Heat and mass transfer laws for fully turbulent wall flows

Abstract

The general method of Izakson and Millikan for the derivation of the well-known Prandtl-Nikuradse skin friction law is applied to the analysis of turbulent heat and mass transfer in pipes, channels, and boundary layers. The formula for the heat (or mass) transfer coefficient (or the Nusselt number) is obtained which contains the dimensionless coefficients of the universal logarithmic equations for the velocity and temperature profiles as parameters of the formula. One of these parameters is a universal function of Prandtl (or Schmidt) number and all the others are constants. The existing velocity and temperature profile measurements in various turbulent wall flows permit the determination of all the necessary coefficients with fair accuracy. The resulting calculations are in satisfactory agreement with numerous experiments on heat and mass transfer in pipes and boundary layers on a flat plate over the Prandtl (or Schmidt) number range from 6 × 10 −3 to 10 6 and over two orders of magnitude of Reynolds (or Péclét) number variations.