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1. Introduction
As the price of energy in the world continues to rise more technology is being developed to increase energy savings. Examples of this include the use of solar panels as
well as wind turbine farms. Alternative and green methods are not the only area of
interest for cost savings. The aspect of monetary savings may also be represented in
existing energy sources such as boiler technology by more efficient operation. Boilers
operate in a variety of applications and locations. This can include marine boilers in
commercial ships such as liquid natural gas (LNG) tankers. Boilers also operate in
commercial nuclear and conventional power stations. No matter what application and
location boilers have one common need. The need to maintain clean heat transfer
surfaces so that the most efficient heat transfer can occur. With proper heat transfer the
cost incurred by the operating company can be reduced.
There are a few basic parts of a conventional boiler. These parts are the tubes,
steam drum, and water drum. Heat is transferred to the water flowing through the tubes
and collects at the steam drum. The steam drum allows the water to boil and a dry pipe
inside of the boiler carries the steam to perform whatever application the boiler is
operating for. The steam that leaves the boiler is a vapor. The steam vapor is not able to
carry any kind of solid material that may be dissolved in the boiler water. This can
result in a concentration of impurities in the boiler steam drum. Depending on how long
the boiler operates the concentration of these impurities can become quite large. This
could cause boiler heat transfer surfaces to become coated with hard scale that would
reduce heat transfer capability. To maintain the required amount of heat transfer with a
scale layer on the heat transfer area increased energy consumption would be required.
There is a simple way to prevent the hard scale build up problem. Typically a certain amount of boiler water is drained and then fresh water is used to refill the boiler.
This operation reduces the concentration of the impurities in the boiler. An unfortunate
result of this operation is that it reduces the amount of heat and pressure inside the boiler
as the fresh water mixes with the hot water in the steam drum. The freshwater must be
heated to saturation temperature and this causes additional fuel consumption. This
method of impurity reduction is known as boiler blow-down. Another method of boiler
blow-down is a continuous boiler blow-down. A certain amount of water is drained from
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the boiler steam drum as the boiler operates. To maintain a constant level in the boiler
the loss in boiler water level is offset by the continuous addition of feed water by the
boiler water feed system. This method of impurity level reduction has the benefit of not
causing a significant reduction in boiler temperature and pressure. The water that is
continuously removed however is thrown away as waste. It may be possible for the
impurities to be removed from some of the high temperature water by evaporation. The
water evaporated could then be condensed and stored to be reused as boiler makeup
water. This could provide additional savings to the managing company.
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2. Theory Methodology
2.1 Evaporator
In able to reuse the boiler water from the steam drum the impurities within the
water must be removed. Boilers operate at high temperature and pressure. The use of
filters or resin beds with fine elements or resins could prove impractical and expensive.
A method to remove salt and other impurities from sea water for consumption by people
and commercial use is to boil the sea water in a reduced pressure. This method is known
as distillation. The heating medium for this evaporator could be low pressure steam.
Once the sea water is boiled off it can be condensed in another portion of the evaporator
chamber where cooling coils are located. The condensed distillate then is collected on
pans and pumped to tanks for use.
A similar approach may be used for the removal of impurities in boiler water. Since
the water being removed is already a heat saturated liquid only the necessary amount of
enthalpy to boil the water would be required. The heating medium for this evaporator
could come from a stage of one of the propulsion turbines. Once the boiler water is
evaporated the impurities could collect in the bottom of the tank and be removed as
waste. This process would help save at least some of the water that would normally be
thrown away as waste.
A complete vaporization of the entire amount of boiler blow down water into dry
saturated steam is not the intent. If this occurred, then the collection tank would just be
completely covered by hard scale from the impurities in the boiler water as these impurities precipitated out of the steam. For this project a quality of 50% vapor was chosen for
the steam water mixture. This would allow the possible saving of 50% of the boiler
blow down water while concentrating the other 50% of the water containing the impurities to collect at the bottom of the tank for removal. It is assumed that the lower density
water vapor will rise in the chamber while the more dense water will collect at the
bottom.
A steam ship was based as the platform for this project. The operating boiler pressure is 600 psig. The steam turbines of this ship use superheated steam for propulsion.
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Due to piping flow reductions from the steam drum to the proposed system a pressure of
514 psig was chosen as the heat saturated boiler water at 472 F. This correlates to 244
C. All aspects of the heat exchanger are unknown so dimensions, material, as well as
operating pressure and temperature of the heating steam need to be determined. The
heat exchanger chosen to be used as an evaporator is a parallel flow annulus type heat
exchanger see [Figure 1]. This was chosen for the simplicity in design and construction.
An inner tube diameter of 1 cm was chosen. A flow rate of 1 gallon per minute was
chosen as the blow down capacity. This flow rate was chosen because it is low enough
to not affect boiler water levels and confuse operators when the ship is maneuvering. A
second reason this flow rate was chosen is that this level reduction should be easily
maintained continuously with a conventional boiler feed system.
Once the application was determined a method was needed to solve the heat balance. Dimensions were unknown as previously stated. Many heat exchangers require
the use of an overall heat transfer coefficient [2]. This was chosen as the starting point
for the analysis. The overall heat transfer coefficient provides the ability to combine the
two methods of heat transfer occurring between the steam and water in the annulus type
heat exchanger as well as account for their material differences [3, page 180]. The two
methods of heat transfer occurring in the evaporator are conduction and convection. The
heat transfer mechanism between the steam and the outer surface area of the inner tube
of the annulus type heat exchanger is convection. Conduction occurs within the steel
pipe. Lastly convection occurs between the steel pipe inner surface area and the boiler
water [see figure 3]. The overall heat transfer coefficient for an annulus type heat
exchanger can be calculated using the following equation [1, page 508].
𝑈𝑜 =
1
𝐴
𝑟
1
𝐴
( 𝑜⁄𝐴 ℎ𝑖 )+( 𝑜 𝑅𝑓𝑖 ) + [(𝐴𝑜 ln 𝑜 )/2𝜋𝑘𝐿]+ 𝑅𝑓𝑜 +( )
𝐴𝑖
𝑟𝑖
ℎ𝑜
𝑖
The ℎ𝑖 , ℎ𝑜 terms in the equation relate to the forced convection on the inner and outer portions of the inner pipe of the annulus heat exchanger. The outer convection heat
transfer coefficient is ℎ𝑜 and ℎ𝑖 is the inner heat transfer coefficient. The convection
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heat transfer coefficients are dependent on many parameters of their fluid flow. These
parameters include viscosity, temperature, and velocity [4].
To calculate ℎ𝑖 the Chen correlation was used [1, page 675]. The boiler water that
has been removed from the steam drum is heat saturated water close to boiling. Since
the boiler water is a heat saturated liquid carrying a significant amount of heat the
transition from bubble and slug flow in flow regimes of boiling quickly turns into the
annular flow regime. For this project it is assumed that the boiling within the evaporator
occurs in the annular flow regime.
Chen has suggested that there is a two part correlation to the boiling heat transfer
coefficient in the annular flow region. The two parts consist of a convection heat
transfer coefficient as well as a nucleate boiling heat transfer coefficient. The two
coefficients are calculated separately and then their affects are additive to create a
singular heat transfer coefficient.
ℎ = ℎ𝑐 + ℎ𝑏
The Chen correlation of the annular flow region was chosen because this correlation
has been tested and the results proven. This specific correlation has provided satisfactory data for water, methanol, cyclohexane, pentane, heptane, and benzene for different
pressures. The pressure ranges evaluated were between 0.5 and 35 atm and the quality
of vapors produced was between 1 and 71% [1, page 675].
Numerous experiments have been conducted on the area of forced convection boiling however at this time it is not yet possible to understand all of the characteristics of
forced convection boiling due to the significant number of variables the process depends
upon as well as the two-phase flow patterns that occur. These two phase flow patterns
occur as the quality of the vapor-liquid mixture increase during vaporization [1, page
667-668]. Most of the data used for the correlations of forced convection represented in
this project are based upon photographs taken by high speed cameras. These photographs are then used to obtain a qualitative description of the process’ [1, page 668].
Chen is one of the first people to suggest a forced convention boiling correlation.
This proposal has proven very useful and is used widespread [5]. Chen proposed a
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major difference between conventional nucleate pool boiling and nucleate boiling in
forced convention. Chen proposed that the large temperature difference of the hot inside
surface of the pipe compared to the temperature of the fluid moving through the pipe
causes a partial suppression of nucleation in boiling sites. This results in a partial
reduction in heat transfer due to nucleate boiling [5]. Chen also noticed that as evaporation took place the vapor voids formed had the effect of increasing the velocity of the
fluid through the pipe which created an increase in the heat transfer coefficient of
convection as would be compared to a regular single phase flow of the fluid [5]. These
effects can be summarized by saying that the higher flow rate caused by the formation of
vapor spaces in the flow channel suppresses bubble growth and increases the convective
heat transfer by increasing turbulence of the fluid flowing through the pipe [6, page
123].
Chen found two dimensionless functions that can be calculated empirically. These
values are S and F. The value of S relates the suppression of the nucleation sites to the
Forster and Zuber micro convective heat transfer relation for boiling [6, page 123]. The
value of F applies to the Dittus-Boelter macro convective heat transfer relation for forced
convection [6, page 123]. The Dittus-Boelter correlation is:
𝑁𝑢 = 0.023(𝑃𝑟 0.4 )(𝑅𝑒 0.8 )
And the Nusselt number is calculated from:
𝑁𝑢 =
ℎ𝐷
𝑘
Therefore the heat transfer coefficient can be calculated by solving for it on one side
of the equation:
ℎ=
𝑁𝑢𝑘
𝐷
This causes the heat transfer coefficient to change to
𝑘𝑙
𝑁𝑢 = 0.023(𝑃𝑟 0.4 )(𝑅𝑒 0.8 ) ( )
𝐷
The value of F is calculated based upon the following equation [1, page 675]:
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𝑤ℎ𝑒𝑛
1
< 0.1
𝑋𝑡𝑡
0.736
1
𝐹 = 2.35 (
+ 0.213)
𝑤ℎ𝑒𝑛
𝑋𝑡𝑡
1
> 0.1
𝑋𝑡𝑡
𝐹 = 1.0
𝑊ℎ𝑒𝑟𝑒
1
𝑖𝑠:
𝑋𝑡𝑡
1
𝑥 0.9 𝑝𝑙 0.5 𝜇𝑣 0.1
=(
) ( ) ( )
𝑋𝑡𝑡
1−𝑥
𝑝𝑣
𝜇𝑙
The use of the Martinelli parameter for the calculation of
1
𝑋𝑡𝑡
is required [5]. The value
of F applies the contribution of the convection heat transfer coefficient on the convection
coefficient [1, page 675]:
ℎ𝑐 = 0.023 [𝐺(1 − 𝑥)𝐷⁄𝜇𝑙 ]
0.8
𝑃𝑟𝑙0.4
𝑘𝑙
𝐷
𝐹
The nucleate pool boiling correlation of Forster and Zuber is indicted below [5].
ℎ𝑏 = 0.00122 (
𝑘𝑙 0.79 𝑐𝑙 0.45 𝑝𝑙 0.49 𝑔𝑐 0.25
0.75
0.24
∆𝑝𝑠𝑎𝑡
0.24 0.24 ) ∆𝑇𝑥
𝜎 0.5 𝜇𝑙 0.29 ℎ𝑓𝑔
𝑝𝑣
This correlation is corrected for forced convection by the parameter S. The value of
S is known as the nucleate boiling suppression factor [5]. This value is calculated from:
1.14 −1
𝑆 = (1 + .12 𝑅𝐸𝑇𝑃
)
0.78 −1
𝑆 = (1 + .42 𝑅𝑒𝑇𝑃
)
𝑆 = 0.1
For
𝑅𝑒𝑇𝑃 < 32.5
For
32.5 < 𝑅𝑒𝑇𝑃 < 70
For
The value of 𝑅𝑒𝑇𝑃 is calculated as follows:
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𝑅𝑒𝑇𝑃 > 70
𝑅𝑒𝑇𝑃 =
𝐺(1 − 𝑥)𝐷 1.25
𝐹
𝑋 10−4
𝜇𝑙
This value is similar to the conventional Reynolds number that is calculated as follows [7, page 88]:
𝑅𝑒 =
𝐷𝐺 4𝑚̇
=
𝜇
𝑝𝜇
The value of F is used to correct the Reynolds number using the Martinelli parameter for the calculation of
1
𝑋𝑡𝑡
[5]. After the value of S has been calculated it is used to
correct the nucleate pool boiling correlation as follows:
𝑘𝑙 0.79 𝑐𝑙 0.45 𝑝𝑙 0.49 𝑔𝑐 0.25
0.75
ℎ𝑏 = 0.00122 ( 0.5 0.29 0.24 0.24 ) ∆𝑇𝑥0.24 ∆𝑝𝑠𝑎𝑡
𝑆
𝜎 𝜇𝑙
ℎ𝑓𝑔 𝑝𝑣
Once these values are obtained the heat transfer coefficients are added to create the
forced convection boiling heat transfer coefficient.
The heat transfer coefficient on the exterior of the inner pipe of the annulus heat exchanger does not have as many terms as the inner heat transfer coefficient. This is due
to no phase change occurring on the exterior surface of the inner pipe. The empirical
correlation chosen for this parameter is an empirical correlation for heat transfer in a
non-circular duct with turbulent flow [8, page 114].
0.25
𝐷2
⁄𝐷 )
1
𝑁𝑢 = .015(𝑃𝑟 0.4 )(𝑅𝑒 0.8 ) (
The 𝐷2 dimension is the exterior diameter formed between the outer surface of the
inner tube of the heat exchanger and the dimension 𝐷1 is the outer diameter of the inner
tube. This correlation was chosen based upon the physical properties of the steam being
used as the heat source. The Pr number was calculated to be greater than 0.6 and the Re
number was calculated to be greater than 7,000.
The Pr number of the heating steam was calculated by the following equation [7,
page88].
Pr =
9
𝜇𝑐
𝑘
The Reynolds number was calculated based upon the equivalent hydraulic diameter for
an annulus. The hydraulic diameter of the annulus was calculated based upon the
following equation [1, page 376]:
𝐷𝐻 = 4
(𝜋⁄4) (𝐷22 − 𝐷21 )
𝜋(𝐷1 + 𝐷2 )
= 𝐷2 − 𝐷1
The flow of the steam is assumed to be fully developed so the Reynolds number was
calculated using the hydraulic diameter from the following equation.
𝑅𝑒𝐷𝐻 =
̅ 𝐷ℎ 𝑝
𝑈
𝜇
To complete the calculation of the overall heat transfer coefficient a rough
estimate was needed for the length of the evaporator heat exchanger. Initially, to obtain
a rough estimate of length it was assumed that the exterior surface of the heat exchanger
was maintained at a constant temperature. This would be true if the steam used as the
heat source was condensing on the outer surface of the inner tube. With the assumption
of phase change occurring on both sides of the heat exchanger calculation of the temperature difference would become simplified. This was performed based upon the fact that
at this time a mean temperature difference had not yet been calculated. Using this
approach the Chen correlation was used in an iterative process to calculate the required
length of the heat exchanger inner tube. The mass flow velocity of the flow internal to
the pipe was calculated using the equation:
𝐺=
̇
𝑚4
𝜋𝐷2 3600𝑠⁄ℎ𝑟
This provided the mass flow rate of the fluid flowing through the tube per second. The
Reynolds number was calculated using the equation for flow through a pipe:
𝑅𝑒 =
10
𝐺𝐷
𝜇𝑙
The iterative process resulted in a table of variable length and qualities of vapor generated [Table 1]. The column on the left hand side of the table is the quality parameter (x).
This is the quality of the vapor and water mixture exiting the evaporator. The step
increase in the quality parameter is the column labeled (∆𝑥). The column located on the
right hand side of the table is the length column (l). This is the length of the annulus
heat exchanger required to obtain the indicated quality of that row. Initially values of 0
were used as quality and length. The values of (x) were changed from 0 all the way up
to the required value of 0.5. This resulted in an increased length of the heat exchanger as
the quality grew. A final value of approximately 0.5 meters was obtained to provide the
required heat input to obtain a 0.5 quality vapor.
1
The values of𝑋 , 𝐹, ℎ𝑐 , 𝑅𝑒𝑇𝑃 , 𝑆, ℎ𝑏 were updated in each row as the quality of the
𝑡𝑡
steam and water mixture (∆𝑥) values changed. Since the values of ℎ𝑐 and ℎ𝑏 change in
each row the combined heat transfer coefficient for forced convection boiling changes as
well.
ℎ = ℎ𝑐 + ℎ𝑏
This iterative method was used based upon the heat flux over a length ∆𝑙 being directly
linked to the increase in quality of the steam and water mixture at its saturation temperature illustrated by the following [1, page 677].
𝑚̇ℎ𝑓𝑔 ∆𝑥 = 𝑞𝜋𝐷∆𝑙
This equation can be rearranged with the values of ∆𝑥 and ∆𝑙 on either side.
∆𝑙 =
𝑚̇ℎ𝑓𝑔 ∆𝑥
𝑞𝜋𝐷
The last row of [table 1] is the most important. As stated above the very last row of
[table 1] indicates the 0.5 meter length required to obtain the 0.5 quality exit quality.
It is important to state that this method was chosen to obtain a rough estimate of
the length of the heat exchanger to obtain the overall heat transfer coefficient. This table
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is updated to reflect a more accurate temperature difference between the steam and water
vapor mixtures once a mean temperature difference is obtained.
After the internal, external, and overall heat transfer coefficients as well as a
rough estimation of size of the heat exchanger were generated the question of what the
outlet temperature of the steam still remained.
When calculating the heat transfer
coefficient the appropriate reference temperature of the fluid bulk temperature is required. The water flowing through the internal pipe is boiling so only the necessary
latent heat of vaporization needs to be added. This does not result in a sensible heat
change or in other words, the temperature of the boiling water within the heat exchanger
does not change. However, as the steam flows over the heat exchanger the temperature
of the heating steam does not remain the same. The steam temperature changes along
the flow path as well as in the direction of heat flow [see figure 4]. A certain cross
section of the heat exchanger needs be chosen to determine the reference point for the
following equation:
𝑞𝑐 = ℎ𝑐 𝐴(𝑇𝑠 − 𝑇𝑓 )
As stated above an accurate representation of the steam temperature 𝑇𝑠 requires
calculation. The calculated temperature is typically an average temperature chosen as a
reference temperature. This is commonly known as average fluid bulk or average
mixing cup temperature [1, page 377]. Prior to obtaining this temperature difference an
outlet temperature of the steam was required. This resulted in use of the heat exchanger
effectiveness method.
The heat transfer capabilities of a heat exchanger can be evaluated by a method
called the heat exchanger effectiveness method [1, page 519]. This method compares
the ratio of the actual rate of heat transfer in a heat exchanger to the maximum heat
exchange rate possible. One of the assumptions in the design of the evaporator heat
exchanger is that the annulus heat exchanger exterior is completely and perfectly insulated [1, page 519]. Assuming that the outer body is completely insulated, then the heat
provided from the steam flows only into the boiler water and no heat escapes to the
environment. The equation for the effectiveness is:
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1−𝑒
𝐶
−[1+( 𝑚𝑖𝑛⁄𝐶
)]𝑈𝐴⁄𝐶
𝑚𝑎𝑥
𝑚𝑖𝑛
1+(
𝐶𝑚𝑖𝑛
⁄𝐶
)
𝑚𝑎𝑥
This equation requires calculation of the heat capacity rate ratio of the hot and
cold fluids. This value is determined from the equation:
𝐶 = 𝑚̇𝑐
Normally, the values of 𝐶𝑚𝑖𝑛 and 𝐶𝑚𝑎𝑥 are calculated by multiplying the mass flow rates
and specific heats of the fluids and evaluating which one is the smaller and which one is
the larger. In other words the mass flow rate of the steam is multiplied by the specific
heat of the steam. The value calculated is specific heat rate of the hot fluid.
The value of (𝐶𝑚𝑖𝑛⁄𝐶
𝑚𝑎𝑥
)
is 0 for an evaporator or condenser. This value is zero be-
cause if one of the fluids temperatures remains zero throughout the streams specific heat
and heat capacity are equal to infinity [1, page 520].
Once the effectiveness is calculated it can be used in the following equation to calculate the exit temperature of the steam.
𝜀𝐶𝑚𝑖𝑛 (𝑇ℎ,𝑖𝑛 − 𝑇𝑐,𝑖𝑛 )=𝐶ℎ (𝑇ℎ,𝑖𝑛 − 𝑇ℎ,𝑜𝑢𝑡 )=𝐶𝑐 (𝑇𝑐,𝑜𝑢𝑡 − 𝑇𝑐,𝑖𝑛 )
A little rearranging of the above equation provides:
𝐶𝑐 𝑇𝑐,𝑖𝑛 +𝜀𝐶𝑚𝑖𝑛 (𝑇ℎ,𝑖𝑛 −𝑇𝑐,𝑖𝑛 )
𝐶𝑐
=𝑇𝑐,𝑜𝑢𝑡
The effectiveness calculated for this heat exchanger was approximately 0.544 which
correlates with [figure 2] quite well for a parallel flow type heat exchanger with
(
𝐶𝑚𝑖𝑛
) equal
⁄𝐶
𝑚𝑎𝑥
to 0.
Once the outlet temperature of the steam was calculated the reference temperature difference of the steam and steam/water mixture could be determined. The log
mean temperature difference was used. Due to this fact a reference temperature known
as the mean temperature difference must be calculated to be used in the calculation
below.
𝑞 = 𝑈𝐴∆𝑇𝑚𝑒𝑎𝑛
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To use the log mean temperature difference method it is assumed that the overall heat
transfer coefficient is constant along the length of the heat exchanger, the kinetic energy
changes of the fluid are neglected, and the heat exchanger is perfectly insulated [1, page
512]. The equation for the log mean temperature difference is illustrated below.
∆𝑇𝑚𝑒𝑎𝑛 =
∆𝑇𝑎 − ∆𝑇𝑏
∆𝑇
𝑙𝑛 ( 𝑎⁄∆𝑇 )
𝑏
The value of ∆𝑇𝑎 is the difference in temperature of the inlet fluids and the value of ∆𝑇𝑏
is the difference in temperature of the outlet fluids.
Once the reference temperature difference was obtained the iterative process of calculating the required length of the annulus heat exchanger could be reperformed. The
same process was performed as [table 1] resulting in [table 2].
Observing [table 2] the values of ℎ𝑏 , h, and q were all updated to reflect the temperature difference term or the ∆𝑇𝑥0.24 term in the equation below.
𝑘𝑙 0.79 𝑐𝑙 0.45 𝑝𝑙 0.49 𝑔𝑐 0.25
0.75
ℎ𝑏 = 0.00122 ( 0.5 0.29 0.24 0.24 ) ∆𝑇𝑥0.24 ∆𝑝𝑠𝑎𝑡
𝑆
𝜎 𝜇𝑙
ℎ𝑓𝑔 𝑝𝑣
The value of q is an important parameter to be observed due to its value being the
required amount of heat being added to the boiler water to create the 50% quality vapor.
This value will be used to ensure the condenser has the required capacity to remove this
amount of heat.
2.2 Condenser
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3. References
[1] Principles of Heat Transfer-fifth edition
[2] http://www.engineersedge.com/heat_transfer/overall_heat_transfer_coef.htm
(7-30-11)
[3]Engineering Formulas Conversions and Tables, Frank Sims
[4] http://www.engineeringtoolbox.com/convective-heat-transfer-d_430.html
(7-30-11)
[5] http://www.wlv.com/products/databook/db3/data/db3ch10.pdf
(7-30-11)
[6] Boiling Heat Transfer and Two-Phase Flow, Tong
[7]Convective Heat and Mass Transfer, Wiliam Kays, Michael Crawford, Bernhard
Weigand.
[8]A Concise Encyclopedia of Heat Transfer, Kutateladze, and Borishanskii
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