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The IUP Journal of Computational Mathematics
A Note on the Mathematical Model of the Chemical Kinetics of a Laminar Premixed Flame
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The paper studies the conservation of mass, momentum, species and energy equations describing the chemical process of lean premixed methane air combustion. It proves the existence of unique solutions and examines the properties of solutions of the time-dependent problems under certain conditions. The time-dependent temperature and species mass fraction profiles are obtained using the finite difference method.

 
 
 

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.

 
 
 

Computational Mathematics Journal, Logistic Regression Models, Business Management, Decision Theory, Logistic Regression Programs, SPSS Nonlinear Program, Proportional Reductions, Statistical Aanalysis Software Package, Statistical Software SPSS, Squared Pearson Correlation .