As mentioned in Chap. 1, the main purpose of combustion science is to aid in performance prediction or design of practical equipment as well as to aid in prevention of fires and pollution. This is done by analyzing chemical reactions with increasing refinements, namely, stoichiometry, chemical equilibrium, chemical kinetics, and finally, fluid mechanics. Such analyses of practical equipment are accomplished by modeling. The mathematical models can be designed to varying degrees of complexity, starting from simple zero-dimensional thermodynamic stirred-reactor models to one-dimensional plug-flow models and, finally, to complete three-dimensional models. At different levels of complexity, the models result in a system of a few algebraic equations, a system of ordinary differential equations, a system of partial differential equations.