Environmental Engineering Reference
In-Depth Information
=
.
and a Prandtl number of
Pr
6
0. The entrance and exit of the cavity was fixed
=
.
=
to
h
0
4
H
, where
H
is the height of the cavity with a length of
W
4
H
.Two
different lengths of the heater plate
W
p
=
W
/
5 and
W
p
=
W
/
3
.
33 were analyzed.
The horizontal and vertical dimensions of the cavity are
W
=
0
.
2m and
H
=
0
.
05m,
respectively.
The governing equations for a non-isothermal incompressible steady-state flow
in a two-dimensional domain
are given by:
1
Re
−
u
+
u
·∇
u
=−∇
p
,
(1)
∇·
u
=
0
,
(2)
1
Re Pr
−
T
+
u
·∇
T
=
Q
.
(3)
The mass transfer by thermal decomposition inside the cavity depends on both
the fluid flow and the temperature distribution, and is given as:
1
Re
Sc
−
C
A
+
u
·∇
C
A
=
R
,
(4)
is the velocity vector, being
u
1
y
u
2
the
horizontal and vertical velocity components, respectively;
p
is the pressure,
T
is the
temperature, and
C
A
is the concentration.
Q
and
R
are the source term in the energy
and mass transport equations, respectively, defined as follows:
In the above equations
u
=
(
u
1
,
u
2
)
r
h
Q
=
T
C
)
,
(5)
ρ
C
p
U
m
(
T
H
−
and
rh
U
m
C
Ac
,
−
R
=
(6)
where
is the density,
Cp
is the specific heat capacity
at constant pressure and
C
Ac
is the concentration of reference. In addition
r
is the
reaction rate defined as:
is the heat of reaction,
ρ
r
=
kC
A
,
(7)
where
k
is the rate constant:
Ae
−
E
/
R
g
T
k
=
.
(8)
Here
A
is the frequency factor,
E
is the activation energy and
R
g
is the fluid constant.
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