Semenov approach of thermal ignition

Semenov first considered the progress of the reaction of a combustible gaseous mixture at an initial temperature T0 in a vessel whose walls were maintained at the same temperature. The amount of heat released due to chemical reaction per unit time (qr ) then can be represented in simplified overall form as 

FIGURE 7.2 Rate of heat generation and heat loss of a reacting mixture in a vessel with pressure and thermal bath variations. 

The heat release 57 is a function of pressure through the density term and qt is a less sensitive function of pressure through h, which, according to the heat transfer method by which the vessel walls are maintained at T0, can be a function of the Reynolds number. 

Shown in Fig. 7.2 is the relationship between qr and qL for various initial pressures, a value of the heat transfer coefficient h, and a constant wall temperature of In Eq. (7.8) qr takes the usual exponential shape due to the Arrhenius kinetic rate term and cp is obviously a linear function of the mixture temperature T. The qt line intersects the qr curve for an initial pressure l at two points, a and b. 

For a system where there is simultaneous heat generation and heat loss, the overall energy conservation equation takes the form 

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