Microsoft Word - 01-07294_1517-1527_.docJournal of Mechanical
Science and Technology 23 (2009) 1517~1527
www.springerlink.com/content/1738-494x
DOI 10.1007/s12206-009-0406-4
Natural convection heat transfer estimation from a
longitudinally
finned vertical pipe using CFD† Hyo Min Jeong1, Yong Hun Lee2,
Myoung Kuk Ji2, Kang Youl Bae3 and Han Shik Chung1,*
1Department of Mechanical and Precision Engineering, The Institute
of Marine Industry, Gyeongsang National University, 445
Inpyeong-Dong, Tong-yeong, Gyeongsang-namdo, 650-160, Korea
2Department of Mechanical and Precision Engineering, Gyeongsang
National University, 445 Inpyeong-dong,Tongyeong, Gyeongsang-namdo,
650-160, Korea
3Machine Industry Tech Center, Gyeongnam Technopark, 445
Inpyeong-dong, Tong-young Gyeongsang-namdo, 650-160, Korea
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Abstract In this study, CFD analysis of air-heating vaporizers was
conducted. A longitudinally finned vertical pipe was used
to represent the air-heating vaporizer in the CFD model. Nitrogen
gas was used as the working fluid inside the vertical pipe, and it
was made to flow upward. Ambient air, which was the heat source,
was assumed to contain no water vapor. To validate the CFD results,
the convective heat transfer coefficients inside the pipe, hi-c,
derived from the CFD results were first compared with the heat
transfer coefficients inside the pipe, hi-p, which were derived
from the Perkins corre- lation. Second, the convection heat
transfer coefficients outside the pipe, ho-c, derived from the CFD
results were com- pared with the convection heat transfer
coefficients, ho-a, which were derived from an analytical solution
of the energy equation. Third, the CFD results of both the
ambient-air flow pattern and temperature were observed to determine
whether they were their reasonability. It was found that all
validations showed good results. Subsequently, the heat transfer
coefficients for natural convection outside the pipe, ho-c, were
used to determine the Nusselt number outside the pipe, Nuo.. This
was then correlated with the Rayleigh number, Ra. The results show
that Ra and Nuo have a propor- tional relationship in the range of
2.7414x1012 ≤ Ra ≤ 2.8263x1013. Based on this result, a relation
for the Nusselt num- ber outside the pipe, Nuo, was proposed.
Keywords: CFD; Natural convection; Heat transfer; Vertical pipe;
Fin
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1. Introduction
To allow liquefied natural gas (LNG) to return to its gaseous
state, LNG is typically fed into a regasifi- cation plant, in which
LNG is vaporized using a heat exchanger called a “vaporizer.” An
air-heating vapor- izer is normally used at the inland/satellite
receiving terminal for such purposes. However, this type of
vaporizer has a constraint: it has small-to-medium production
capacity due to the small heat capacity of
air used as its heat source [1]. Therefore, to meet the increasing
demand for
LNGs in inland areas (where pipelines do not exist or are difficult
to construct), some studies aiming to develop the best-performing
air-heating vaporizers are currently underway.
Computational Fluid Dynamics is considered a powerful and an almost
essential tool for the design, development, and optimization of
engineering appli- cations. [2] investigated the effect of fin
quantity, fin thickness, and fin length for the heat transfer rate
of longitudinally finned air-heating vaporizers using 2D numerical
analysis. [3] and [4] conducted 2D numeri- cal analysis to
determine the optimum dimensions of
†This paper was recommended for publication in revised form by
Associate Editor Man Yeong Ha
*Corresponding author. Tel.: +055 640 3185, Fax.: +055 640 3188
E-mail address:
[email protected] © KSME & Springer 2009
1518 H. M. Jeong et al. / Journal of Mechanical Science and
Technology 23 (2009) 1517~1527
longitudinally finned air-heating vaporizers. They proposed a 4-fin
type of vaporizer with a fin thickness of 2 mm as the optimum
dimension. [5] numerically analyzed the laminar free convection
around a hori- zontal cylinder having longitudinal fins of finite
thickness.
A vaporizer is actually a heat exchanger. Many studies on heat
exchangers have been conducted in the past. One of the main
problems in heat exchangers, however, has been frost formation due
to the conden- sation and freezing of the water vapor present in
air. These ice deposits lead to a decreased heat transfer rate
because the thermal conductivity of ice is less than one-fortieth
of that of aluminum alloy.
In general, heat transfer efficiency is less for thicker ice. In
addition, when fins are covered with thick ice (in the case of
vaporizers such as finned type vaporiz- ers), the effective heat
transfer area decreases until their configuration becomes almost
invisible [6]. [7] conducted experiments to determine the effects
of various factors (fin pitch, fin arrangement, air tem- perature,
air humidity, and air velocity) on the frost growth and thermal
performance of a fin-tube heat exchanger. General solutions for the
optimum dimen- sions of convective longitudinal fins with base-wall
thermal resistance capacities were solved analytically by [8].
Meanwhile, [9] conducted studies to deter- mine the optimal values
of the design parameters for a fin-tube heat exchanger in a
household refrigerator under frosting conditions. [10-11] conducted
both numerical and experimental studies on the frost for- mation in
fin-and-tube heat exchangers.
It is well known that an LNG vaporizer consists of a vaporizing
section and a heating section. In this study, we focused on the
heating section of a vapor- izer in which there is no phase change
in the working fluid inside (i.e., the fluid remains in the gas
phase). Aiming to determine the correlation of the Nusselts number
for natural convection occurring outside the vaporizer, a 3D CFD
analysis of a longitudinally fin- ned air-heating vaporizer
(represented by a longitudi- nally finned vertical pipe) with 4
fins, a fin length of 75 mm, and a fin thickness of 2 mm (denoted
by 4fin75le) was conducted. The correlation equation between the
Nusselt number outside the pipe and the Rayleigh number (Ra) is
given in the form of Eq. (1):
m
oNu C(Ra)= . (1) The vaporizers were chosen to be 4-fin type on
the
basis of a 2D numerical analysis conducted by Jeong et al. (2006);
they concluded that the optimum vapor- izer geometry is a vaporizer
with an angle of 90o be- tween fins and a fin thickness of 2 mm.
This implies that the vaporizer should have 4 longitudinal fins.
They asserted that this is because such vaporizers would have an
optimum heat transfer rate taking into consideration the presence
of frost deposit (Jeong et al., 2006).
2. Numerical simulation
Fig. 1 and Fig. 2 show the 3D mesh model used for CFD analysis,
while
Fig. 3 shows the dimensions of the basic model. The mesh was
constructed using a commercial soft- ware, Star-CD, which was built
by the CD adapco Group. The cell quantity amounted to 272,892
cells. The model consists of ambient air as the heat source, a
finned vertical pipe whose length is 1000 mm, and nitrogen gas
flowing upward inside the pipe. Given that there is heat transfer
from the fluid to the solid phase, the Star-CD conjugate heat
transfer mode was used. The length and thickness of the fins were
75 mm (from the outer surface of the pipe) and 2 mm, respectively.
The inner and outer diameters of the pipe were 24 mm and 30 mm,
respectively. The mesh model created was made one-fourth of the
real model in order to accelerate the iteration.
Natural convection refers to the heat transfer that occurs between
ambient air and the finned vertical pipe . After calculating the
predictions of the Grashof number for natural convection along a
1000 mm ver- tical pipe (under the assumption that the average
outer surface temperature of the pipe was the same as the nitrogen
inlet temperature), it was expected that the downward flow of
ambient air as caused by the cool- ing effect was turbulent flow
(Gr > 109), [12]. Hence, a k-omega-SST-turbulent low Reynolds
number model was used as the turbulence model. It is more accurate
in predicting phenomena in such cases as when turbulent natural
convection or buoyancy forces play a major role in driving the
flow. The K-omega- SST model applies a combination of the k-omega
model equations implemented near the wall region; the k-epsilon
turbulence model must be employed in the bulk or free flow region
[13, 14].
The mesh of ambient air near the pipe was made finer so that the
results for a low Reynolds model could be more accurate; the
dimensions were 0.6–6 mm measured from the wall. Moreover, the “
hybrid
H. M. Jeong et al. / Journal of Mechanical Science and Technology
23 (2009) 1517~1527 1519
(a) Whole mesh model
(b) Detail A
Fig. 1. Figure of the whole mesh model and the detailed view of the
inlet section.
Fig. 2. Explode figure of the 3D model
Fig. 3. Cross-sectional drawing of the finned vertical pipe.
wall” boundary condition was chosen for the near- wall ambient air
so that we need not ensure a suffi- ciently small near-wall value
for y+ (by creating a sufficiently fine mesh next to the wall).
Such hybrid wall boundary condition provides valid boundary
conditions for momentum, turbulence, energy, and species variables
for a wide range of near-wall mesh densities [15].
The PISO algorithm was used to solve pressure terms because the
calculation of natural convection problems could be easier using
this algorithm. The differencing schemes used were the Monotone Ad-
vection and Reconstruction Scheme (MARS) for momentum, temperature,
and density calculations, and the up-wind scheme for turbulence
kinetic energy, as well as turbulence dissipation rate
calculations.
The boundary conditions used for ambient air far from the pipe
(side ambient air) were “wall” under slip conditions and a
temperature of 293 K (tempera- ture of the ambient air).
“Symmetry”” boundary con- ditions were applied at the top and
bottom areas of the ambient air model. In this numerical analysis,
the buoyancy effect on the temperature profile has been neglected
because a conjugate model was applied in this analysis to calculate
the body (pipe) parameters (see Fig. 2 and Fig. 3). The boundary
condition of the solid-fluid interface was automatically set to
“con- ducting no-slip wall” whenever the conjugate heat transfer
mode was used. In this CFD analysis, ambient air was assumed to
contain no water vapor (dry air) since it was focused on the basic
heat trans- fer characteristics of the pipe. The air properties
other than density were constant. The density changed only with
temperature and followed the ideal gas law. The thermal
conductivity of the pipe (pure aluminum) was set to 269.5 W/mK or
237 W/mK, depending on whether the average pipe temperature was
predicted as approximately 150 K or 200 K, respectively.
The flow inside the pipe was assumed to be fully developed. At the
pipe inlet, the “pressure” boundary condition was used with the
pressure maintained con- stant at 2 bar absolute, while the inlet
temperature was varied.
Furthermore, at the inlet, the turbulence length scale value was
based on 7% of the hydraulic diame- ter, and the turbulence
intensity was based on the following equation:
1 8I 0.16Re
− = . (2)
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Technology 23 (2009) 1517~1527
Table 1. The conditions used for the simulation.
No flow rate (kg/s)
Tb inlet (K)
T ambient (K)
Inlet pressure (bar)
1 0.015 111 2 0.020 111 3 0.030 100 4 0.015 131 5 0.010 131 6 0.005
151 7 0.010 151 8 0.005 171 9 0.010 171 10 0.005 191 11 0.010 191
12 0.005 211 13 0.010 211 14 0.005 231 15 0.010 231 16 0.025 111 17
0.030 111 18 0.020 131 19 0.025 131 20 0.015 151 21 0.020 151 22
0.015 171 23 0.020 171 24 0.025 151
293 2
The pipe outlet boundary condition was “outlet”
with the mass flow rate set at various values. The turbulence model
used for the nitrogen flowing
inside was a k-epsilon high Reynolds number because the flow was
fully turbulent (R e> 104). The steady state simulation was
conducted under 24 different conditions as listed in Table 1.
3. Calculations and validation
The CFD results were used to calculate the convec- tive heat
transfer coefficient inside the pipe, hi-c, and outside the pipe,
ho-c, using the following equations:
( ) ( )out in i c si si bim i i h A T T •
−− = − and (3)
( ) ( )out in o c so all so allm i i h A T T •
− − ∞ −− = − . (4)
The enthalpy data were taken from NIST [16] with
ASHRAE Standard State Convention. To validate the CFD results,
first, the convection
Fig. 4. Thermal circuit at the outer side of the pipe.
heat transfer coefficients inside the pipe, hi-c which were
calculated using Eq. (3) were compared with the convection heat
transfer coefficients, hi-p, which were derived from the Perkins
and Worsoe-Schmidt corre- lation [17], along with Nusselt number
definition.
The Perkins correlation is as follows:
0.7 0.70.7
0.8 0.4 si si i p b in b in
b in i b in
T TNu 0.024Re Pr 1 T d T
− −
− − − − −
= +
2
N
All data used were taken from the input data and
CFD results, after which the convection heat transfer coefficient,
hi-p, was determined. Second, the convec- tion heat transfer
coefficients outside the pipe, ho-c, that were calculated using Eq.
(4) were compared with the convection heat transfer coefficients,
ho-a, which were derived using an analytical solution of the energy
equation. These convection heat transfer coef- ficients outside the
pipe, ho-a, were calculated by si- multaneously solving Eqs.
(7)-(14) given below. The value of ho-a was obtained by
substituting the data from the experimental results in the energy
equation. These equations were analytically derived from the energy
equation [18].
Fig. 4 shows the thermal circuit of the outer side of the pipe; it
also illustrates the heat transfer from the pipe to ambient air.
This coefficient, ho-a, was as- sumed to be homogenous across the
outer side of the pipe.
so
e
−= + (8)
H. M. Jeong et al. / Journal of Mechanical Science and Technology
23 (2009) 1517~1527 1521
b o a o
1R ; h (2πr nt)−
T TR Q
(mL) (h /mk ) (mL) ; (h Pk A ) ( (mL) (h /mk ) (mL))
(10) 1/ 2o a
cA t;= ×l (13)
so f all fins
Given that all values above are known (from the
input data and CFD results) with the exception of ho-a, the
convection heat transfer coefficients outside the pipe, ho-a, can
thus be calculated. Third, to ensure the validity of the CFD
results, the ambient air flow pat- tern and temperature were
observed to determine their reasonability.
Next, after validation, the Nusselt numbers outside the pipe, Nuo,
were calculated using:
o c c
These Nusselt numbers outside the pipe Nusselt
numbers, Nuo, were correlated with the Rayleigh numbers, Ra , which
were in turn determined using:
( ) 3
β να
Nuo and Ra is defined as follows:
( )o
d
This characteristic length was used to consider the
fin length and thickness under the assumption that the fin
thickness was so small that the base surface cov- ered by the fin
is almost a flat plane.
4. Results and discussions
The heat transfer coefficients, hi-c, of the inner pipe, which were
calculated using the CFD results, showed a good agreement with the
heat transfer coefficients, hi-p, of the inner pipe, which were
determined through the Perkins’ correlation, as shown in Table 2.
It is considered that the Perkins Nusselt correlation has
limitations in the ratio of surface temperature to inlet bulk
temperature (Tsi/Tb-in) 1.24 < Tsi/Tb-in < 7.54.
From the value of “Tsi/Tb-in”in Table 2 (marked by an asterisk), it
can be seen that there are only 12 data sets that meet the
requirement of the Perkins correla- tion, provided that the limit
is considered to be one digit after the decimal point, that is, 1.2
< Tsi/Tb-in < 7.5. Nevertheless, these 12 data sets
sufficiently dem- onstrated that the 3D model was valid for
simulation, implying that the other CFD simulation results were
valid. The second validation, that is, the comparison of ho-a to
ho-c, showed good results. Their discrepancy was within 4%, as
shown in Table 2.
The results of these two validations imply that the CFD results of
heat transfer were valid. Table 2 also shows that for constant
temperature, the increase in mass flow rate leads to a significant
increase in the convection heat transfer coefficient inside the
pipe.
The above results only validate the results of CFD on heat
transfer. Therefore, as the third step, and to ensure that the CFD
results outside the pipe are also valid (i.e., actual natural
convection), the flow pattern of ambient air and its temperature
were observed. Due to the fact that the phenomena for ambient air
were logically acceptable, it can be concluded that the CFD results
were quite promising in predicting the natural convection heat
transfer outside the pipe. The relevant explanations are as
follows.
From Fig. 5, Fig. 6, and Fig. 7, it can be seen that ambient air
flowed downward with increasing veloc- ity. This is because the low
temperature of the wall decreases the temperature of ambient air
such that the density of air near the wall increases, while the
den- sity of ambient air sufficiently far from the pipe does not.
Moreover, the upward flow of nitrogen causes the wall temperature
on the upstream to be lower than that on the downstream. This
condition results in the constantly increasing density of the
near-wall ambient air as it flows downward. The fluid velocity near
the wall is zero because of the no-slip condition; the ve- locity
then continues to increase as the distance from the wall increases
until it reaches a maximum. How-
1522 H. M. Jeong et al. / Journal of Mechanical Science and
Technology 23 (2009) 1517~1527
Fig. 5. Flow pattern of ambient air for the simulation condition of
inlet temperature and mass flow rate 231 K and Re = 3.5367E+4,
respectively. Ra = 2.7414E+12.
Fig. 6. Flow pattern of ambient air for the simulation condition of
inlet temperature and mass flow rate 171 K and Re = 6.9342E+4,
respectively. Ra = 9.4131E+12.
Table 2. Comparison of hi-c to hi-p and ho-c to ho-a.
No Mass flow rate (kg/s) Tb-in (K) hi-c hi-p Discrepancy
between
hi-c and hi-p (%) Tsi/Tb-in ho-c ho-a Discrepancy between
ho-c and ho-a (%) 1 0.0150 111 91.00 89.41 2 (+) 1.34* 2.26 2.18 4
(+) 2 0.0200 111 117.30 115.16 2 (+) 1.30* 2.44 2.36 4 (+) 3 0.0300
100 166.10 155.44 7 (+) 1.31* 3.00 2.90 3 (+) 4 0.0150 131 93.30
96.72 4 (-) 1.24* 3.83 3.72 3 (+) 5 0.0100 131 65.40 67.84 4 (-)
1.30* 2.14 2.07 4 (+) 6 0.0050 151 37.20 39.71 6 (-) 1.32* 1.97
1.91 4 (+) 7 0.0100 151 67.80 72.70 7 (-) 1.22* 1.69 1.63 4 (+) 8
0.0050 171 38.10 42.41 10 (-) 1.23* 1.87 1.80 4 (+) 9 0.0100 171
69.40 76.73 10 (-) 1.16 1.58 1.53 4 (+) 10 0.005 191 39.70 44.80 11
(-) 1.16 1.77 1.71 3 (+) 11 0.010 191 73.50 80.20 8 (-) 1.11 1.48
1.43 3 (+) 12 0.005 211 40.20 46.83 14 (-) 1.11 1.71 1.66 3 (+) 13
0.010 211 76.10 83.07 8 (-) 1.08 1.37 1.33 3 (+) 14 0.005 231 42.00
48.63 14 (-) 1.07 1.68 1.63 3 (+) 15 0.010 231 80.70 85.55 6 (-)
1.05 1.27 1.24 3 (+) 16 0.025 111 154.90 140.95 10 (+) 1.25* 1.73
1.68 3 (+) 17 0.030 111 188.10 164.40 14 (+) 1.23* 1.17 1.14 3 (+)
18 0.020 131 121.10 123.63 2 (-) 1.22* 1.92 1.88 3 (+) 19 0.025 131
149.50 148.76 1 (+) 1.20* 2.60 2.51 3 (+) 20 0.015 151 98.90 102.85
4 (-) 1.18 2.92 2.83 4 (+) 21 0.020 151 132.60 130.80 1 (+) 1.16
2.39 2.32 4 (+) 22 0.015 171 103.40 107.74 4 (-) 1.13 2.76 2.68 4
(+) 23 0.020 171 141.40 136.30 4 (+) 1.12 2.09 2.02 3 (+) 24 0.025
151 170.40 156.85 9 (+) 1.15 2.45 2.37 3 (+)
* Simulations that meet the Perkins-correlation requirement of 1.2
< Tsi/Tb-in < 7.5
H. M. Jeong et al. / Journal of Mechanical Science and Technology
23 (2009) 1517~1527 1523
Fig. 7. Flow pattern of ambient air for the simulation condition of
inlet temperature and mass flow rate 100 K and Re = 1.07276E+5,
respectively. Ra = 2.8263E+13.
ever, when the distance from the wall increases, the velocity
begins decreasing until it reaches zero due to the decrease in
density difference. This velocity pro- file is also influenced by
the viscosity of the fluid. The ambient air far from the pipe is
quiescent.
Fig. 9 (refer to detail A of Fig. 8 to read this figure) shows a
comparison of the turbulence kinetic energy of the flow between
three simulations with an increas- ing Rayleigh number, that is, it
illustrates a compari- son between the lowest, middle, and highest
Ra re- sults from the simulations. In all simulations, the flow is
turbulent. The turbulence intensity increases when the Rayleigh
number increases. As shown in Fig. 9, there are significant
temperature differences between the wall and air. This may be due
to the higher Rayleigh number brought about by the increasing
temperature difference between the atmosphere and the external wall
of the pipe.
Fig. 10 (refer to detail A of Fig. 8 to read this fig- ure)
illustrates the temperature of ambient air with three different
simulations. The temperature on the lower side of the pipe was
lower than that on the up- per side because of the upward flow of
nitrogen in- side the pipe. All these phenomena show that the CFD
results represent turbulent natural convection.
Fig. 8. Drawing view which is used for Fig. 9 and Fig. 10.
Fig. 9. Figures of ambient air beside the pipe (excluding the
ambient air on the top and the bottom of the pipe). This illus-
trates the turbulence kinetic energy of near-wall ambient
air.
1524 H. M. Jeong et al. / Journal of Mechanical Science and
Technology 23 (2009) 1517~1527
Fig. 10. Figures of ambient air beside the pipe (excluding the
ambient air on the top and the bottom of the pipe). This illus-
trates the temperature of near-wall ambient air.
Fig. 11. Graph of Nusselt numbers outside the pipe vs. the Rayleigh
numbers.
Fig. 12. Nusselt numbers outside the pipe derived from the
regression equation vs. the Nusselt numbers outside the pipe of the
original CFD results.
Next, after this validation, the outer-pipe Nusselt numbers were
determined using Eq. (15). These were then correlated with the
Rayleigh number calculated using Eq. (16). The results are shown in
Table 3 and Fig. 11. This table has been sorted by ascending
Rayleigh numbers. From the table and figure, it can be concluded
that Nuo is proportional to Ra over the range of 2.7414x1012 ≤ Ra ≤
2.8263x1013; the regres- sion equation is as follows:
( ) 0.40880.0033oNu Ra= , (19)
and the correlation coefficient is 2 0.8208=R .
In this case, the multiple correlation coefficients, R, and the
coefficient of determination, R2, are both measures of how well the
regression model describes the data. R values near 1 indicate that
the equation is a good description of the relation between the
inde- pendent and dependent variables. R equals 0 when the values
of the independent variable do not allow any prediction of the
dependent variables, and it equals 1 when the dependent variables
can be predicted per- fectly from the independent variables. This
regression equation has uncertainty within 27%, as shown in Table 3
and Fig. 12. Additional simulations should be conducted to obtain
more accurate Nuo correlations over a wider Ra range.
5. Conclusions
Here, CFD analysis was conducted on a 1000 mm long, longitudinally
finned vertical pipe with 4 fins, a fin length of 75 mm, and a fin
thickness of 2 mm in which nitrogen gas was made to flow; the pipe
was heated by using static dry-ambient air outside the pipe.
Therefore, the conditions under which these simula- tions were
performed were non-uniform wall heat flux and non-uniform wall
temperature conditions. The objective was to obtain natural
convection corre- lation outside the pipe. The correlation equation
pro- posed is as follows:
( ) 0.40880.0033oNu Ra=
for the Rayleigh number in the range of 2.7414x1012 ≤ Ra ≤
2.8263x1013; the uncertainty was equal to 27% with the correlation
coefficient
2 0.8208R =
H. M. Jeong et al. / Journal of Mechanical Science and Technology
23 (2009) 1517~1527 1525
Additional numerical analysis should be conducted to obtain a more
accurate correlation for the Nusselt number over a wider Rayleigh
number range. More- over, this correlation equation must be
validated by an experiment.
Acknowledgement
The authors are grateful for the support provided by the Brain
Korea 21 Project, the Ministry of Com- merce, Industry, and Energy
(MOCIE), and the Korea Industrial Technology Foundation (KOTEF)
through the Human Resource Training Project for Regional
Innovation.
Nomenclature-----------------------------------------------------------
Ac : Fin cross-sectional area, m2 Asi : Inside pipe surface area,
m2 Aso-all : Outside pipe surface area (including the fins),
m2
di : Inside diameter of the pipe, m do : Outside diameter of the
pipe, m g : Gravitational acceleration, m/s2 Grx : Local Grashof
number hi-c : Average heat transfer coefficient inside the
pipe derived from the CFD results, W/m2K hi-p : Average heat
transfer coefficient inside the
pipe derived from the Perkins correlation, W/m2K
ho-c : Average heat transfer coefficient outside the pipe derived
from the CFD results, W/m2K
ho-a : Average heat transfer coefficient outside the pipe derived
from the analytical solution of the energy equation, W/m2K
iin : Enthalpy at pipe inlet, Joule/kg iout : Enthalpy at pipe
outlet, Joule/kg kal : Thermal conductivity of aluminum, W/mK kN2 :
Thermal conductivity of nitrogen, W/mK k∞ : Thermal conductivity of
ambient air, W/mK L : Fin length (radial direction), m
Table 3. Calculated Rayleigh numbers and the Nusselt numbers
outside the pipe.
No Mass flow rate (kg/s) Tb-in (K) Ra ambient air Nuo CFD Nuo
regression Discrepency (%)
1 0.005 231 2.7414E+12 391.528 401.012 2 (+)
2 0.010 231 3.0697E+12 534.433 419.990 21 (-)
3 0.005 211 3.9165E+12 431.856 463.971 7 (+)
4 0.010 211 4.6059E+12 535.139 495.766 7 (-)
5 0.005 191 5.2944E+12 473.843 524.820 11 (+)
6 0.010 191 6.4691E+12 557.623 569.622 2 (+)
7 0.005 171 6.7748E+12 518.085 580.476 12 (+)
8 0.005 151 8.4583E+12 563.191 635.605 13 (+)
9 0.010 171 8.6274E+12 590.722 640.769 8 (+)
10 0.015 171 9.4131E+12 703.418 664.012 6 (-)
11 0.020 171 9.6818E+12 882.479 671.696 24 (-)
12 0.010 151 1.1201E+13 638.121 712.935 12 (+)
13 0.015 151 1.2547E+13 723.740 746.788 3 (+)
14 0.020 151 1.3188E+13 851.205 762.155 10 (-)
15 0.025 151 1.3384E+13 1043.895 766.765 27 (-)
16 0.010 131 1.4262E+13 690.870 786.942 14 (+)
17 0.015 131 1.6360E+13 762.283 832.355 9 (+)
18 0.020 131 1.7479E+13 856.698 855.174 0 (-)
19 0.025 131 1.7965E+13 991.500 864.816 13 (-)
20 0.015 111 2.0787E+13 824.090 917.967 11 (+)
21 0.020 111 2.2695E+13 899.121 951.521 6 (+)
22 0.025 111 2.4734E+13 967.440 985.582 2 (+)
23 0.030 111 2.5444E+13 1091.474 997.051 9 (-)
24 0.030 100 2.8263E+13 1133.577 1040.811 8 (-)
1526 H. M. Jeong et al. / Journal of Mechanical Science and
Technology 23 (2009) 1517~1527
l : Length of the pipe, m l c : Characteristic length of the pipe,
m •
m : Mass flow rate, kg/s n : Number of fin Nui-p : Nusselt number
inside the pipe calculated
using Perkins correlation Nuo : Nusselt number outside the pipe Pr
: Prandtl number Q •
: Total heat transfer rate, W fQ
•
: Heat transfer rate from the fin, W R : Multiple correlation
coefficient R2 : Coefficient of determination Ra : Rayleigh number
Re : Reynolds number Rb : Pipe base thermal resistance, K/W Re :
Equivalent thermal resistance, K/W Rf : Fin thermal resistance, K/W
t : Fin thickness, m Tbi : Fluid mean bulk temperature inside the
pipe, K Tb-in : Fluid bulk temperature at the inlet of the
pipe,
K Tf : Film temperature, K Tsi : Pipe inner surface mean
temperature, K Tso : Pipe outer surface mean temperature
(exclud-
ing the fin temperature), K Tso-all : Pipe outer surface mean
temperature (base
and fin temperature), K T∞ : Ambient temperature, K α : Thermal
diffusivity, m2/s β : Coefficient of thermal expansion, K-1 ν :
Kinematic viscosity, m2/s
References
[1] K. Sugano, Aug. LNG Vaporizers, Research and Development, Kobe
Steel Engineering Reports, 56, No. 2 (2006).
[2] S. C. Lee, Y. H. Lee, H. S. Chung, H. M. Jeong, C. K. Lee and
Y. H. Park, Effects on Heat Transfer of Super Low Temperature
Vaporizer Respect with of Geometric Parameters, 2nd International
Confer- ence on Cooling and Heating Technologies, Dalian, China,
July 26 – 30 (2006).
[3] H. M. Jeong, H. S. Chung, S. C. Lee, T. W. Kong and C. S. Yi,
Optimum Design of Vaporizer Fin with Liquefied Natural Gas by
Numerical Analysis, Journal of Mechanical Science and Technology
(KSME Int. J.), 20, No. 4, (2006) 545-553.
[4] T. W. Kong, S. C. Lee, Y. H. Lee, H. S. Chung and H. M. Jeong,
A Study on The Air Vaporizer for
Liquefied Natural Gas with Super Low Tempera- ture, Proceedings of
the 3rd Asian Conference on Refrigeration and Air-conditioning, May
21-23, Gyeongju, South Korea (2006).
[5] S. C. Haldar, G. S. Kochhar, K. Manohar and R. K. Sahoo,
Numerical Study of Laminar Free Convec- tion about A Horizontal
Cylinder with Longitudinal Fins of Finite Thickness, International
Journal of Thermal Sciences, article in press (2006).
[6] N. Morimoto, S. Yamamoto, Y. Yamasaki, T. Shi- mokawatoko,
(Osaka Gas CO., LTD.), K. Shinkai, (KOBE STEEL, LTD.), S. Egashira
and K. Konishi, (KOBELCO RESEARCH INSTITUTE, INC.), De- velopment
and Practical Application of A High Per- formance Open-rack LNG
Vaporizer (SUPER- ORV).
[7] K. S. Lee and W. S. Kim, The Effects of Design and Operating
Factors on The Frost Growth and Thermal Performance of A Flat Plate
Fin-tube Heat Exchanger Under The Frosting Condition, KSME
International Journal, 13, No. 12 (1999) 973-981.
[8] B. T. F. Chung, Z. Ma and F. Liu, General Solu- tions for
Optimum Dimensions of Convective Lon- gitudinal Fins with Base Wall
Thermal Resistances, Heat Transfer 1998, Proceedings of 11th IHTC,
5 (1998), August 23-28, Gyeong-ju, Korea.
[9] D. K. Yang and K. S. Lee, Simon Song, Fin Spac- ing
Optimization of A Fin-tube Heat Exchanger un- der Frosting
Conditions, Int. J. of Heat and Mass Transfer 49 (2006)
2619-2625.
[10] D. Seker, H. Karatas and N. Egrican, Frost Forma- tion on
fin-and-tube Heat Exchangers. Part I - Mod- eling of Frost
Formation on Fin-and-tube Heat Ex- changers, Int. J. of
Refrigeration 27 (2004) 367-374.
[11] D. Seker, H. Karatas and N. Egrican, Frost Forma- tion on
fin-and-tube Heat Exchangers. Part II - Ex- perimental
investigation of frost formation on fin- and-tube heat exchangers,
Int. J. of Refrigeration 27 (2004) 375-377.
[12] S. Kakac and Y. Yener, Convective Heat Transfer, 2nd edition,
CRC Press (1995) 304.
[13] K. Dhinsa, C. Bailey and K. Pericleous, Low Rey- nolds Number
Turbulence Models for Accurate Thermal Simulations of Electronic,
5th Int. Conf. of Thermal and Mechanical Simulation and Experi-
ments in Micro-electronics and Micro-systems, Eu- roSimE2004
(2004).
[14] T. Norton, Sun Da-Wen, J. Grant, R. Fallon and V. Dodd,
Applications of Computational Fluid Dy- namics (CFD) in The
Modelling and Design of
H. M. Jeong et al. / Journal of Mechanical Science and Technology
23 (2009) 1517~1527 1527
Ventilation Systems in The Agricultural Industry: A Review, Int. J.
of Bioresource Technology 98, (2007) 2386-2414.
[15] Star-CD, V3.24, Methodology, CD adapco Group (2004) 6-1,
6-9.
[16] NIST on-line Thermophysical Properties of Fluid System
(http://webbook.nist.gov/chemistry/fluid/).
[17] S. Kakac and Y. Yener, Convective Heat Transfer, 2nd edition,
CRC Press (1995) 301.
[18] F. P. Incropera and D. P. Dewit, Fundamentals of Heat and Mass
Transfer, 4th edition, John Wiley and Sons, Inc. (1996)
113-118.
Hyomin Jeong is currently a professor of Mechanical and Precision
Engineering at Gyeongsang Nation University. He received his ph.D.
in me- chanical engineering from the University of Tokyo in 1992
and he joined Arizona State
University as a visiting professor from 2008 to 2009. His research
interests are in fluid engineering, CFD, cryogenic system, cascade
refrigeration system and ejector system, mechanical vapor
compression
Hanshik Chung is a professor of Mechanical and Precision
Engineering at Gyeongsang Na- tional University. He obtianed his
Ph.D. in Mechanical Engi- neering from Donga University. He joined
Changwon Master’s College and Tongyeong Fisher
National College as an assistant Professor in 1988 and 1993,
respectively. His research fields extend into the thermal
engineering, heat transfer, solar heating & cooling system, LNG
vaporizer optimum, solar cell, hydrogen compressor for fuel cell
and making fresh water system from sea water
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