A critical comparison of approximate solutions for enhancement factor for irreversible second-order reaction

In this paper, the exact numerical solution for the enhancement factor for mass transfer accompanied by an irreversible second-order reaction based on the film theory is presented. The accuracy of the numerical solution is enhanced by using non-uniform discretization steps and Richardson extrapolation. Approximate analytical solutions available in the literature for the enhancement factor for an irreversible second-order reaction were compared with presented numerical solution. All approximate solutions are able to predict the values of the enhancement factor with the relative deviations within 10% compared to the exact numerical solution for the film theory. However, the applicability of the model and some approximate solutions is limited to the fast reaction regime. The approximate solution of DeCoursey (1974), originally developed for the surface renewal theory, was adapted to the film theory by using a correction factor. The maximum relative deviation of the modified approximate solution is as low as 2.2% for entire range of parameters Ha and Ei (Hatta number and enhancement factor for instantaneous reaction), which is the best accuracy that has ever been reported for an explicit expression for the enhancement factor for an irreversible second-order reaction.