Diagrammatic Models in the Engineering Sciences

Abstract

This paper is concerned with scientific reasoning in the engineering sciences. Engineering sciences aim at explaining, predicting and describing physical phenomena occurring in technological devices. The focus of this paper is on mathematical description. These mathematical descriptions are important to computer-aided engineering or design programs (CAE and CAD). The first part of this paper explains why a traditional view, according to which scientific laws explain and predict phenomena and processes, is problematic. In the second part, the reasons of these methodological difficulties are analyzed. Ludwig Prandtl’s method of integrating a theoretical and empirical approach is used as an example of good scientific practice. Based on this analysis, a distinction is made between different types of laws that play a role in constructing mathematical descriptions of phenomena. A central assumption in understanding research methodology is that, instead of scientific laws, knowledge of capacities and mechanisms are primary in the engineering sciences. Another important aspect in methodology of the engineering sciences is that in explaining a phenomenon or process spatial regions are distinguished in which distinct physical behaviour occur. The mechanisms in distinct spatial regions are represented in a so-called diagrammatic model. The construction of a mathematical description of the phenomenon or process is based on this diagrammatic model.