Chemical Engineering Science 238 (2021) 116600

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Chemical Engineering Science

journal homepage: www.elsevier.com/locate/ces

Numerical study on acid condensation and corrosion characteristics of

three-dimensional finned tube surface
J.L. Wang, Y.B. Tao ⇑, J. Liu
Key Laboratory of Thermo-fluid Science and Engineering, Ministry of Education, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China

h i g h l i g h t s

A heat and mass transfer model of flue gas on finned tube surface was developed.

Acid dew point temperature and condensation characteristics were investigated.

Effects level of operation parameters were examined.

Corrosion characteristics were analyzed.

Optimal operation parameters were recommended.

a r t i c l e i n f o a b s t r a c t

Article history: Low temperature corrosion is a key factor affecting the performance and safety of heat exchanger for
Received 13 August 2020 industrial waste heat recovery system. Acid dew point temperature and vapor condensation characteris-
Received in revised form 15 March 2021 tics are two major parameters to evaluate corrosion behavior. However, previous studies focused solely
Accepted 18 March 2021
on acid dew point temperature or condensation characteristics. In present paper, a numerical model was
Available online 22 March 2021
established to investigate the heat and mass transfer process of flue gas on three-dimensional finned tube
surface and predict the acid dew point temperature and condensation characteristics simultaneously.
Keywords:
Firstly, the effects of operation parameters were examined both by single variable method and orthogo-
Three-dimensional finned tube
Heat and mass transfer
nal method. The results show that the flue gas inlet velocity and acid vapor concentration have the most
Acid dew point significant effects on acid dew point temperature; the tube wall temperature and water vapor concentra-
Acid vapor condensation tion have the most significant effects on the condensed acid solution concentration. Then, the corrosion
Corrosion characteristics characteristics was discussed and the optimization working parameters (the water vapor concentration
in flue gas below 10.12% and the tube wall temperature above 349.3 K) are recommended.
Ó 2021 Elsevier Ltd. All rights reserved.

1. Introduction fore, it is particularly important to predict the corrosion character-

istic during the heat and mass transfer process of industrial flue
The combustion of coal releases sulfur trioxide and water vapor, gas, which is helpful to performance enhance and anticorrosion
and the sulfur trioxide combines with water vapor to form sulfuric design of heat exchanger.
acid vapor. When the flue gas temperature is between 176 °C and The acid dew point temperature is a key index used to evaluate
400 °C, the three components coexist simultaneously, while when the low temperature corrosion characteristics of flue gas, because
the temperature is lower than 176 °C, the equilibrium is all toward it determines whether the acid vapor condenses on heat exchanger
H2SO4 (Vorgelegt, 2004). For the heat exchanger used in waster surface and gives the reasonable exhaust temperature to avoid low
heat recovery system, the sulfuric acid vapor always condensates temperature corrosion. The previous researches on acid dew point
on the finned tube surface and causes serious low temperature cor- temperature are mainly based on experimental and theoretical
rosion, when the wall temperature is lower than the flue gas acid method, where the corresponding formulae are fitted, as listed in
dew point temperature. Actually, low temperature corrosion is Table 1 (Haase and Borgmann, 1961)- (Wang and Tang, 2016).
one of the key factors that affect the efficiency and safety of heat Although there are many empirical formulae, the flue gas acid
exchanger used in industrial waste heat recovery system. There- dew point temperature of a certain flue gas calculated from differ-
ent formulae varies greatly. Furthermore, in practical applications,
⇑ Corresponding author. the water and acid vapor volume fractions or partial pressure are
E-mail address: yubingtao@mail.xjtu.edu.cn (Y.B. Tao). variable during the heat and mass transfer process especially

https://doi.org/10.1016/j.ces.2021.116600
0009-2509/Ó 2021 Elsevier Ltd. All rights reserved.
J.L. Wang, Y.B. Tao and J. Liu Chemical Engineering Science 238 (2021) 116600

Nomenclature

A area, m2 Vcell grid volume, m3

ai, bi, ci constants in ideal-gas heat capacity w velocity components in z-directions, ms1; or fin width,

ai activity m
cp specific heat at constant pressure, Jkg1K1 W computational domain width, m

Cl pi paritial-molar heat capacity, Jkg1K1 x, y, z Cartesian coordinates, m
C1e,C2e turbulence model constant xi mole fraction of species i in flue gas
Dij binary mass diffusion coefficient, m2s1 yi mass fraction of species i in flue gas

fl w liquid-phase fugacity Xi mole fraction of species i in solution
h fin height, m Yi mass fraction of species i in solution
H computational domain height, m
DHv i heat of vaporization, Jkg1 Greek symbols
k thermal conductivity, Wm1k1; or turbulent kinetic ai partial-molar heat capacity coefficient
energy, m2s2 ak, ae Inverse effective Prandtl numbers for k and e
K0, K1 equilibrium constants d fin thickness, m
L computational domain length, m e turbulent energy dissipation rate
Ll i partial molar enthalpy, Jkg1 /io apparent fugacity coefficient
mi mass condensation rate of species i, kgm2s1 k thermal conductivity, Wm1K1
M molecular weight, kgmol1 l dynamic viscosity, kgm1s1
Ni mole condensation rate of species i, molm2s1 q density, kgm3
Nu Nusselt number t kinematic viscosity, m2s1
P pressure, Pa
pi partial pressure of species i, Pa
Subscripts
pio apparent partial pressure, Pa a sulfuric acid component
Re Reynolds number based on tube diameter adp acid dew point
Rv gas constant of water vapor, Jkg1K1 dp dew point
ri latent heat of i component, Jkg1
eff effective
Sct Schmidt number g flue gas
Se energy source term, Jm3s1 H2O water vapor
DSv i entropy of vaporization, Jkg1K1
in inlet parameter
Sm mass or species source term, kgm3s1 s saturation
T absolute temperature, K SO3 Sulphur trioxide
t Celsius, oC w water component
U velocity vector, ms1
wall wall condition
u velocity components in x-directions, ms1
v velocity components in y-directions, ms1; or diffusion
volumes, m3mol1

accompanied by condensation process of vapors. Consequently, the dioxide conversion into sulfur trioxide in flue gas through experi-
applicability of empirical formulae is strictly restricted by the ments, proposed a new formula for estimating acid dew point of
actual values and distributions of the corresponding parameters, flue gas. Xiang et al. (Xiang et al., 2016) proposed a semi-
which are difficult to obtain. In order to overcome the limitations empirical prediction model by comparing the previous prediction
of empirical formula, in recent years, some new algorithm, new models of acid dew point temperature, and compared the new
model and new measuring method are established and used to model with the previous. Subsequently, a device for the measuring
investigate the acid dew point temperature. ZareNezhad and Ami- of acid dew point temperature was designed based on the principle
nian (ZareNezhad and Aminian, 2010) predicted the acid dew point of a conductive dew point meter (Xiang et al., 2016). The acid dew
temperature in flue gas through a multilayer feed-forward neural point temperature under different flue gas conditions was mea-
network, and presented a prediction model with wide ranges of sured and compared with the previous semi-empirical formula.
sulfur trioxide and water vapor concentrations. Li et al. (Li et al., Wang and Tang (Wang and Tang, 2016) used the acid dew point
2016) studied the heterogeneous and homogeneous effect of sulfur estimation formula derived from thermodynamic theory to

Table 1
Empirical formulae for the sulfuric acid dew point in flue gas.

Name Correlation
Haase &Borgmann (Haase and Borgmann, 1961) t adp ¼ 255 þ 27:6lgpSO3 þ 18:7lgpH2 O
Müller (Müller, 1959) t adp ¼ 116:5515 þ 16:06329lgV SO3 þ 1:05377lgðV SO3 Þ2
Okkes (Okkes, 1987)
2:19
t adp ¼ 10:8809 þ 27:6lgpH2 O þ 10:83lgpSO3 þ 1:06 lgpSO3 þ 2:9943
Verhoff (Verhoff and Banchero, 1974) 1000
ðt adp þ273:15Þ ¼ 2:988  0:138lgpH2 O  0:267lgpSO3 þ 0:0329lgpH2 O lgpSO3
Bapahoba (Cen et al., 1994) t adp ¼ 186 þ 20lg/H2 O þ 10:83lg/SO3
Halstead (Cen et al., 1994) t adp ¼ 113:0219 þ 15:0777lgV SO3 þ 2:0975lgðV SO3 Þ2
 
Thermodynamic analysis (Wang and Tang, 2016) t adp ¼ 1= tadp;0 þ273:15
1
 DRQ ln cpaap  273:15

2
J.L. Wang, Y.B. Tao and J. Liu Chemical Engineering Science 238 (2021) 116600

examine the influence index of flue gas containing ash on acid dew densation rates of sulfuric acid vapor and water vapor in the cir-
point, and pointed out that the fin structure containing bleeding cular tube, and also corrected thermodynamic properties
dimples and longitudinal vortex generators can reduce the acid parameters to estimating the acid dew point temperature. Zhang
dew point temperature of flue gas. Chen et al. (Chen et al., 2017) (Zhang, 1991) established a finite difference model to predict the
studied the corrosion of sulfuric acid on three bulk enamels with condensation rates of sulfuric acid and water vapor on the flow
different silica contents through experiments. Wei et al. (Wei passage wall. Vorgelegt (Vorgelegt, 2004) calculated the dew
et al., 2017) predicted the acid dew point temperature and ana- point temperature for the binary system H2O-H2SO4 based on
lyzed the influence of temperature, acid vapor content and water the vapor–liquid equilibrium model, and developed a numerical
vapor content on the condensation of sulfuric acid through orthog- model applied to 3D geometries to preliminarily obtain the con-
onal experiment. Zuo et al. (Zuo et al., 2020) summarized the pre- densation rate of sulfuric acid vapor. Han et al. (Han et al.,
vious methods for determining the acid dew point temperature 2013) established a new numerical model by using the update
and pointed out that it is an urgent need for a new method to fugacity equation, and predicted the condensation characteristic
reveal the sulfuric acid vapor condensation process. It can be con- of sulfuric acid vapor on H-type finned tube surfaces. Subse-
cluded that the previous research on the acid dew point merely quently, the influence of several geometric parameters and Rey-
focused on the acid dew point itself without considering the con- nolds number on the acid deposition characteristics was
densation of sulfuric acid vapor. In fact, the acid dew point and studied, and a correlation of the Sherwood number of sulfuric
vapor condensation are inseparable and interactive in low temper- acid vs H-type fin geometries for the tube bank with 10 rows
ature corrosion. The acid vapor condensation process must be fur- was obtained (He et al., 2015). Karvounis et al. (Karvounis et al.,
ther investigated to predict acid corrosion characteristics 2018) numerically and experimentally studied the condensation
appropriately. process of sulfuric acid and water in the marine diesel engine
The heat and mass transfer process of flue gas in heat exchanger using the fluid film model. From the above literature review, it
is the foothold of condensation characteristics of vapors. Moskovits can be seen that the research on condensation characteristics
(Moskovits, 1959) presents the relationship between sulfuric acid only focuses on itself and ignores the influence of acid dew point.
condensation rate and corrosion rate, and pointed out that the cor- In the other hand, it is known that there inevitably exists con-
rosion rate also seems to depend on the concentration of con- tact thermal resistance between the parent tube and the fin of
densed acid solution and the temperature of the metal wall. Able the heat exchange tube manufactured by tube expansion technol-
(Abel, 1946) originally derived the expression of sulfuric acid vapor ogy, such as H-type finned tube heat exchanger widely used in the
partial pressure in the vapor phase above the sulfuric acid solution waste heat recovery system. However, the influence of contact
system based on the thermodynamic relations. Haasse and Borg- thermal resistance is neglected in most of the previous numerical
mann (Haase and Borgmann, 1961) measured the partial pressures studies. In recent years, due to the advanced manufacturing tech-
of vapors above the sulfuric acid solution, and proposed an empir- nology, the three-dimensional integral finned tubes was designed
ical formula for calculating the acid dew point temperature. Gmitro and there is no contact thermal resistance between the parent tube
and Vermeulen (Gemitro and Vermeulen, 1964) further deduced and the fin. Researchers have widely studied the fluid flow and
the vapor–liquid equilibrium for sulfuric acid solution. Based on heat transfer performance of the integral 3-D finned-tube heat
Prigogine and Defay Chemical Theory, Pessoa et al. (Pessoa et al., exchangers. Li et al. (Li et al., 2005) experimentally studied the
2006) developed a new thermodynamic model to calculate the characteristics of the single-phase flow and flow-boiling heat
vapor–liquid phase equilibrium of the sulfuric acid solutions in transfer of three-dimensional internally finned tubes as well as
the whole concentration range, but the model is only suitable for micro-finned helical tubes. Through experiments and simulations,
temperature between 0 and 150 °C. Verhoff and Banchero Zhang et al. (Zhang et al., 2008) studied the flow heat transfer char-
(Verhoff and Banchero, 1972) predicted the sulfuric acid vapor acteristics of a spiral baffle heat exchanger combined with 3D
pressure and dew point with the previous experimental data, and external finned tube. Xu et al. (Xu et al., 2018) simulated the flow
pointed out that the precise measurement of thermodynamic and heat transfer characteristics of three-dimensional externally
properties needs to be further improved. Jeong and Levy (Jeong finned tube bank, and investigated the values of the comprehen-
and Levy, 2012) theoretically and experimentally investigated the sive evaluation index for fluid flow and heat transfer performance
sulfuric acid condensation in flue gas flowing through a condensing under different structural parameters. However, the current
heat exchanger, and found that the mass transfer process of sulfu- researches on the 3-D finned tube mainly focus on the fluid flow
ric acid condensation exhibits two main trends: steep reduction of and heat transfer performance with different fin parameters, tube
acid concentration within the inlet region and smaller reductions bundle arrangements and operation conditions. Therefore, it is
further downstream. Wei et al. (Wei et al., 2018) experimentally urgently needed to study the corrosion characteristic of three-
studied the effects of fouling layer on heat transfer efficiency of dimensional finned tube surface for the application in waster heat
heat exchanger. After that a one-dimensional model was devel- recovery system.
oped to numerical predict the sulfuric acid condensation and the Acid dew point temperature and acid vapor condensation are
effects of wall temperature, acid vapor and water vapor contents two key indexes to evaluate low temperature corrosion, and the
of flue gas were investigated. two indexes are closely interrelated and influence each other.
Affected by process complexity and experimental level, it is However, most of the previous studies only focused on acid dew
difficult to accurately descript the details of acid vapor condensa- point temperature or vapor condensation, which virtually inter-
tion process, especially the local distribution of the condensation rupted their unity in heat and mass transfer. In present paper, both
characteristics on heat exchanger surface. With the development the acid dew point temperature and sulfuric acid vapor condensa-
of computer and numerical simulation technology, many tion are taken into account to analyze the low temperature
researchers pay attention to develop multidimensional numerical corrosion characteristics of integral finned tube heat exchanger.
model to predict the condensation process of acid vapor. In addi- A three-dimensional heat and mass transfer model for the multi-
tion, numerical prediction method has been proved to be a more component transmission process was established based on the
convenient way for engineering application with less time and commercial software FLUENT. Subsequently, the effects of flue
costs compared to experimental method. Wilson (Wilson, 1989) gas temperature, flue gas velocity, sulfuric acid vapor concentra-
derived the fugacity-coefficient equation for a binary system tion and water vapor concentration on acid dew point tempera-
based on first principles, and then predicted the steady-state con- ture, condensation rates of vapors and condensate solution
3
J.L. Wang, Y.B. Tao and J. Liu Chemical Engineering Science 238 (2021) 116600

concentration were examined. Finally, the suitable operating con- process mostly occurs on the finned tube surface, this assumption
ditions are proposed to reduce low temperature corrosion. has little effects on the simulation results but can efficiently reduce
the simulation difficulty.
(2) Ignore the effects of liquid film on the system. And the tem-
2. Model description and numerical method
perature of the condensed acid solution is the same as the surface
temperature of the finned tube. Although, after the vapor con-
2.1. Physical model
denses, a liquid film will be formed on the surface of the heat
exchanger, previous study (Goldbrunner, 2003) has shown that
The physical model of the three-dimensional integral external
the influence of the liquid film on the total heat resistance is 1–
finned tube is shown in Fig. 1(a) and (b), which is a circular tube
3%. Therefore, the assumptions and simplifications are suitable
with 20 fins distributed uniformly along the circumference. The
for the engineering application.
geometry parameters of the finned tube are listed in Table 2.
(3) Ignore, the effects of vapors condensation on the thermo-
Fig. 1(c) shows the computational domain for the finned tube,
physical properties of flue gas. The magnitude of water vapor mole
where a section of the tube was chosen as the computational unit
fraction in the flue gas is about 10-1, which is far greater than that
due to the geometry and the inlet and outlet parts of the finned
of sulfuric acid vapor (10-5-10-6). And the condensation rates of
tube region were appropriately extended to ensure calculation
water vapor and sulfuric acid vapor are of the same order of mag-
accuracy. The temperature of the tube surface is a fixed value,
nitude. So the amount of water and acid vapor condensation is very
and the flue gas outside the tube is composed of sulfuric acid
small compared to the bulk of flue gas, which has little effects on
vapor, water vapor and air.
thermophysical properties.
(4) Ignored the influence of condensation on the momentum
2.2. Governing equations and source terms equation due to the small amount of vapor condensation.
The RNG k-e equation model is selected to solve the turbulence
Prediction the corrosion characteristics including flue gas acid flow. Base on the above assumptions, the governing equations are
dew point and vapor condensation is a complex process involving as follows.
heat and mass transfer. Therefore, appropriate simplification is Continuity equation:
needed to meet the needs of numerical simulation. The assump-
r  ðqUÞ ¼ Sm ð1Þ
tions and simplifications used in present paper are described as
follows. Momentum equation:
(1) Ignore the condensation of water vapor and sulfuric acid
1
vapor in the flow channel, and only consider the condensation of U  rU ¼ tr2 U  rP ð2Þ
q
vapors on the wall surfaces. Because the heat and mass transfer

(a) Schematic of the finned tube

(b) Cross-section for the finned tube

(c) Computational domain

Fig. 1. A schematic diagram of the external finned tube model.

4
J.L. Wang, Y.B. Tao and J. Liu Chemical Engineering Science 238 (2021) 116600

Table 2 The concentration of the condensed sulfuric acid solution is

Geometry parameters of the external rectangular-finned tube heat exchanger. described as follow:
D (mm) w (mm) h (mm) d (mm) H (mm) L/D L1/D W/D
Ra
32 2.5 2 0.2 3 14 3.75 1.5 Xa ¼ ð14Þ
Rw þ Ra

Energy equation: 2.3. Prediction model of acid dew point

  X !  !
@ !  !
ðqEÞ þ r  v ðqE þ pÞ ¼ r  keff rT  hj J j þ seff  t þ Se A variety of empirical formulae for the acid dew point has been
@t j present in Table 1. However, most of them has its own limitation.
ð3Þ Both Muller curve fitting formula (Müller, 1959) and Halstead for-
mula (Cen et al., 1994) are derived from their experimental data,
Species equation: but the formulae only consider a single factor, ignoring the effect
  of water vapor on the flue gas acid dew point, which is discon-
lt
r  ðqUyi Þ ¼ r  qDi;eff þ r y i þ Si ð4Þ nected from engineering applications. The Okkes formula (Okkes,
Sct
1987) is an estimation formula based on Muller experimental data
Kinetic energy equation: (Müller, 1959), which has a wide application range, but the calcu-
 lation accuracy is slightly worse. The Verhoff & Banchero formula
@ @
 @k
ðqkui Þ ¼ ak l þ lt þ lt S2  qe ð5Þ (Verhoff and Banchero, 1974) is more accurate when calculating
@xi @xj @xj
high-temperature flue gas, with an error of about 4 K, but it is
Dissipation rate equation: not ideal for low-temperature flue gas. The calculated value of
 the Bapahoba formula (Cen et al., 1994) is not in line with reality
@ @
 @e e e2
ðqeui Þ ¼ ae l þ lt þ C 1 e l t S2  C 2 e q  R e ð6Þ when the sulfuric acid content is low. The estimation formula of
@xi @xj @xj k k
thermodynamic analysis is derived from the derivation of thermo-
where ak = ae = 1.393, C1e = 1.42 and C2e = 1.68 are used in the dynamic theory, lacking engineering practice, and ignoring the
numerical simulation. The turbulent viscosity can be calculated influencing factors in engineering. After comparison, the Haase &
from lt = clqk2/e with cl = 0.085. Borgmann formula (Haase and Borgmann, 1961) is finally selected
To define the source items in the governing equations, the mass to calculate the acid dew point temperature during the simulation
condensation rate of vapors (including water vapor and acid vapor) process, as shown in Eq. (15).
at the finned tube surface is needed, which can be calculated by Eq.
(7). tadp ¼ 255 þ 27:6lgpSO3 þ 18:7lgpH2 O ð15Þ
 
lt
mi ¼  qDi;eff þ ryi ð7Þ 2.4. Boundary conditions
Sct
Where, the effective diffusivity coefficients, Di,eff, is calculated from The partial boundary conditions used in the numerical calcula-
the binary diffusivity coefficients Dij. tion are shown in Fig. 1(c). In addition, at the inlet boundary, the
Xn
xj uniform velocity, temperature and the flue gas component content
Di;eff ¼ ð1  xi Þ= ð8Þ are given, and the temperature of the finned tube wall surface is
j¼1
Dij
j–i
350 K. A no slip condition is used for wall surfaces. For the species
equation, the fugacity equation (Gemitro and Vermeulen, 1964) is
The empirical correlation for the binary diffusivity coefficients used to solve the vapor saturation partial pressure in the flue gas,
Dij can be expressed as (Wilson, 1989): as shown below.

1=2
0:0104T 1:75 1=M i þ 1=M j v v l l 
Dij ¼ hP
P 1=3 2i ð9Þ lnpi ¼ ai A þ bi B þ ci C þ DHi D þ DSi E þ C pi F þ Li G þ ai H þ lnai ð298Þ
P ð v i Þ1=3 þ vj ð16Þ
Where vi and vj are the diffusion volumes obtained by summing where pi is the saturation partial pressure of acid or water vapor at
atomic-diffusion volumes for each constituent of the binary gas the vapor–liquid phase interface; A-H are the explicit functions of
system. temperature of acid condensate, as shown in Eq.17- Eq.24; ai, bi, ci
Source terms Si, Sm, Se appear in the species, continuity and are the ideal-gas heat capacity coefficients, whose values are shown
energy equations, respectively, which are redefined as: in Table 3; DHv i and DSv i are the heat of vaporization and entropy
Si;m ¼ mi Aface =V cell ð10Þ of vaporization, respectively;  Cl pi,  Ll i, ai and  ai are the partial-
molar heat capacity, the partial-molar heat of mixing, the partial-
Sm ¼ Sa;m þ Sw;m ð11Þ molar heat-capacity coefficient and the liquid activity logarithm,
respectively.
Se ¼ ðma r a þ mw rw ÞAface =V cell ð12Þ The explicit functions of temperature in the fugacity equation
are as follows.
where ra and rw are the condensation latent heat of acid vapor and
  
water vapor, Aface and Vcell are the area and volume of the first layer 1 T 298
A¼ ln þ 1 ð17Þ
mesh adjacent to the wall where the condensation occurs. R 298 T
The calculation of the molar condensation rate is as follows:
" #
mi 1 2982 T
Ri ¼ ð13Þ B¼ þ  298 ð18Þ
Mi R 2T 2

5
J.L. Wang, Y.B. Tao and J. Liu Chemical Engineering Science 238 (2021) 116600

Table 3 acid vapor. Therefore, it is assumed that the water vapor content
Ideal-gas heat capacity coefficients. at the vapor–liquid phase interface is the same as the water vapor
ai bi (10-3 ci (10-6 content in the flue gas (Wilson, 1989). Then calculate the concen-
(calmol1K1) calmol1K2) calmol1K3) tration of condensed acid solution according to the fugacity equa-
Water 6.9647 3.4609 0.4829 tion, namely Eq. (16), and the subscript of parameters in Eq. (16) is
Sulfuric 19.506 45.30 1.111 take as w. Secondly, the saturated partial pressure of sulfuric acid
acid vapor at the vapor–liquid phase interface is calculated according to
the acid solution concentration obtained in the previous step, and
" # the subscript of the parameter in Eq. (16) is taken as a. Thirdly,
1 2983 2982 T 2 determine whether there is condensation based on the acid partial
C¼  þ ð19Þ
R 3T 2 6 pressure in the flue gas and the saturated acid partial pressure at
the vapor–liquid phase interface. If condensation does not occur,
1 the concentration gradient of acid and water vapor near the wall
D¼ ð20Þ is 0. Otherwise, the first class boundary condition is given and
RT
the vapor condensation rates and acid concentration are calcu-
1 lated. Fourthly, the acid solution concentration calculated in the
E¼ ð21Þ previous step is substituted into Eq. (16) to solve the saturated par-
R
tial pressure of water vapor at the vapor–liquid phase interface.
   Subsequently, the difference between the calculated value and
1 298 298
F¼ ln  þ1 ð22Þ the assumed value is compared to judge whether it converges or
R T T
not.

1 1 1
G¼  ð23Þ 2.5. Numerical method
R T 298
"   # The aforementioned governing equations were solved by the
1 T 2982 T
H¼ 298ln þ  ð24Þ FLUENT software, combined with a series of UDFs, which are used
R 298 2T 2 to calculate the physical properties of the mixture including ther-
mal conductivity, density and heat capacity, gas–liquid interface
In fact, the saturation partial pressure of vapors calculated by
boundary conditions, source terms, effective diffusion coefficient,
the fugacity equation are not the final values selected in the
the vapor condensation rates and flue gas acid dew point temper-
numerical simulation, because the following two reversible reac-
ature. The calculation of physical properties used corresponding
tions, as shown in Eq. (25) and (26), occur in the mass transfer pro-
mixture rules as shown in Ref. (Wilson, 1989). The SIMPLE algo-
cess, which leads to a slight deviation between the value calculated
rithm was selected to solve the velocity pressure coupling while
by the fugacity equation and the actual value.
second-order upwind discretization schemes were used for the
H2 SO4 () SO3 þ H2 O K 0 ð25Þ convective terms. Enhanced wall treatment is used to treat the
near-wall turbulence.
H2 SO4 þ H2 O () H2 SO4  H2 O K 1 ð26Þ
Therefore, Wilson (Wilson, 1989) introduced the fugacity coef- 3. Numerical model and grid independence validation
ficient to modify the saturated vapor partial pressure, which is
expressed as: The fluid flow and heat transfer characteristics are the funda-
mental problem in the study of three-dimensional external finned
pi
pi;o ¼ ð27Þ tubes, and it is also a prerequisite for further research on the sur-
/i;o
face corrosion characteristics. In this paper, the simulation results
of the flow and heat transfer characteristics of the three-
pw
/ao ¼ ð28Þ dimensional external finned tube are firstly compared with the
pw þ K 0 þ K 1 ðpw Þ2 experimental values (Wu, 2002) to verify the applicability of the
present numerical model. The experimental correlations of the
1 Nusselt number and Euler number (Wu, 2002) are as follows:
/wo ¼ ð29Þ
1 þ K 1 pa
Nu ¼ 0:2017Re0:6765 ð30Þ
where pi,o and /io are the apparent partial pressure and the appar-
ent fugacity coefficient, respectively.
Eu ¼ 3:1597Re0:0604 ð31Þ
The comparison between the present calculated values of the
saturated vapor partial pressure and the experimental values can After the grid-independency validation, the final calculation
be found in our previous study (Wang et al., 2019). results for flow and heat transfer characteristics with the present
From the above analysis, it can be seen that the decisive param- model are compared with experimental correlations, as shown in
eters of the fugacity equation include three categories, namely, sat- Fig. 3. It can be seen from Fig. 3 that under low Reynolds number,
urated partial pressures of species, temperature and concentration the difference between the simulated Euler number and the exper-
of condensed solution. Therefore, the saturation partial pressure imental values is relatively large, but the maximum relative error
can be simply obtained as long as the values of the other two is lower than 12.30%. As the Reynolds number increases, the differ-
parameters are determined. So, the iterative solution of the bound- ence between the calculated value and the experimental value
ary conditions of the species equation is needed as shown in Fig. 2. gradually decreases. Within the calculation range, the average
Firstly, it can be found from the calculation formula of the con- relative error is 5.83%, which can meet the requirements of engi-
densed acid solution concentration that the vapor condensation neering application. It can also be seen from Fig. 3 that as the Rey-
rates are in the same order of magnitude, however, the content nolds number increases, the difference between the simulated
of water vapor in the flue gas is much larger than that of sulfuric Nusselt numbers and the experimental values gradually increases,
6
J.L. Wang, Y.B. Tao and J. Liu Chemical Engineering Science 238 (2021) 116600

Fig. 2. Iterative solution of the boundary conditions of the species equation.

but the maximum relative error is less than 6%. In summary, the Fig. 4 shows the comparison between the numerical results of
present numerical results are in good agreement with the experi- the sulfuric acid vapor condensation rates and the experimental
mental results, which indicates that the present numerical model values. As can be seen from Fig. 4, the numerical results are in good
can be used to predict the flow and heat transfer characteristics agreement with the experimental values. The detailed discussion
of the three-dimensional external finned tube. on condensation rate verification can be found in our previous
In order to validate the applicability of the present numerical study (Wang et al., 2019). In summary, the present numerical
method for the mass transfer problems, according to the experi- model is also suitable for mass transfer problems.
mental parameters in Ref. (Wilson, 1989), a numerical simulation In order to judge whether the acid dew point calculation model
of the laminar mass transfer inside the pipe was carried out. is reliable, the calculation results of the acid dew point were also

7
J.L. Wang, Y.B. Tao and J. Liu Chemical Engineering Science 238 (2021) 116600

0.40 140 170

Eu-Cal. xa
Eu-Exp. [31] 160 5%
0.35 Nu-Cal. 120 10%
Nu-Exp. [31] 150 15%
20%
0.30 100 25%
140 +3%
30%

Nu
Eu

(°C)
0.25 80 +5%
130 -5%

Cal
tadp
0.20 60 120 -3%

110
0.15 40
4000 6000 8000 10000 12000 14000
100
Re 100 110 120 130 140 150 160 170
Fig. 3. Verification of flow and heat transfer characteristics. tExp
adp
(°C)

Fig.5. Verification of acid dew point temperature prediction model.

compared with the Ref. (ZareNezhad and Aminian, 2010), as shown
in Fig. 5. In the verification, 84 data points with a sulfur trioxide
content of 1–100 ppm and a water vapor content of 5%-30% are 2.01 million, 2.38 million and 3.46 million, respectively. The aver-
selected. It can be seen that the deviation between the calculated age value of the acid dew point temperature on all the fins is used
results and the experimental value is within 3% in 79 data points, as the evaluation index. The obtained corresponding acid dew
and only 5 data points have a deviation between 3% and 5%. The point temperatures at vin = 6 ms1, Tin = 420 K, xa = 15 ppm,
comparison results validate that the selected acid dew point esti- xw = 10% and Twall = 350 K are 123.21 °C (grid number 1.29 million),
mation formula is reliable. 126.49 °C (grid number 1.53 million), 129.00 °C (grid number 2.01
The meshes of the calculation domain are generated by the pre- million), 130.36 °C (grid number 2.38 million) and 130.96 °C (grid
processor GAMBIT. To ensure the accuracy of the calculation, the number 3.46 million), respectively. It can be found that with the
local area is treated differently. The calculation domain can be grid number increases from 2.38 million to 3.46 million, the acid
divided into the inlet section, the outlet section and the core sec- dew point temperature only augments 1.05%. It is worth mention-
tion. The coarser mesh is used in the inlet and outlet section. The ing that the size of the dimensionless distance y+ in the calculation
finer mesh was used in the core section, which includes the finned is checked before finalizing the grid scheme. The maximum value
tube. The Y-Z plane adjacent to the inlet section and the core sec- of y+ in this study is less than 4.5 to meet the needs of turbulent
tion adopts the same grid, while a thinner grid is used along the X- flow. Therefore, the mesh number of about 2.38 million is finally
axis direction. The structured hexahedral meshes are adopted in all used for numerical calculation.
the calculation domain. The generated grid system is shown in
Fig. 6. 4. Numerical results and discussion
The grid-independence was verified by calculating the average
flue gas acid dew point temperature on the surface of the present 4.1. Distribution of acid dew point temperature on finned tube surface
three-dimensional external finned tube. Under the same working
conditions, the acid dew point temperature on the finned surface The area-weighted average values of the acid dew point tem-
was calculated with the grid number of 1.29 million, 1.53 million, perature on each fin are selected as the object to discuss the distri-
bution of acid dew point temperature on fins surface conveniently.
The angle h is selected to represent the location of a certain fin,
which is defined as follows. The line connecting the center of a
fin to the origin may be denoted as li, and h is the angle between
1.2 the li and the positive x-axis along the counterclockwise direction.
Cal. Fig. 7 shows the distribution of flue gas acid dew point tempera-
1.0 Exp. [22] ture on fin surface, under the operation condition that finned tube
wall temperature is 350 K, the inlet velocity and temperature are
8 ms1 and 420 K, and the mole fractions of sulfuric acid vapor
ma(10-6kg⋅m-2⋅s-1)

0.8
and water vapor are 15 ppm and 10% respectively. It can be seen
0.6 that the flue gas acid dew point temperature presents the symmet-
ric distribution along the circumferential direction due to the sym-
metric distribution of the fluid flow and heat transfer
0.4
characteristics. The flue gas acid dew point temperature reaches
the maximum at h = 90° (h = 270°), which is the minimum cross-
0.2 section of the flow channel. The minimum value is obtained at
h = 18° (h = 342°). The acid dew point temperature of the fin surface
0.0 is different at different positions, and the maximum difference is
12 K. The detailed explanations for above phenomena are as
-0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
follows.
L(m) Since the acid dew point temperature is symmetrically dis-
tributed along the circumference, only the results within the range
Fig. 4. Comparison of sulfuric acid vapor condensation rate (ma). of 0°- 180° are analyzed in the following section. Firstly, in the
8
J.L. Wang, Y.B. Tao and J. Liu Chemical Engineering Science 238 (2021) 116600

(a) Core section

(b) Junction of inlet section and core section (c) Top view of the finned tube
Fig. 6. Grid system.

126
performance, and leads to the steadily increase of acid dew point
124 temperature. For the fin at h = 90°, the flow velocity of flue gas
increases reaches the maximum value due to the minimum flow
122
cross section, where the acid dew point temperature gets the max-
120 imum. However, the values of acid dew point temperature on the
tsld (ºC)

leeward side (0°-90°) is generally lower than that on the windward

118
side (90° 180°). This is because as the vapors condense, the con-
z
116 centration of condensable gas in the flue gas decreases, thus reduc-
ing its partial pressure in the flue gas, which weakens the mass
114 y
transfer on the leeward side and results in a lower acid dew point
112 x θ temperature. On the windward side, with h increasing from 90° to
180°, the flow cross section increases, resulting in a decrease of flue
110
0° 45° 90° 135° 180° 225° 270° 315° 360° gas velocity and insufficient mass transfer, thus resulting in the
drop of acid dew point temperature of flue gas. At the location of
θ h = 180°, affected by the impact of incoming flow, the local acid
Fig. 7. Distribution of acid dew point temperature along the circumference.
dew point temperature is relatively higher. From the above analy-
sis, it can be obtained that the acid dew point temperature of the
flue gas is generally higher on the windward side than that on
reflux region with the range of h = 0° and 36°, due to the weaker the leeward side, which means that more attentions should be paid
heat and mass transfer performance, the acid dew point tempera- to the windward side for the anticorrosion design of heat
ture is relatively lower. And the influence of reflux at h = 0° is more exchanger.
significant compared with that at h = 18°, which enhances the mass In order to analyze the influence of various factors on the corro-
transfer of flue gas. So the acid dew point temperature at h = 0° is sion characteristics of flue gas, the area-weighted average of acid
higher than that at h = 18°. Due to the occurrence of flow separa- dew point temperature, sulfuric acid vapor condensation rate and
tion around h = 36°, the acid dew point temperature is minimized sulfuric acid solution concentration on the surface of all finned
at this point. Subsequently, with h increasing from 36° to 90°, the tubes was used as the evaluation indexes. At the same time, when
flow cross-sectional area decreases due to the effect of tube, the the influence of a certain factor is examined in the following sec-
flow is accelerated, which enhances the heat and mass transfer tions, only this factor changes and other factors remain the same.

9
J.L. Wang, Y.B. Tao and J. Liu Chemical Engineering Science 238 (2021) 116600

4.2. Effect of flue gas velocity 4.3. Effect of sulfuric acid vapor concentration

The fluid velocity varies at different stages in the industry, Different kinds of coal contain different amounts of sulfur and
which is the starting point for examining the influence of flue produce different amounts of sulfur trioxide. The influence of sul-
gas inlet velocity on the corrosion characteristics. Fig. 8 shows furic acid vapor concentration on the corrosion characteristic is
the effects of flue gas inlet velocity on acid dew point temperature, shown in Fig. 9. It can be seen from Fig. 9(a) that as the inlet sulfu-
sulfuric acid vapor condensation rate and the condensed sulfuric ric acid vapor concentration increases from 5 ppm to 30 ppm with
acid solution concentration. In totally, the flue gas inlet velocity a difference of 5 ppm, the flue gas acid dew point temperature
has little effect on acid dew point temperature and acid solution obviously increases steadily and has a trend of being gradually flat,
concentration. When the inlet velocity increases from 6 ms1 to which is consistent with the logarithmic form of most acid dew
10 ms1, the acid dew point temperature and solution concentra- point temperature estimation formulae. This can be explained as
tion increase by only about 1 K and 0.2%. However, the acid con- follows: when the concentration of sulfuric acid vapor at the inlet
densation rate increases with flue gas inlet velocity as shown in increases, the driving force for mass transfer of sulfuric acid vapor
Fig. 8(b). In terms of mass transfer, the increase in the inlet flue is correspondingly increased; that is, the concentration gradient
gas velocity increases the partial pressure of sulfuric acid vapor and saturated vapor pressure of the sulfuric acid vapor near the
and the amount of acid vapor, which enhances the mass transfer wall is increased, which causes the increases of acid dew point
of acid vapor and results in the increase of acid dew point temper- temperature of flue gas as shown in Fig. 9(a) and the condensation
ature and acid condensation rate as shown in Fig. 8(b). In terms of rate of the sulfuric acid vapor, as shown in Fig. 9(b). It can also be
heat transfer, the increase of flue gas flow velocity increases the found in Fig. 9(b) that the concentration of sulfuric acid solution
heat transfer between the flue gas and wall surface, resulting in remains basically unchanged, with the maximum fluctuation being
fin surface temperature increasing, that is, the temperature of the only 0.07%. This is because the increase in the sulfuric acid vapor
condensed acid solution. The higher solution temperature results condensation rate will increase the concentration of sulfuric acid
in a higher saturated vapor pressure at the vapor–liquid interface solution, which in turn leads to a decrease in the saturated partial
and increases the mass transfer resistance. The increase of mass pressure of water vapor at the vapor–liquid phase interface and an
transfer resistance leads to the decrease of acid dew point temper- increase in the condensation rate of water vapor. The increasing
ature of flue gas. The comprehensive effect of the above two water vapor condensation rate causes the concentration of sulfuric
aspects results in an overall increase of the acid dew point temper- acid solution decreasing. The comprehensive effect of the above
ature on the three-dimensional external fin surface with the two aspects makes the concentration of the acid solution tend to
increase of inlet velocity, but the increment is very small. For the be substantially unchanged.
concentration of the acid solution, due to both the condensation When the sulfuric acid vapor concentration at the inlet
rates of acid vapor and water vapor increasing with inlet velocity, increased from 5 ppm to 30 ppm, the corresponding increase value
the concentration almost keeps constant.

136

131.7 134

132
131.4
130
tsld(°C)
tsld(°C)

131.1 128

126
130.8
124
130.5 122
0 5 10 15 20 25 30 35
130.2
6 7 8 9 10 xa(ppm)
v(m⋅s-1) (a) Flue gas acid dew point temperature
(a) Flue gas acid dew point temperature
12 22.20
ma
6.5 22.20
ma 10 Xa 22.15

Xa
ma(10-5 kg⋅m-2⋅s-1)

22.15
ma(10-5 kg⋅m-2⋅s-1)

6.0 8 22.10
22.10 0.07%
Xa(%)

6 22.05
5.5
Xa(%)

22.05
4 22.00
5.0 22.00
2 21.95
21.95
4.5 0 21.90
0 5 10 15 20 25 30 35
21.90
6 7 8 9 10 xa(ppm)
v (m⋅s ) -1
(b) Sulfuric acid vapor condensation rate and
(b) Sulfuric acid vapor condensation rate and sulfuric acid solution concentration
sulfuric acid solution concentration
Fig. 9. Effect of the inlet sulfuric acid vapor concentration on corrosion
Fig. 8. Effect of the flue gas inlet velocity on corrosion characteristic. characteristic.

10
J.L. Wang, Y.B. Tao and J. Liu Chemical Engineering Science 238 (2021) 116600

of the flue gas acid dew point temperature is 5.12 K, 3.03 K, 2.16 K, vapor partial pressure in flue gas. According to the vapor–liquid
1.48 K and 1.41 K respectively, and the total increase in the entire phase equilibrium theory, the decrease of sulfuric acid solution
calculation range is 13.20 K. Compared with the effect of flue gas concentration directly leads to the decrease of the saturated partial
velocity, it can be concluded that, under the condition of increasing pressure of sulfuric acid vapor at the vapor–liquid phase interface,
the same multiple, the increasing of sulfuric acid vapor concentra- and to some extent increases the gradient difference of sulfuric
tion at the inlet has a great influence on the acid dew point temper- acid vapor pressure at the vapor–liquid phase interface. That is
ature than the increasing of inlet velocity. to say, the mass transfer driving force of sulfuric acid vapor is

4.4. Effect of water vapor concentration

Table 4
The concentration of water vapor in flue gas produced by the Orthogonal factor levels table.
same type of coal at different combustion temperatures is differ-
ent, which is the main motive to investigate the influence of water Number of levels Factor

vapor concentration in flue gas on corrosion characteristic, and the v (ms1) xa (ppm) xw (%) Tin (K) Twall (K)
results are depicted in Fig. 10. It can be seen from Fig. 10(a) that the 1 6 5 10 400 330
acid dew point temperature of the flue gas increases logarithmi- 2 7 10 12 410 340
cally with the increase of the inlet water vapor concentration. 3 8 15 14 420 350
4 9 20 16 430 360
When the inlet water vapor concentration increased from 6% until
to 16%, the flue gas acid dew point temperature generally increases
by 10.54 K. This is because with the increase of water vapor con-
centration, the mass transfer force of water vapor in flue gas 30
v xa xw Tin Twall
increases, which promotes the condensation of water vapor and
leads to a decrease in the concentration of condensed sulfuric acid
solution, as shown in Fig. 10(b). The decrease in the concentration
25
of sulfuric acid solution leads to a decrease in the saturated partial
pressure of sulfuric acid vapor at the vapor–liquid phase interface.
The condensation rate of sulfuric acid vapor increases slightly as
ma(10-5 kg m-2 s-1)

shown in Fig. 10(b) because the saturation partial pressure at the 20

⋅ ⋅

vapor–liquid phase interface is smaller than that of sulfuric acid

15

136

134 10

132
tsld(°C)

130 5
6 8 0 10 20 9 12 15 400 420 330 345 360
128 v(m⋅s-1) xa(ppm) xw(%) Tin(K) Twall(K)

126
(a) Factors effect on sulfuric acid vapor condensation rate

124 v xa xw Tin Twall

4 6 8 10 12 14 16 18
60
xw(%)
(a) Flue gas acid dew point temperature
50
6.0 28
mw(10-5 kg m-2 s-1)

ma
⋅ ⋅

40
5.8 Xa 26
ma(10-5 kg⋅m-2⋅s-1)

24
5.6 30
Xa(%)

22
5.4
20
20
5.2
18

5.0 16 10
4 6 8 10 12 14 16 18
xw(%) 6 8 0 10 20 9 12 15 400 420 330 345 360
v(m⋅s-1) xa(ppm) xw(%) Tin(K) Twall(K)
(b) Sulfuric acid vapor condensation rate and
sulfuric acid solution concentration (b) Factors effect on water vapor condensation rate
Fig. 10. Effect of the inlet water vapor concentration on corrosion characteristic. Fig. 11. Effects of operating parameters on condensation characteristics.

11
J.L. Wang, Y.B. Tao and J. Liu Chemical Engineering Science 238 (2021) 116600

24
v xa xw Tin Twall
22

20

18
Xa(%)

16

14

12

10

6
6 8 0 10 20 9 12 15 400 420 330 345 360
v(m⋅s-1) xa(ppm) xw(%) Tin(K) Twall(K)
(c) Factors effect on sulfuric acid solution concentration
Fig. 11 (continued)

enhanced, and the condensation of sulfuric acid vapor is promoted,

which is finally reflected in the increase of acid dew point temper-
ature of flue gas.
Through data processing and analysis, it is found that when the
sulfuric acid vapor concentration increased from 5 ppm to 10 ppm,
the acid dew point temperature increased by 5.12 K; when the
water vapor concentration increased from 6% to 12%, the acid
dew point temperature increased by 7.50 K. The effect of inlet
water vapor concentration is larger than that of inlet acid vapor
concentration. Therefore, under the condition of increasing the
same multiple, the influence on the flue gas acid dew point tem- Fig. 12. Effects of two more significant factors on condensation characteristics.
perature from small to large is the flue gas inlet velocity, the inlet
sulfuric acid vapor concentration and the inlet water vapor concen-
tration, respectively.
concentration, the flue gas velocity, the sulfuric vapor concentra-
tion, the flue gas temperature.
4.5. Orthogonal calculation of condensation characteristics Based on the corresponding relationship between the corrosion
rate and sulfuric acid concentration (mass fraction) (Cen et al.,
As mentioned above, the vapor condensation characteristics are 1994), the serious corrosion phenomenon will occur when the sul-
the basis for judging the corrosion of the wall surface. In order to furic acid concentration ranges from 44.4% to 54.3%, and the corro-
comprehensively and effectively analyze the effect level of various sion rate is above 75 gm1h1, where the corresponding molar
factors on the condensation characteristics, the orthogonal calcula- fraction Xa of sulfuric acid solution ranges from 12.8% to 17.9%.
tion was further performed. An orthogonal array L16 (45) is used to Therefore, the proper operating conditions can be determined by
establish an orthogonal factor arrangement. The factors considered analyzing and discussing the two factors (water vapor concentra-
in orthogonal calculation and their values are shown in Table 4. tion and tube wall temperature) that have the most significant
Taking into account the variation in the other four factors, influence on the condensed acid solution concentration, as
Fig. 11 respectively illustrates the effect of the flue gas inlet veloc- described below.
ity, sulfuric acid vapor concentration, water vapor concentration, Firstly, the effect of water vapor concentration on corrosion
flue gas temperature and tube wall temperature on the condensa- characteristics is shown in Fig. 12(a). The corresponding inlet
tion characteristics. According to the variance analysis, it can be water vapor concentration range for the severe corrosion zone is
found that the effect level of the five factors on the sulfuric acid from 10.12% to 15.6%, which are clearly and intuitively marked
vapor condensation rate from high to low sequence is the sulfuric with the violet dotted straight lines. So, in practical applications,
vapor concentration, the flue gas velocity, the tube wall tempera- the water vapor concentration between 10.12% and 15.6% should
ture, the flue gas temperature and the water vapor concentration. be avoided. When the water vapor content is greater than 15.6%,
The effect level of the five factors on the water vapor condensation it can be seen from Section 4.4 that excessive water vapor concen-
rate from high to low sequence is the tube wall temperature, the tration will cause a sharp rise in acid dew point temperature,
sulfuric vapor concentration, the water vapor concentration, the although it leaves the severely corroded zone. Simultaneously,
flue gas velocity and the flue gas temperature. The effect level of the greater the difference between the acid dew point temperature
the five factors on the condensed acid solution concentration from and the wall surface temperature, the more severe the corrosion
high to low sequence is the tube wall temperature, the water vapor (Cen et al., 1994). Therefore, appropriate measures should be con-
12
J.L. Wang, Y.B. Tao and J. Liu Chemical Engineering Science 238 (2021) 116600

sidered to reduce the concentration of water vapor in the flue gas, Declaration of Competing Interest
and the recommended value is less than 10.12%.
The effect of tube wall temperature on corrosion characteristics The authors declare that they have no known competing finan-
is shown in Fig. 12(b). It can be seen that the corresponding tube cial interests or personal relationships that could have appeared
wall temperature range for the severe corrosion zone is from to influence the work reported in this paper.
338.93 K to 349.3 K, which means this tube wall temperature range
should be avoided in practical applications. When the temperature
is lower than 338.93 K, the difference between the wall tempera- Acknowledgements
ture and the acid dew point temperature will inevitably increase
even if it leaves the severely corroded zone. As a result, lowering The present work is supported by the National Key R&D Pro-
the tube wall temperature will only aggravate the corrosion but gram of China (2016YFB0601100).
not alleviate it. Therefore, increasing wall temperature is an effec-
tive method to reduce the corrosion, and it is recommended that
the tube wall temperature be maintained above 349.3 K for engi- References
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