Scaling analysis as a pedagogical tool in teaching transport and reaction processes

Abstract

This paper describes the use of scaling analysis as a pedagogical tool in teaching courses in fluid dynamics, heat transfer, mass transfer, transport phenomena, mass transfer with chemical reaction, and process modeling. Scaling analysis is a systematic method for nondimensionalizing a system of describing equations for transport or reaction processes so that all the dimensionless variables as well as their derivatives have a magnitude no greater than approximately one. This permits assessing the importance of various terms on the basis of the values of the dimensionless groups that multiply them. As such, scaling analysis is an invaluable tool for educators since it provides a systematic way to arrive at model approximations. It thereby permits presenting disparate topics in transport and reaction processes in a unified and integrated manner. Highlights are given of how scaling analysis has been used in teaching graduate-level courses. An eight-step procedure is outlined for applying scaling analysis and then is applied to an illustrative problem involving interpreting data obtained from a permeation cell used to determine the properties of a membrane. This example illustrates how scaling analysis can be used to both interpret performance data as well as to extract useful characterization parameters from the data. As such, it underscores the advantages of scaling analysis as a learning tool to hone students' intuition. © American Society for Engineering Education, 2007.