Asymptotic analysis of heat transfer in turbulent Rayleigh–Bénard convection

Based on asymptotic considerations a heat transfer law for turbulent Rayleigh–Bénard convection is found that differs from existing correlations which often are of a power law type with respect to their Rayleigh number dependence. From the asymptotic temperature profile, derived by matching temperature gradients in the overlap region of the wall layer and the core layer, a Nusselt number follows which includes a logarithmic term. This correlation is in good agreement with data from highly accurate Rayleigh–Bénard experiments for Rayleigh numbers between 10⁵ and 10¹⁵ and Prandtl numbers larger than 0.5. It is an alternative to existing power laws or more complicated correlations for Nu = Nu(Ra,Pr).