horizontal flat plates is assumed to consist of three distinctive layers ; namely a conduction layer, a buffer layer and a convection layer. And three sets of characteristic velocity, length and temperature scales for those layers are proposed to analyse the mean thermal structure is a turbulent thermal convection without mean motion. These scales are formulated based on molecular or turbulent eddy contribution to the momentum and heat transport in each layer. Using the proposed scales and applying a gradient matching technique at the interface between two adjacent layers, Kraichnan``s (Phys.Fluids, 5, p.1374, 1962) multi-layered structure of the mean temperature gradient profile is reestablished. If the conduction scales are used to non-dimensionalize mean temperature gradient data near the wall, they form a plausible correlation curve that is nearly independent of the Prandtl number and the Rayleigh number for the range of available experiments. From the correlation curve, it is found that the convection layer or the similarity layer with the slope of -4/3 begins to appear at about $z_+~15$ and the proportionality constants of the similarity law is found to be 0.6, i.e.$dθ_+/dz_+=0.6z_+\frac^{-4/3}$, whereθ and $z_+$ are non-dimensional temperature and distance scaled by the respective conduction scales. Further, a wall-layer model for the mean temperature gradient profile is formulated in accordance with the power law, $dθ/dz_+~z_+^{-α}$, across the layers, which is in good agreement with the data. The buoyancy-driven thermal convection is also analysed by the Reynolds stress model. Turbulent third-order transport model includs the effect of buoyancy. Results show that the temperature profiles are in excellent agreement with the experimental data and kinetic energy, disspation, temperature fluctuations and the kinematic heat flux are fairly predicted. The 1/3 power theory of vertical velocity fluctuations and...