Average and extremal properties of heat transfer and shear stress on a wall surface in Rayleigh-Benard convection

In this study surface-averaged and extremal properties of heat transfer and shear stress on the upper wall surface of Rayleigh-B,nard convection are numerically examined. The Prandtl number was raised up to 10(3), and the Rayleigh number was changed between 10(4) and 10(7). As a result, average Nusselt number Nu and shear rate tau/Pr depends on Pr, Ra, and the entire numerical results are distributed between two correlation equations corresponding to small and large Pr. The small and large Pr equations are closely related to steady and unsteady flow regimes, respectively. Nevertheless, a single relation tau/Pr similar to Nu (3.0) exists to explain the entire results. Similarly the change of local maximal properties Nu (max) and tau (max)/Pr depends on Pr, Ra, and these values are also distributed between two correlation equations corresponding to small and large Pr cases. Despite such complicated dependence we can obtain a correlation equation as a form of tau (max)/Pr similar to Nu (max) (2.6) , which has not been obtained theoretically.