Untitled - Aerobib - Universidad Politécnica de Madrid

146 CHAPTER 6. LAMINAR FLAMES
In this expression, n is the order of reaction and k a function of temperature, which,
generally, is of the form
k = A
( T
T f
) δ
e −E/RT , (6.56)
where A is a constant and E is the activation energy of the reaction.
It is convenient to eliminate the density from Eq. (6.55) so that only two variables
appear explicitly: the temperature and the mass fraction of products.
Let M r and M p be the molar masses of reactants and products, respectively,
and a the relation
Then, the mean molar mass of the mixture is 4
a = M r
M p
− 1. (6.57)
M =
M r
1 + aY , (6.58)
and the density of the mixture may be expressed as a function of pressure and temperature
in the form
By taking now Eq. (6.56) and (6.59) into (6.55), we finally obtain for the reaction
velocity
ρ = pM r
RT
1
1 + aY . (6.59)
w = A
( ) n ( ) n ( ) δ pMr 1 − Y T
e −E/RT . (6.60)
RT 1 + aY T f
It is advantageous to bring forth in Eq. (6.60) the dimensionless temperature θ =
T/T f as defined in the preceding paragraph, and to introduce dimensionless activation
temperature θ a as defined by
Now, Eq. (6.60) may be written
θ a =
E
RT f
. (6.61)
( ) n 1 − Y
w = Bθ δ−n e −θ a/θ , (6.62)
1 + aY
where
( ) n pMr
B = A
(6.63)
RT f
is a constant of the process. Eq. (6.62) is the form of the reaction velocity that will be
used in the following.
4 See Chap. 1, Eq. (1.36).