Combustion includes many chemical chain reactions and many intermediate species
are involved. To model this combustion process, we assume that the reaction satisfies
the one-step reaction mechanism of a convectional hydrocarbon fuel:
Many gas-phase mixture or pure substances that react or decompose
exothermically are capable of supporting a low-velocity subsonic decomposition
wave, which is called a flame (Bartok and Sarofim, 1991). Mallard and Le Chatelier
(1883) divided the flame into two zones. Zone I is the preheat zone, in which the
gases are heated by conduction and reach ignition at the ignition boundary. Zone II is the chemical reaction zone, in which chemical enthalpy is converted into sensible
enthalpy. The reaction rate was not specified by Mallard and Le Chatelier (1883) at
any particular temperature. However, their analysis suggests that the flame speed is
proportional to the square root of the product of thermal diffusivity and reaction
rate. Zel’dovich and Frank-Kamenetsky (1938), Zel’dovich and Semenov (1940)
and Zel’dovich (1948) adopted the idea of Mallard and Le Chatelier of dividing
the flame into two zones (preheat and reaction zones). However, instead of
considering the energy equation alone, they used the species-conservation equation
together with the energy equation. They proposed that the ignition temperature is
very close to the adiabatic flame temperature and consequently replace i T with f T
in their estimation of reaction rates.
The objective of this paper is to study mathematically the chemical kinetics of a
laminar premixed flame. We assume that the fuel is the limiting species, so that
combustion is lean. We prove the existence and uniqueness of solution. We also
examine the properties of solution. To simulate the model, we assume that the
incoming mixture is at the burner temperature.
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