Prediction of fully developed turbulent convection with minimal explicit empiricism

Abstract

Abstract From a purely theoretical analogy between energy and momentum transfer in fully developed turbulent Convection, an expression without explicit empiricism, and which appears to be applicable for all channels, all modes of heating on the surface(s), all values of Re in the turbulent regime, and all moderate and large values of Pr, was deduced for Nu. An analogous complementaly expression for small values of Pr has the same generality, but incorporates one explicit empirical exponent. The numerical implementation of these two expressions for Nu for specific values of Re and Pr introduces some empiricism, but the resulting uncertainty in Nu, including that associated with the aforementioned exponent, is truly negligible. Because of their accuracy and generality, these two expressions, together with several supplementaly relationships, appear to be superior to all existing ones for design calculations. Because of their simple and fundamental structure, they appear to be equally superior for educational purposes.