
291Flame Impingement
Mass
∂
ρ
∂
ρ
ur
vr
()
+
= 0
(12.54)
Momentum
ρ
∂
∂
ρ
∂
∂
∂
∂
∂
∂
µ
∂
∂
u
u
x
v
u
y
p
xy
u
y
+=−+
(12.55)
∂
=
0 (12.56)
Energy
ρ
∂
∂
ρ
∂
∂
∂
∂
∂
∂
∂
∂
∂
u
h
x
v
h
yy
k
t
yy
u
y
+=
+−
E
2
1
1
2
Pr
(12.57)
where the chemical diffusion-reaction effects are
included in the modied thermal conductivity k
E
(Butler
and Brokaw).
84
Thermal diffusion was neglected. Using
the coordinate transformation from (x,y) to (η) suggested
by Lees:
85
=
e
(12.58)
dening
η
ρ
=
()
∫
ee
e
ur
x
y
2
05
.
d (12.59)
and
=
∫
ρµ
eee
2
d (12.60)
substituting the transformations into the conservation
equations and rearranging leads to the following ordi-
nary differential equations: ...