General Remarks

In the previous chapters we noted that the dimensionless boundary-layer conservation equations for momentum, thermal energy, and mass species are mathematically similar. This similarity among these dimensionless equations suggests that the mathematical solution for one equation should provide the solution of the other equations. One may argue that the empirical correlations for friction factor, heat transfer coefficient, and mass transfer coefficient represent empirical solutions to the momentum, energy, and mass-species conservation equations, respectively. Thus a correlation for friction factor of the form f = f (Re) is the empirical solution to the momentum conservation equation for a specific system and flow configuration, whereas an empirical correlation of the form Nu = Nu (Re, Pr) for the same system is an empirical solution to the energy equation and an empirical correlation of the form Sh = Sh(Re, Sc). Thus, using the analogy arguments, knowing an empirical correlation for either of the three parameters f, Nu, or Sh for a specific system will allow us to derive empirical correlations for the remaining two parameters.

The usefulness of the analogy approach becomes clear by noting that measurement of friction factor is usually much simpler than the measurement of heat or mass transfer coefficients.