Environmental Engineering Reference
In-Depth Information
=
(
)
˙
˙
Rmm
rec
(2.5)
in
The maximum temperature in the furnace,
T
fmax
, is given by Equation 2.6 as it
is assumed to be equal to the adiabatic flame temperature neglecting the effect of
dissociation.
Q
f
T
=+
(
T
(2.6)
f
in
2
)
(
)
Cm
˙
1
+
R
max
in
2.2.4.2.2 Heat Transfer in Furnace
A simple heat transfer model is introduced to express the relationship between
combustion gas and the materials to be heated without taking into account the details
of the actual heat transfer process taking place in a furnace. The amount of heat,
Q
m
, gained by the heated materials is expressed by Equation 2.7 as the sum of the
radiation,
Q
rad
, and the convection heat transfer,
Q
conv
, from the combustion gas,
using
f
representing heat transfer ratio
Q
rad
/
Q
conv
here.
Q
m
=
Q
rad
+
Q
conv
=
Q
conv
(1 +
f
)
(2.7)
Equation 2.8 is given by rewriting
f
as a function of temperature ratio,
r
T
, of
combustion gas,
T
g
, and materials,
T
m
, and coefficient, φ
CG
.
(
)
φσ
4
4
TT
-
(
)
()
=
CG
g
m
3
2
3
fr
=
CT
1
+
r
+
r
+
r
(2.8)
(
)
T
rg
T
T
T
hT
-
T
g
m
where,
r
T
=
T
m
/
T
g
,
C
r
= φ
CG
σ/
h
where σ = Stefan-Boltzmann constant, φ
CG
= overall thermal absorption coefficient,
and
h
= convection heat transfer coefficient.
In a furnace,
f
(
r
T
) generally is affected by flow condition, the temperature profile
of the combustion gas and of the heated surface configuration or furnace shape. The
following three assumptions were made to simplify the heat balance calculation:
•
C
r
is constant, 0.17 × 10
9
defined under the condition of
T
g
ref
= 2000 K,
T
m
ref
= 600 K and
f
ref
= 2.
•
f
is a function of
T
g
,
T
m
and
T
out
.
•
r
T
v
aries with time proportionally when time is 0 ≤
t
≤ τ, and becomes
constant when τ ≤
t
≤ 1 as shown in
Figure 2.25
.
In this study, 0.5 is used
as a fixed value of τ.
According to the above assumption, time averaged heat transfer ratio,
fr
()
can
be expressed by the equation 2.9.
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