New heat transfer law for turbulent natural convection between heated horizontal surfaces of large extent

An analysis is presented of the fully developed turbulent flow between horizontal parallel heated surfaces of large extent (the so-called turbulent Rayleigh problem). The flow is shown to consist of two layers: an inner layer in which viscous and conduction effects are important, and an outer layer in which these effects are negligible. Scaling laws for each region are proposed and inner and outer profiles for the temperature are identified. Matching these profiles in the limit as the ratio of outer to inner scales goes to infinity leads to the identification of a buoyant sublayer in which the mean temperature profile varies as z^-1/3 with an additive constant. A further matching of the inner and outer representations leads to a heat transfer law which is valid at finite as well as infinite Rayleigh number,