Dimensional Analysis

International Communications in Heat and Mass Transfer 33 (2006) 287 – 294 www.elsevier.com/locate/ichmt

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

C.N. Madrid, F. Alhama ⁎

Department of Applied Physics, Technical University of Cartagena, Campus Muralla del Mar. Cartagena 30202. Spain Available online 17 January 2006

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. © 2006 Elsevier Ltd. All rights reserved.

Keywords: Dimensional analysis; Discrimination; Dimensionless groups; Rotating disk; Forced convection

1. Introduction. A review of dimensional analysis Historically, dimensional analysis has been considered as a first, low-cost step for studying engineering problems, particularly in the fields of heat transfer and fluid dynamics. Even today, many modern and classical textbooks widely used in these subjects teach and apply this method to a greater or lesser extend [1,2]. Nevertheless, the...