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Theory and Modeling of Chemically Reacting
Boundary Layers
Robert J. Kee, Laxminarayan L. Raja, and Michael E. Coltrin
1. Introduction
2. Fluid Kinematics
This chapter develops the generalized fluid-mechanical stress-strain relationships
that are the fundamental underpinning of the Navier-Stokes equations.
The derivations are presented in cylindrical coordinates and in general
vector-tensor form.
3. The Conservation Equations
This chapter presents derivations of the conservation equations for mass
continuity, momentum (Navier-Stokes), energy and thermal energy, and species
continuity. The development and discussion use both three-dimensional
cylindrical coordinates and general vector formalisms.
4. Parallel Flows
This chapter concentrates on the broad class of Òparallel flows,Ó in which
only one velocity component. In many cases, these flows are solvable by
analytic techniques. However, the chapter uses parallel flows to introduce
basic computational techniques and discusses how spreadsheets can be used
to program solutions. The chapter also uses specific problems to reinforce
the fundamental, but general, concepts developed in the previous chapters.
5. Stagnation Flows
This chapter is devoted to a class of boundary layers called stagnation
flows, which are reduced to ordinary-differential-equation boundary-value
problems. Even though the flow field is described by two, or three, velocity
components, the temperature and species fields are a function of only
one independent variable. The governing equations are exact reductions
of the Navier-Stokes equations, rather than approximations that are asymptotically
exact in the limit of some parameter. Such flows are prominant in materials-processing
applications like semiconductors and other high-value thin films.
6. External Boundary Layers and Ducts
This chapter develops the general concepts of boundary layers, in which
certain terms become vanishingly small as physical parameters vary. After
reviewing and discussing the general apporaches for external flows, the
focus is on internal flow in channels and ducts. These flows are prominant
in a number of chemical processes, including chemical vapor deposition
reactors and catalytically active honeycomb monoliths.
7. Numerical Methods for Stiff Systems
To this point in the book, equations have been derived in general
settings and then reduced for application to specific flow configurations.
While complex chemical reaction has been included in general formalisms,
specific problems have neglected chemistry. Without complex chemistry,
numerical solution can be accomplished with straightforward techniques.
Once complex chemistry is introduced, the computationl techniques must
handle a phenomena called stiffness. This chapter presents numerical techniques
for solving initial and boundary value problems that are specifically
designed to be efficient and accurate for complex chemistry problems.
8. Chemical Thermodymanics and Thermochemical Properties
Formulation and solution of chemically reacting flow problems requires
therochemical properties (e.g., specific heats, enthalpies, and entropies)
for every species in the system. Quite often these may not be known and
require estimation. After reviewing fundamental concepts in kinetic theory,
statistical mechanics, and quantum chemistry, the chapter develops techniques
to estimate thermodynamic properties for use in chemically reacting flow
simulation.
9. Molecular Transport and Transport Properties
In addition to thermodynamic properties, transport properties (e.g.,
viscosity, thermal conductivity, and diffusion coefficients) are also
needed to describe chemically reacting flow processes. This chapter takes
a kinetic-theory and statistical-mechanics approach to develop the formalism
for transport-property description. It also develops techniques to estimate
needed properties.
10. Chemical Kinetics and Reaction Rates
This chapter reviews the general concepts of chemical reaction theory.
It considers both gas-phase homogeneous chemistry as well as heterogeneous
chemistry at surfaces. It discusses the use and validity of ab-initio
quantum-chemical approaches, although the techniques themselves are outside
the scope of this book. Nevertheless, the intent is to equip the reader
to incorpoate and use the results ab-initio rate-expression estimation
in chemically reacting flos simulation.
11. Chemically Reacting Stagnation Flows
This chapter returns to stagnation flows (introduced in Chapter 5) to
incorporate complex chemistry and transport. It uses specific examples
from semiconductor processing and combustion to illustrate fundamental
issues in problem formulation and solution. These problems bring together
all the fluiid-mechanical and chemical concepts developed in earlier chapters.
The problems also serve to introduce and use important concepts like the
identification of rate-limiting processes.
12. Chemically Reacting Duct Flows
This chapter continues in the spirit of the previous chapter, but focuses
attention on internal boundary layers. Examples are drawn from channel-flow
chemical-vapor-deposition reactors, flow reactors for chemical processing,
and flow in catalyst monoliths.
A. Examples of Spreadsheet Solution to Boundary-Layer Problems
B. General Vector-Tensor Relationships
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