**2. Formulation**

252 Mass Transfer in Chemical Engineering Processes

On the other hand, when the surface temperature is high, step (iii) is known to be much faster than steps (i) and (v). The combustion rate is then controlled by the diffusion rate of oxidizing species (say, oxygen) to the solid surface, at which their concentrations are negligibly small. In this diffusionally controlled regime, therefore, the combustion rate strongly depends on the boundary layer thickness and weakly on the surface temperature

Since oxygen-transfer to the carbon surface can occur via O2, CO2, and H2O, the major

At higher temperatures, say, higher than 1000 K, CO formation is the preferred route and the relative contribution from (R1) can be considered to be negligible (Arthur, 1951). Thus,

Comparing (R2) and (R3), as alternate routes of CO production, the C-O2 reaction is the preferred route for CO production at low temperatures, in simultaneous presence of O2 and CO2. It can be initiated around 600 K and saturated around 1600 K, proceeding infinitely fast, eventually, relative to diffusion. The C-CO2 reaction of (R3) is the high temperature route, initiated around 1600 K and saturated around 2500 K. It is of particular significance because CO2 in (R3) can be the product of the gas-phase, water-catalyzed, CO-oxidation,

referred to as the CO-O2 reaction. Thus, the C-CO2 and CO-O2 reactions can form a loop. Similarly, the C-H2O reaction (R4), generating CO and H2, is also important when the combustion environment consists of an appreciable amount of water. This reaction is also of

referred to as the H2-O2 reaction, constituting a loop of the C-H2O and H2-O2 reactions. The present monograph, consisting of two parts, is intended to shed more light on the carbon combustion, with putting a focus on its heat and mass transfer from the surface. It is, therefore, not intended as a collection of engineering data or an exhaustive review of all the pertinent published work. Rather, it has an intention to represent the carbon combustion by use of some of the basic characteristics of the chemically reacting boundary layers, under recognition that flow configurations are indispensable for proper evaluation of the heat and mass transfer, especially for the situation in which the gas-phase reaction can intimately

affect overall combustion response through its coupling to the surface reactions.

Among various flow configurations, it has been reported that the stagnation-flow configuration has various advantages, because it provides a well-defined, one-dimensional flow, characterized by a single parameter, called the stagnation velocity gradient. It has even been said that mathematical analyses, experimental data acquisition, and physical

2H2 + O2 2H2O , (R6)

C + O2 CO2 , (R1)

2C + O2 2CO , (R2)

C + CO2 2CO , (R3)

C + H2O CO + H2 . (R4)

2CO + O2 2CO2 , (R5)

(*T*0.5~1.0), with exhibiting surface regression in the course of combustion.

reaction (R2) will be referred to as the C-O2 reaction.

significance because H2O is the product of the H2-oxidation,

surface reactions can be

Among previous studies (Tsuji & Matsui, 1976; Adomeit, et al., 1976; Adomeit, et al., 1985; Henriksen, et al., 1988; Matsui & Tsuji, 1987), it may be noted that Adomeit's group has made a great contribution by clarifying water-catalyzed CO-O2 reaction (Adomeit, et al., 1976), conducting experimental comparisons (Adomeit, et al., 1985), and investigating ignition/extinction behavior (Henriksen, et al., 1988). Here, an extension of the worthwhile contributions is made along the following directions. First, simultaneous presence of the surface C-O2 and C-CO2 reactions and the gas-phase CO-O2 reaction are included, so as to allow studies of surface reactions over an extended range of its temperatures, as well as examining their coupling with the gas-phase reaction. Second, a set of generalized coupling functions (Makino & Law, 1986) are conformed to the present flow configuration, in order to facilitate mathematical development and/or physical interpretation of the results. Third, an attempt is made to identify effects of thermophysical properties, as well as other kinetic and system parameters involved.
