Overview

We use the term "network modeling" to describe actual networks (e.g., electrical circuits), as well as systems that are linear in configuration (i.e., devoid of branches and loops) but lead to sets of simultaneous equations. The networks thus defined, which we consider here, are thermal, chemical, hydraulic, mechanical, and electrical. Some of them occur more than once, and the mathematical tools we use are matrix methods and Laplace transformations as well as standard ODE solution procedures.

Example 7.1 considers a network made up of a stirred tank and a heat exchanger through which the contents of the tank are circulated. The system is analogous to that of the artificial kidney, that is to say the process of dialysis. In Example 7.2 we analyze the behavior of a radioactive decay series using the Laplace transformation. Hydraulic networks are taken up in Example 7.3, and since the systems are taken to be at steady state, the solution method is strictly algebraic. In Example 7.4 we turn to the first of two electrical networks for which we apply the Laplace transformation. Some difficulties arise in the solution of this problem, and the reader is introduced to the notion of "going around the brick wall" rather than confronting the difficulty head on. Example 7.5 considers a mechanical system consisting of vibrating masses, which are again analyzed by means of the Laplace transformation.

Examples 7.6 to 7.9 all use matrix methods as the analytical tool. The first two of these consider simultaneous linear algebraic...