For these equations, we assume 1-dimensional flow with uniform inlet conditions. The governing conservation equations reduce to:

(13–1)

(13–2)

(13–3)

(13–4)

In these equations denotes the spatial coordinate; the mass flow rate (which is independent of ); the temperature; the mass fraction of the k th species (there are gas species); the pressure; the velocity of the fluid mixture; the mass density; the molecular weight of the k th species; the mean molecular weight of the mixture; the universal gas constant; the thermal conductivity of the mixture; the constant-pressure heat capacity of the mixture; the constant pressure heat capacity of the k th species; the molar rate of production by chemical reaction of the k th species per unit volume; the specific enthalpy of the k th species; the diffusion velocity of the k th species; the heat loss due to gas and particle radiation; and the cross-sectional area of the stream tube encompassing the flame (normally increasing due to thermal expansion) normalized by the burner area. The user may provide an area profile (APRO) or alternatively a subroutine to specify the area as a function of the spatial coordinate. By default, the stream tube area is taken to be constant and equal to unity.

The net chemical production rate of each species results from a competition between all the chemical reactions involving that species. We presume that each reaction proceeds according to the law of mass action and the forward rate coefficients are in the modified Arrhenius form,

(13–5)

The details of the chemical reaction equations and the thermochemical properties are found in Gas-phase Chemical Rate Expressions and Thermodynamic Expressions , which discuss the evaluation of these expressions.

In addition to chemical reaction rates, we must also be concerned with the transport properties of the species, that is, thermal conductivities and diffusion coefficients. Stockmayer potentials are used throughout in evaluating transport properties, as described in Gas-phase Species Transport Properties . The user has the option of evaluating transport properties using mixture-averaged formulas or a multicomponent diffusion model. Although details of the calculation of transport properties are available in Gas-phase Species Transport Properties , a brief description is also provided here.