Discrimination: A fundamental and necessary extension of classical dimensional analysis theory

Abstract

Despite the widespread use of dimensional analysis in text books and research literature, the results provided by this technique, although inexpensively obtained and immediate, are restricted and can be substantially improved. The fundamental limitation in classical dimensional is the fact that it is a “scalar” theory. The present study attempts to widen the fundamental dimensions of the dimensional basis, whatever the reason by which the basis could be increased in each problem. It is all about discrimination, an idea that directly deals with a reduction in the number of dimensionless groups that play an independent role in the problem, thus making the solution more precise. Many of the controversial dimensionless groups provided by classical dimensional analysis, and many commonly used geometrical form factors, are not recognized as such by discriminated dimensional analysis and, instead, new dimensionless groups arise. After a review of the literature in connected with this subject, we shall tackle two applications in the field of heat transfer.