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A NOVEL BOILER DESIGN FOR HIGH-SODIUM COAL IN POWER GENERATION
Song Wu, Wengang Bai, Chunli Tang, Xiaowen Tan, Chang'an Wang, Defu Che* State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University
Xi’an, Shaanxi, 710049, P.R. China. *Tel: +86-029-82665185, Fax: +86-029-82668703
Email:[email protected]
ABSTRACT Considering the severe fouling of high temperature
convection pass in the boilers using high-sodium coals, a novel
boiler design with a furnace exit gas temperature (FEGT) below
800 °C was proposed. The design was evaluated in different
kinds of boilers with various capacities by examining thermal
system arrangement, heat transfer, ignition and combustion, and
steel consumption. The results indicate that, more radiation
heating surface should be used in the thermal system
arrangement of the novel boiler besides the volume-enlarged
furnace. A marked decrease in the converted coefficient of
radiation heat transfer is found in a volume-enlarged furnace
due to the reduction in the average temperature of the flame.
Moreover, the volume-enlarged furnace can adversely affect
ignition and combustion. The cyclone-fired boiler is considered
to be the most appropriate application for the novel design, for
its combustion and heat transfer in furnace are carried out
in divided chambers. A comparison of steel consumption
demonstrates the expense of the novel boiler is approximately
increased by 10% relative to the conventional one. In addition,
an improved application with flue gas recirculation is described
in detail, owing to its advantages of controlling FEGT and
maintaining the level of convection heat transfer capability of
the boiler.
Keyword: Fouling; High-sodium coal; Furnace exit gas
temperature; Thermal system arrangement; Cyclone furnace;
Flue gas recirculation
INTRODUCTION
There is a wide distribution of high-sodium coals in
America, Australia and China. For example, Zhundong
coalfield, found in Xinjiang of China several years ago,
contains 390 billion tons of coal resources approximately.
Moreover, the Zhundong coal also has the advantages of low
ash content, excellent performance of coal ignition and burnout,
and strong combustion stability. However, when used in the
fossil-fired power plant, the high-sodium coal can result in
severe fouling of high temperature convection pass in the boiler
[1-4]. The fouling of heating surfaces will threat both economy
and safety of the boiler, such as decreasing boiler output and
efficiency, corroding pressure parts, causing unit outages for
cleaning and repairs etc [5, 6]. As compared with the
conventional coals, the fouling caused by the high-sodium coals
is much more excessive and can’t be controlled with
sootblowers. As shown in Fig. 1, the high temperature reheater
in a 125 MW unit was fouled heavily after firing the Zhundong
coal. The bonded deposit covered almost all the tubes of the
bank in Fig. 1(b) and what’s worse, the flow passages of flue
gas have been partly blocked. Therefore, the fouling has been
the key problem that is restricting the efficient use of high-
sodium coals. The ultimate analysis and ash composition
analysis of the Zhundong coal are shown in Table 1 and Table 2,
respectively.
The forming of high temperature bonded deposit leads to
the severe fouling while the fuel with high alkali metal content
is burned. The majority of this deposit occurs in the high
temperature convection zone. It is formed with chemical
reactions and can’t be removed easily [7]. It’s generally
believed that the alkali metal in fuel plays a very important role
in this deposition process [8-12]. Volatile forms of the alkali
metal are vaporized in the furnace during combustion. Then the
vaporizations diffuse onto the tube walls and condense, making
significant contribution to the formation of the bonded deposit
on convection heating surface.
Proceedings of the ASME 2015 Power Conference POWER2015
June 28-July 2, 2015, San Diego, California
POWER2015-49167
1 Copyright © 2015 by ASME
(a) Before firing the Zhundong coal
(b) After firing the Zhundong coal
Fig. 1 Fouling of the high temperature reheater in a 125 MW unit
Table 1 Ultimate analysis of the Zhundong coal (wt %, as-received base)
Car Har Oar Nar Sar Aar Mt Qnet,ar /(MJ/kg)
54.99 2.32 9.16 0.41 0.55 5.27 27.30 19.13
Table 2 Ash composition analysis of the Zhundong coal
Ash Composition (wt %) Ash Melting Point /°C
SiO2 Al2O3 Fe2O3 CaO MgO Na2O K2O TiO2 SO3 DT ST HT FT
17.08 6.99 11.6 27.87 7.66 6.08 0.46 0.61 21.65 1320 1330 1340 1350
Much work has been devoted to the formation mechanisms
of high temperature bonded deposit related to the alkali metal.
The study on alkali metal occurrence mode in coal [13-16]
indicated that the alkali metal in coal can be classified into
organic alkali metal and inorganic alkali metal. The organic
alkali metal exists in forms of carboxylates and nitrogen or
oxygen functional groups, while the inorganic alkali metal
exists in forms of chloride crystals, hydrated ions as well as
aluminosilicates etc. Especially, Weng et al. [17] conducted an
experimental investigation on alkali metal occurrence mode in
Zhundong coal by extraction method. Research results showed
that the sodium content in Zhundong coal is significantly higher
than other types of coals, but the potassium content is lower.
And the majority of the sodium in Zhundong coal exists in the
form of water soluble sodium. Some researchers [18-21]
reported that the soluble alkali metal in coal will generate
gaseous alkali metal compounds to be released in combustion or
gasification conditions, while the insoluble alkali metal that
exists in the form of aluminosilicates will be left in the ash.
Kosminski et al. [22] detected that the release of sodium is
nearly half of that of chlorine and inferred to be in the form of
sodium chloride vapor during gasification and pyrolysis of low-
rank coal. Tomeczek et al. [9] agreed that the chlorides are the
main existing form of the alkali metal in the high temperature
flue gases. As condensing on downstream heating surfaces or
gas-turbine vanes, they will react with SO3, O2 and water vapor
in the flue gases to produce alkali metal sulfates with low
melting points. Shimogori et al. [12] conducted a series of
slagging tests in a 1.5 MWth pilot plant and pointed out that the
predominant mechanism in the formation of the initial layer of
deposit differs for bituminous and sub-bituminous coals.
Additionally, many investigators [23-25] have explored the bed
agglomeration and defluidization during fluidized-bed
combustion and gasification of fuels containing high levels of
alkali metal. They agreed that the low melting eutectics formed
by alkali metal are responsible for these problems. These
research efforts are very useful to recognize how the high
temperature bonded deposit forms.
Currently, a number of measures have been proposed to
prevent excessive fouling of high temperature convection pass
in the boilers firing high-sodium coals. Water washing [26, 27]
is an effective pretreatment method to remove the alkali metal
in the fuel and much attention has been focused on it. Because
of high capital cost, high energy consumption as well as high
water resource consumption, water washing is not suitable to be
used as the preferred option in the coal-fired power plants.
Another method is to add the additives or adsorbents to the
furnace [28, 29]. However, the efficient additives and
adsorbents are still under research, and the huge consumptions
required for the power plants restrict the practical application of
this method deeply. The Babcock & Wilcox Company [30]
advises that the side spacings in the convection banks should be
widened in the design of the boilers using severe fouling coals.
Recently, the blending combustion has become popular in the
utilization of the Zhundong coal, but the blend ration of the
Zhundong coal is restrained and generally no more than 40% is
allowed [31]. Besides, some power plants are using the
Zhundong coal by reducing the load to a low level. Since these
measures can’t solve the fouling problem both effectively and
economically, it’s more desirable to find a better method for the
utilization of high-sodium coals.
2 Copyright © 2015 by ASME
The purpose of this study is to propose a novel boiler
design for high-sodium coal. By providing more radiation
heating surface in the furnace, this design can reduce the
furnace exit gas temperature (FEGT) below 800 °C to avoid the
high temperature bonded deposit. In order to explore the
feasibility of the design, different kinds of boilers with various
capacities are selected to discuss its thermal system
arrangement, heat transfer as well as ignition and combustion.
Also a comparison of steel consumption between a novel boiler
and a conventional one is conducted to consider the economy of
the design. In addition, for the convenience of adjusting and
controlling the FEGT, an improved application with flue gas
recirculation is described in detail.
NOVEL BOILER DESIGN FOR HIGH-SODIUM COAL AND THERMAL PERFORMANCE CALCULATIONS Control principle of fouling
In the boilers firing high-sodium coals, the severe fouling
is defined as the formation of high temperature bonded deposit
on convection heating surfaces. As previously noted, it is the
volatile alkali metal that should be responsible for the formation
of high temperature bonded deposit. Thus, in order to control
the excessive fouling, it is necessary to focus on the
transformation of the volatile alkali metal in coal along the flue
gas flow. As illustrated in Fig. 2, volatile forms of the alkali
metal are vaporized in the hot flue gas when coals are burned in
the furnace. Later the vaporizations leave the furnace outlet and
enter the high temperature convection pass. With diffusing onto
the cool tube walls, they condense and produce a glue which
results in the formation and growth of the bonded deposit. Areas
where the high temperature bonded deposit occurs are marked
in grey. As the flue gas temperature is reduced, the
vaporizations that are not captured by the banks condense on
ash particles in flue gas and are solidified. Hence, the fouling of
low temperature convection pass is mainly in the form of loose
deposit which can be removed by sootblowers easily.
According to the above analysis, the key to successfully
prevent the formation of the high temperature bonded deposit is
to reduce the vaporizations content in the flue gas passing
through the high temperature convection banks. The phases of
the vaporizations are mainly determined by temperature, so it is
available to transform these vaporizations by flue gas
temperature control. A feasible and effective method is to
control the FEGT. If the FEGT is reduced to a desired level at
which the majority of the vaporizations are solidified, there will
be few vaporizations entering the high temperature convection
pass. As a result, the formation of the high temperature bonded
deposit can be avoided.
Fig. 2 Transformation of the volatile alkali metal in coal along the flue
gas flow
Determination of FEGT Generally, the determination of FEGT primarily depends
on deformation temperature of the ash in a conventional boiler
design. However, considering the control of high temperature
bonded deposit, a specific FEGT is required to solidify the
vaporizations of the alkali metal in the flue gas leaving the
furnace outlet. Melting points of common sodium compounds
released in the flue gas are shown in Table 3. Since the release
of sodium is mainly in the form of sodium chloride vapor, the
desired FEGT should be lower than the melting point of NaCl.
Accordingly, a novel boiler design for high-sodium coal is
proposed, providing an FEGT below 800 °C during normal
operation. Table 3 Melting points of common sodium compounds
Sodium Compound Melting Point /°C
Na2O 611
Na3Fe(SO4)3 623
Na3Al(SO4)3 646
NaCl 801
Na2CO3 851
Na2SO4 884
Na2SiO3 1088
Na4SiO4 1088
Boiler configuration for high-sodium coal The furnace of a large pulverized coal, oil or gas fired
boiler is both the place where combustion of fuel occurs and the
place where heat transfer occurs. Radiation basically controls
heat transfer to the furnace enclosure walls. An important
function of the furnace is to reduce the hot flue gas temperature
to a level acceptable to superheaters. For the purpose of firing
high-sodium coal, a decreased FEGT below 800 °C is required
in the novel boiler design. To meet this design requirement, the
3 Copyright © 2015 by ASME
novel boiler provides more radiation heating surface to cool the
combustion products in the furnace. As shown in Fig. 3, the
width, depth and height of the furnace are all increased in the
novel design, and the platen cooled by superheat steam in the
upper furnace is also enlarged. As a result, more heat of
combustion products can be removed in the furnace and the
desired FEGT can be achieved. In addition, with the total
convective heat transfer reduced, the novel boiler provides a
decreased scale of convection pass correspondingly, though the
configuration of a single bank may change a little.
Fig. 3 Furnace configuration comparison between a novel boiler and a
conventional one
Thermal performance calculations A well-designed and operated boiler results from an
accurate thermal performance calculation. The thermal
performance calculation of a boiler can be classified into design
calculation and verification calculation, depending upon
whether a new boiler is being designed or an existing piece of
equipment is being analyzed. Both design calculation and
verification calculation are based on the same heat transfer
principles. Besides, identical equations and diagrams are used.
Heat transfer of radiation heating surface in furnace is
expressed by: 4
radiation fur 0 flaQ A a T (1)
where A is the furnace enclosure wall area, ψ is defined as the
thermal effectiveness factor, afur is known as the furnace
emissivity which is a hypothetic emissivity corresponding to the
radiosity of the flame, σ0 is the Stefan-Boltzmann constant and
Tfla is the average temperature of the flame. Heat transfer of
convection heating surface can be given as:
convection cQ UA t (2)
where U is the heat transfer coefficient, Ac is the area of
convection heating surface and Δt is the temperature difference.
In this paper, the converted coefficient of radiation heat transfer
is defined as:
radiationrad
fla wf( )
Q
A T T
(3)
where Twf is the average temperature of the working fluid. αrad
reflects the intensity of radiation heat transfer in furnace, which
is related to many different factors, including flue gas physical
properties, temperature, furnace configuration, variation of slag
or ash buildup on heating surface, and so on. In the novel
design, since radiation in furnace takes more proportion, it is
more significant to increase αrad in range of reasonable
parameters.
RESULTS AND DISCUSSION Thermal system arrangement
Fig. 4 illustrates the effect of the FEGT on relative heat
absorption of furnace and convection pass when the Zhundong
coal is used. As the FEGT declines, the heat absorbed by
furnace increases. Conversely, the heat absorption of convection
pass decreases. A reduction of 100 °C in the FEGT
approximately leads to a 5% shift in relative heat absorption of
furnace or convection pass. Especially, when an FEGT of
800 °C is determined in the novel boiler design, heat absorption
of furnace is nearly twice more than that of convection pass.
Thus, more heating surface should be arranged in the furnace to
accomplish the heat absorption distribution of boiler system.
Fig. 4 Relative heat absorption of furnace and convection pass at
different FEGTs (Heat absorbed by air heater is included in the total
absorption)
With such a low FEGT, the thermal system arrangement of
a boiler also should be adjusted simultaneously. Taking a 220
t/h boiler system for instance, flue gas outlet temperatures of
heating surfaces along the flue gas flow are shown in Fig. 5. If
the FEGT is maintained at a level of 800 °C, the removal of
heat absorbed by secondary superheater and part of high
temperature superheater will be accomplished in the furnace.
That means the secondary superheater and part of the high
4 Copyright © 2015 by ASME
temperature superheater should be arranged in the furnace as
radiant superheaters, taking the form of widely spaced (700 mm
or larger side spacing) superheat platens or wall superheaters
which are similar to water-cooled wall in configuration. This
analysis is based on the assumption that the heat absorbed by
water-cooled wall remains unchanged. In practice, when the
furnace is enlarged, the water-cooled wall absorbs more heat.
Correspondingly, the heat which should be absorbed by the
economizers is decreased. Eventually, more heating absorption
and superheating absorption will be obtained in the furnace by
radiation heat transfer.
Fig. 5 Flue gas temperature distribution in a 220 t/h boiler system
The effect of boiler capacity on the relative heat absorption
of economizer, water-cooled wall, superheater, reheater and
novel furnace (FEGT = 800 °C, if applied) is shown in Fig. 6.
As the capacity increases, the amount of heat required to
generate saturated steam or reach the critical point declines.
However, the variation in the heat absorption distribution of
boiler system is not significant when the boiler capacity is more
than 1000 t/h. If the novel design is applied to the boilers, the
furnace will achieve about 80% total heat absorption, regardless
of boiler capacity. To meet the requirement, a considerable part
of heat absorbed by superheater, reheater and economizer
should be transferred in the furnace instead. Thus, more radiant
superheaters or reheaters and even radiant economizers are used
in the thermal system arrangement of the novel boiler besides
the volume-enlarged furnace.
Fig. 6 Relative heat absorption for selected boilers with various
capacities
Heat transfer Heat transfer in furnace is closely related to both the
effective thickness of radiant layer (s) and the radiant
attenuation factor (k). Fig. 7(a) illustrates the effect of furnace
volume and shape (H/d) on s, where H is the furnace height and
d is the averaged equivalent diameter of the furnace cross
section. As the furnace volume increases, s increases. The
reason is that the increase in volume is faster than that in
enclosure wall area when a furnace is enlarged. For a given
furnace volume, an increase in H/d leads to a fall in s, but the
variation is small. This means the shape of furnace has a very
weak effect on the furnace emissivity. In addition, if the platens
are arranged in a furnace, s will be decreased due to the
significant rise in furnace enclosure wall area. It can be seen
from Fig. 7(b) that as the FEGT is reduced, k is raised. When an
FEGT is given, a decrease in k is found with an increase in s.
therefore, k may not have a marked variation in a volume-
enlarged furnace, owing to both a fall in the FEGT and a rise in
s.
5 Copyright © 2015 by ASME
(a)
(b)
Fig. 7 Effect of furnace configuration and FEGT on radiation
parameters
Fig. 8 shows the radiation heat transfer characteristic in the
volume-enlarged furnace. These calculations are carried out in a
1000 t/h subcritical space-fired boiler and the variation of slag
or ash buildup on heating surface is elided. As d increases, both
the furnace volume and enclosure wall area (A) are raised.
Thus, more heat of combustion products is removed in the
furnace and the FEGT is reduced, as shown in Fig. 8(a).
Further, Fig. 8(b) indicates the furnace emissivity (afur)
increases with d. As previously discussed, the variation in k is
small, so the rise in afur is mainly caused by the increase in s.
Additionally, it is found that the converted coefficient of
radiation heat transfer (αrad) falls as d increases. Notably, when
d is raised, though the increase in afur is beneficial for enhancing
radiation heat transfer in furnace, αrad still has a significant
decrease. This results from the reduction in the average
temperature of the flame that affects the intensity of radiation
heat transfer strongly.
(a)
(b)
Fig. 8 Radiation heat transfer characteristic in the volume-enlarged
furnace (H/d = 3)
Heat transfer principle in convection pass is unchanged
between a novel boiler and a conventional one. However, such a
low FEGT in the novel boiler can lead to a remarkable decrease
in the temperature difference of convection pass, which
increases the steel consumption and makes it difficult to
maintain the rated steam temperature. Thus, an optimized
thermal system is required in the novel boiler, considering the
heat transfer of both furnace and convection pass.
Ignition and combustion Ignition and combustion are very important factors in the
boiler furnace design. A volume-enlarged furnace is used to
reduce the FEGT in the novel design, which can adversely
affect ignition and combustion. Considering a space-fired
boiler, as the FEGT is reduced, both the average temperature of
the flame (Tfla) and the heat release rate per unit furnace cross-
sectional area (qF) decline (see Fig. 9). The lower qF and Tfla
are, the smaller the intensity of mix and combustion will be.
Eventually, the boiler will not be able to maintain the normal
operation if the FEGT is reduced to such a low level. For a
grate-fired boiler, the volume-enlarged furnace has a small
effect on the ignition and combustion due to the arrangement of
furnace arches, but the low boiler efficiency immensely limits
its utilization in power generation. Similarly, when the novel
6 Copyright © 2015 by ASME
design is applied in a circulation fluidized bed boiler, the
difficulty in ignition and combustion still exists. Moreover, the
bed agglomeration and defluidization are also exacerbated
during the combustion of high-sodium coals. In a cyclone-fired
boiler, combustion and heat transfer in furnace are carried out
in divided chambers. Combustion mostly occurs inside the
cyclone barrel while radiation heat transfer mostly occurs inside
the main furnace. When the main furnace is enlarged, ignition
and combustion within the cyclone barrel are almost unaffected.
Thus, the cyclone-fired boiler is considered to be the most
appropriate application for the novel design. Because of high
combustion temperatures, cyclone furnaces have high NOx
emissions. Considering an increasing public demand for
reducing pollution, the cyclone units became less popular.
However, with the development of air staging technology,
considerable reductions in NOx levels have been demonstrated
in some cyclone boilers using staged combustion.
Fig. 9 Effect of FEGT on ignition and combustion in a space-fired
boiler
Steel consumption A comparison of steel consumption between a novel boiler
and a conventional one is demonstrated in Fig. 10. This
evaluation is conducted in a 220 t/h boiler, using the Zhundong
coal as designed coal. Physical arrangement parameters of the
boiler components are listed in Table 4. In the novel boiler, the
secondary superheater is arranged in the furnace as a platen
radiant superheater and the FEGT is maintained at a level of
800 °C. The steel consumption is measured by the heating
surface area. For the welded membrane water-cooled wall used
here, the area is calculated in terms of the single-side exposed
surface size of the enclosed furnace volume. For the sake of
comparison, the double area of water-cooled wall is counted
when the whole boiler is considered. It can be seen that the steel
consumption of water-cooled wall and secondary superheater is
raised in the novel boiler. Conversely, other main components
of the novel boiler cost less. According to the results of the
whole boiler, the expense of the novel boiler is approximately
increased by 10% relative to the conventional one.
Fig. 10 Comparison of steel consumption between a novel boiler and a
conventional one [1- Water-cooled wall, 2- Secondary superheater, 3-
High temperature superheater, 4- Low temperature superheater, 5-
Turning cavity, 6- Economizers, 7- Whole boiler (not including air
heaters)]
Table 4 Physical arrangement of the components in a 220 t/h novel (conventional) boiler
Furnace Other Components
Parameter Units Water-cooled
wall
Parameter Units Secondary
superheater
High
temperature
superheater
Low
temperature
superheater
Economizers
Width m 11 (7.6) Tube OD mm 42 (42) 42 (42) 38 (38) 32 (32)
Depth m 11 (7.6) Sidespacing mm 1000 (582) 100 (100) 100 (100) 60 (60)
Height m 31 (21.3) Backspacing mm 59 (59) 89 (89) 80 (80) 88 (88)
Volume m3 3518 (1116) Heating surface m2 790 (613) 920 (1060) 780 (815) 1680 (2038)
Surface m2 1154 (691) Free flow area m2 - (57) 35 (26) 30 (21) 27 (19)
Improved application with flue gas recirculation An alternate method to control FEGT is gas tempering by
flue gas recirculation. The cool recirculated flue gas is directly
mixed with hot flue gas near the furnace exit in this method.
The FEGT can be reduced with less furnace surface. However,
to achieve an FEGT below 800 °C, a recirculation ratio of 50%
is approximately required when the recirculated flue gas is from
boiler exhaust. As a result, the capital cost of boiler rises due to
a marked reduction in the average thermal head for heat transfer
of the whole boiler, and the expense on fan maintenance and
7 Copyright © 2015 by ASME
power requirement also reaches a high level. If the flue gas
recirculation is applied in the novel design, an improved
application is developed. The improved application provides a
two-stage control of FEGT. The first stage reduces the FEGT to
a relative lower level (such as 900 °C) by arranging more
radiation heating surface. Correspondingly, the second stage
reduces the FEGT to the desired level by flue gas recirculation.
Thus, the furnace surface or recirculation ratio can be
decreased, as compared with the cases which only adopt the
first stage or the second stage, respectively. In addition,
performances of the boiler will be improved significantly. The
FEGT can be maintained at a stable level by adjusting the
amount of recirculated flue gas when the operating conditions
change. On the other hand, the increased flue gas weight can
improve the level of convection heat transfer capability of the
boiler. Further, when the improved application is used in
practice, the optimization of thermal system arrangement and
operating parameters is of great significance for cost reduction.
CONCLUSION In this study, a novel boiler design was proposed to
prevent the severe fouling of high temperature convection pass
in the boilers firing high-sodium coals. The design was explored
and evaluated in different kinds of boilers with various
capacities by considering thermal system arrangement, heat
transfer, ignition and combustion, and steel consumption. The
following conclusions can be drawn:
(1) As the FEGT declines, the heat absorption of furnace
increases while the convection pass decreases. To achieve an
FEGT below 800 °C, more radiation heating surface should be
used in the thermal system arrangement of the novel boiler
besides the volume-enlarged furnace.
(2) When the furnace volume is enlarged, the effective
thickness of radiant layer increases while the radiant attenuation
factor varies slightly, which resulting in the increase in the
furnace emissivity. Moreover, the converted coefficient of
radiation heat transfer reduces significantly due to the reduction
in the average temperature of the flame.
(3) In a space-fired boiler, the volume-enlarged furnace
can adversely affect ignition and combustion. The cyclone-fired
boiler is considered to be the most appropriate application for
the novel design, for its combustion and heat transfer in furnace
are carried out in divided chambers.
(4) The steel consumption of the novel boiler is
approximately increased by 10% relative to the conventional
one.
(5) An improved application with flue gas recirculation is
probed owing to its advantages of controlling FEGT and
maintaining the level of convection heat transfer capability of
the boiler.
NOMENCLATURE afur furnace emissivity [-]
A furnace enclosure wall area [m2]
Ac area of convection heating surface [m2]
d averaged equivalent diameter of the furnace cross
section [m]
H furnace height [m]
k radiant attenuation factor [1/(MPa·m)]
qF heat release rate per unit furnace cross-sectional area
[MW/m2]
s effective thickness of radiant layer [m]
Tfla average temperature of the flame [K]
Twf average temperature of the working fluid [K]
U heat transfer coefficient [W/(m2·K)]
Greek symbols
αrad converted coefficient of radiation heat transfer
[W/(m2·K)]
Δt temperature difference [°C]
σ0 Stefan-Boltzmann constant [W/(m2·K4)]
ψ thermal effectiveness factor [-]
Subscripts
0 constant
c convection
F face
fla flame
fur furnace
rad radiation
wf working fluid
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8 Copyright © 2015 by ASME
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