Untitled - Aerobib - Universidad Politécnica de Madrid

6.14. HYDRAZINE DECOMPOSITION FLAME 183
Energy equation
When mean specific heat is assumed to be constant and the influence of radicals on
the energy of the mixture is neglected, the energy equation may be written
( )
λ dT 17
m dx = q r
32 − ε 2 − c p (T f − T ), (6.196)
where q r is the reaction heat per gram of ammonia produced. If reduced temperatures
θ = T T f
and θ 0 = T 0
T f
(6.197)
are introduced into Eq. (6.196) and taking into consideration the conditions at the cold
boundary, θ = θ 0 , ε 2 = 0, this equation may be written
where
λ
mc p
Chemical reaction and diffusion equations
The reaction equation for ammonia is
dθ
dx = (1 − θ 0)(1 − ε) − (1 − θ), (6.198)
ε = 32
17 ε 2. (6.199)
m dε 2
dx = w 2. (6.200)
The diffusion equation corresponding to the same is given by Fick’s law and written
dY 2
dx = m (Y 2 − ε 2 ). (6.201)
ρD 2m
Coordinate x is eliminated from the above two equations through Eq. (6.198), and the
following system results
where
and
dε
dθ = 32
17
is the Lewis-Semenov number.
λ
m 2 c p
w 2
(1 − θ 0 )(1 − ε) − (1 − θ) , (6.202)
dY
dθ = L Y − ε
(1 − θ 0 )(1 − ε) − (1 − θ) , (6.203)
Y = 32
17 Y 2, (6.204)
L =
λ
ρDc p
(6.205)