Theory and Applications of Distributed Systems
Nayef Ghasem · 2018
Distributed parameter systems vary continuously from one point to another, and thus the system state variables vary in space and in time. The mathematical description of a distributed system includes partial differential equations. The most important difference between the lumped and distributed systems is that, in the distributed system, the resultant differential equation is in most cases not solvable in analytic form. Appropriate mathematical modeling of the process is crucial to many applications such as system control design and optimization, analysis, and numerical simulation. Chapter 3 presents microscopic balances in distributed parameter systems. The general balance equations in multidimensional conditions are considered. Equations of change are derived for the three main components of transport phenomena: mass transport, fluid dynamics, and heat transfer. Examples of each component are presented in detailed. Mathematical models start from general differential equations and are simplified based on rational assumptions.