Energy and Mass Transfers

4 Dimensional Analysis

4.1. Introduction

Various physical phenomena of interest to engineering are described by a number of magnitudes, laws and equations that sometimes involve several parameters. The values of these parameters define the state of the system (Langhaar, 1951).

For example, we saw in Chapter 2 that the magnitude “heat flux transmitted by conduction” depends on a closely-defined set of parameters: the heat conductivity of the material considered, the transfer area and the temperature gradient.

Yet, generally speaking, when we come to study a phenomenon for the first time, in principle we do not tend to know the set of parameters concerned. We therefore apply common sense and physical analysis of the transformations underway, in order to deduce the parameters that could potentially influence the phenomenon being studied.

Nevertheless, this physical analysis is often not enough to be able to determine all of the parameters that can be involved, all the more so when defining the relation that has to exist between these parameters and the magnitude studied.

Put simply, dimensional analysis is, firstly, a technique for defining the dimensions (temperature, length, mass, time, etc.) occurring in a given magnitude. Velocity, for example, involves the dimensions “length” and “time”. Secondly, this technique can be be used to reveal the relations that describe a given physical phenomenon.

Dimensional analysis is thus used as a mathematical technique to methodically ...