Governing equations of mass and energy balance

Here o is the density of the reactant mixture (perhaps measured in units of kg m-3), c the specific heat capacity (J K-1 kg-1), S the surface area, and X the surface heat transfer coefficient (Wm 2K 1). We have assumed a Newtonian cooling term for the transfer of heat to the surroundings. 

The feedback in this model arises from the thermal coupling represented in the form k1(T). An increase in the temperature Tincreases the value of /c1 and hence of the rate of production of heat. The feedback is highly non-linear, following the Arrhenius temperature dependence given by eqn(4.1). 

Typical values for the various physico-chemical quantities, as might be appropriate to a gaseous system, are given in Table 4.1. The initial conditions might be 

Representative values for dimensional and dimensionless parameters. The quantities E, c, o, y, and Q match those for the decomposition of di-tertiarybutyl peroxide in a glass vessel at low pressures 

Equation (4.2) involves only the variable p and so can be integrated to give 

---