Chapter 1 - Introduction

Abstract

This chapter introduces and defines the term “concept or idea” and its characteristics, mathematical formulation, and simplification of rate equation. A concept is a unit of thought. Any part of experience that can be organized into an idea is a concept, such as man's concept of cancer is changing all the time as new medical information is gained as a result of experiments. The basic concepts are applied both at the microscopic and the macroscopic levels. At the microscopic level, the basic concepts appear as partial differential equations in three independent space variables and time. Basic concepts at the microscopic level are called “the equations of change,” that is, conservation of chemical species, mass, momentum, and energy. The chapter explains the definition of mathematical functions, their notations, steady state and equilibrium conditions, and flux with various examples. A concept or idea defined by the general inventory rate equation is first translated into mathematical terms (rate equation) with inlet/outlet terms, rate of generation term, and rate of accumulation term. The accumulation rate may be either positive or negative depending on whether the quantity is increasing or decreasing with time within the volume of the system. The general rate equation is simplified for two special cases: (1) steady-state transport without generation, and (2) steady-state transport with generation.