Environmental Engineering Reference
In-Depth Information
where
K
m
= overall coefficient of heat transfer,
L
m
= length of the heat exchanger,
and
b
m
= the sum of reciprocal of the heat capacity
2.2.4.2.3 Heat Output
The amounts of heat flowing out of the furnace,
Q
out
, and flowing out of the counter
type heat exchanger,
Q
exh
, is given by Equations 2.12 and 2.13, respectively.
QQQQQ
=+
--
out
in
2
f
m
loss
(2.12)
QQ
Cm
+
m
loss
TT
=
−
out
f
(
)
(
)
˙
1
+
R
max
in
EQQ
=−
exh
out
ev
(2.13)
Q
Cm
TT
=−
(
ev
)
exh
out
˙
in
2.2.4.2.4 Equation Arrangement
Through the above heat balance analysis, a relationship between combustion gas
temperature at the furnace outlet,
T
out
, and other variables was obtained as Equation
2.12. Another relationship in terms of the quantity of the heat transferred from
combustion gas to the heated materials in the furnace,
Q
m
, was also obtained as
Equation 2.7 by estimating the convection and radiation heat transfer rate based on
the same assumptions, which simplifies the actual heating process.
Equations 2.7 and 2.12 can be rewritten with the use of the basic variables shown
in Equations 2.14 and 2.15, respectively. These equations can be calculated as two
simultaneous equations numerically when specific values are given to those variables
except for two arbitrary variables. It is necessary to provide initial conditions for
heat input with fuel,
Q
f
, heat loss in furnace,
Q
loss
, and temperature of fuel and air,
T
cold
. For example,
Q
m
and
T
out
are calculated from these two equations by giving
certain values to other variables,
R
, α, ξ
h
, ξ
m
, τ, (
C
m
˙
)
in
, (
C
m
˙
)
m
.
{
}
(
)
(
)
˙
˙
QFQTR
=
,
,
,
αξξ τ
,
,
,
,
m m
,
(2.14)
m
1
m
out
h
m
in
m
{
}
(
)
(
)
˙
˙
TFQTR
=
,
,
,
αξξ τ
,
,
,
,
m
,
m
(2.15)
out
2
m
out
h
m
in
m
2.2.4.3
Calculation Results
2.2.4.3.1 Effect of Gas Recirculation
Increasing the gas recirculation ratio of the model furnace caused the maximum
flame temperature to decline and the flue gas temperature at the furnace outlet to
rise gradually when there was no heat loss from the recirculating gas, i.e., α = 1.0.
Some heat loss (i.e., α < 1.0) from the recirculating gas has a considerable effect
in lowering both temperatures,
T
fmax
and
T
out
.
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