The transport portion of the conservation equation of species in the gas phase is
 | (6–78) |
where v and ρ are the
velocity and density of the gas mixture, respectively, 
and 
are the mass fraction and diffusion coefficient of species
i, and 
is the source term from vaporization.
Summation of Equation 6–78 gives the species conservation equation for the two-species system (fuel and air) as
 | (6–79) |
where yF is the total mass fraction of fuel species, D is the average diffusion coefficient of the fuel species, and Sg is the total vaporization source term.
The energy conservation equation for the gas phase is
 | (6–80) |
where T is the temperature, 
is the thermal conductivity, 
is the mixture specific heat, C
PA is the specific heat of air, and 
is the average value of the product of specific heat and the diffusion
coefficient of the fuel species. The last term in Equation 6–80
represents energy transport due to
inter-diffusion of species.