Biomedical Engineering Reference
In-Depth Information
char particle,
λ
g
is the thermal conductivity of the gas, and
σ
is the
Stefan
Boltzmann constant.
A similar heat balance for the gas in an element dz in length can be car-
ried out as:
d
P
j
F
gj
C
pg
T
g
dZ
0
1
"
#
A
X
9
k
5
6
ξ
k
Δ
@
A
52
H
k
ð
T
g
Þ
2
4
3
5
(7.91)
π
r
c
N
c
A
λ
g
r
c
ð
T
g
2
T
c
Þ
1
e
p
σð
T
g
2
T
c
Þ
4
2
T
g
2
T
w
Þπ
2
½
h
conv
ð
T
g
2
T
w
Þ
1
e
w
σð
D
r
where
ξ
k
is the extent of the gas-phase kth reaction with the heat of reaction,
Δ
H
k
(T
g
); h
conv
is the gas-wall convective heat transfer coefficient; and D
r
is
the reactor's internal diameter.
The first term on the right of
Eq. (7.91)
is the net heat absorption by the
gas-phase reaction, the second is the heat transfer from the gas to the char
particles, and the third is the heat loss by the gas at temperature T
g
to the
wall at temperature T
w
.
The equations are solved for an elemental volume, A
r
dL
r
, with boundary
conditions from the previous upstream cell. The results are then used to solve
the next downstream cell.
SYMBOLS AND NOMENCLATURE
cross-sectional area of bed or reactor (m
2
)
A
preexponential coefficient in
Eq. (7.42)
(s
2
1
)
A
0
A
b
,
A
w
preexponential coefficients
in
Eqs.
(7.44)
and
(7.47)
,
respectively
(bar
2
n
s
2
1
)
A
j
total number of atoms of element j entering the reactor (
)
a
i,j
number of atoms of jth element in ith species (
)
a
jk
mass of jth gas, required for the kth reaction (kg)
molar concentration of ith gas (mol/m
3
)
C
i
C
p
c
specific heat of char (kJ/kg K)
C
p
g
specific heat of the bulk gas
D
r
internal diameter of the reactor(m)
D
g
,j
diffusion coefficient of the jth gas in the mixture of gases
(m
2
/s)
d
b
diameter of the bubble (m)
E
activation energy (kJ/mol)
e
p
emissivity of char particle (
)
F
gl0
initial flow-rate of the gas (mol/s)
F
gl
molar flow-rate of the lth gas (mol/s)
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