Prediction of rates of heat or mass transfer in complex situations by interpolating between simpler limiting cases

This paper emphasizes the generality of a simple algebraic procedure suggested in 1962 by the author to predict the rate of heat or mass transfer in complex situations. It consists in replacing the terms in the convective diffusion equation by expressions involving scaling quantities multiplied by constants. Thus the convective-diffusion equation is replaced by an algebraic equation for the mass transfer coefficient containing a number of constants. The constants are determined from the solutions available for some simpler limiting cases. To illustrate the procedure a variety of examples are given which include: penetration theory for diffusion with chemical reaction, laminar flow along a plate accompanied by a chemical reaction, diffusion with chemical reaction in a turbulent liquid, mass transfer from a drop to a continuous phase, unsteady heat transfer to a liquid in steady laminar flow along a plate and free convection superimposed on forced convection. Numerous other complex situations have been or can be treated by interpolation between some simpler limiting cases.