Momentum, heat, and mass transfer analogy for drag-reducing solutions

Abstract

The new, generalized form of the analogy among momentum, heat, and mass transfer for both Newtonian and drag-reducing solutions is presented. This work rests on the understanding that the shift in turbulent spectra due to the presence of additives must be taken into account because different portions of the turbulent spectra unequally affect the rates of momentum, heat, and mass transfer. These effects are accounted for through the turbulent Schmidt (Sc t ) or turbulent Prandtl (Pr t ) number in a manner analogous to the way that Sc (or Pr) number accounts for contributions of molecular transport. The proposed approach was verified by (1) comparing the qualitative prediction for Sc t number and the calculated values from mass transfer data and (2) comparing predicted and experimental data for heat transfer.