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Mishra2010-GunBarrelTemperature.PDF
Avanish Mishra
Department of Mechanical Engineering and
Mining Machinery Engineering,
Indian School of Mines,
Dhanbad,
Jharkhand, 826004, India
e-mail: [email protected]
Amer Hameed
e-mail: [email protected]
Bryan Lawton
Weapon Systems and Engineering Dynamics
Group, DA-CMT,
Cranfield University,
Shrivenham, Swindon,
Wilts SN6 8LA, UK
A Novel Scheme for Computing
Gun Barrel Temperature History
and Its Experimental Validation
An accurate modeling of gun barrel temperature variation over time is important to
assess wear and the number of shot fires needed to reach cook-off. Using lumped parameter methods, an internal ballistics code was developed to compute heat transfer to the
gun barrel for given ammunition parameters. Subsequently the finite element method was
employed to model gun barrel temperature history (temperature variation over time).
Simulations were performed for a burst of nine shots and the results were found to match
satisfactorily to the corresponding experimental measurements. Wear or erosion of the
barrel during a gun fire is very sensitive toward the maximum bore surface temperature.
The proposed scheme can accurately simulate gun barrel temperature history; hence
improved wear calculations can be made with it. An important and unique advantage of
the developed scheme is that it easily couples internal ballistics simulations with the finite
element methods. 关DOI: 10.1115/1.4001740兴
Keywords: cook-off, gun barrel, wear, finite element method, temperature history
1
Introduction
During firing, gun barrels are subjected to a large amount of
heat input at the bore surface. Heat transfer is mostly due to
forced convection from the hot combustion gases generated inside
the barrel. In between shot fires, the gun barrel is naturally cooled
by convection and radiation at its outer surface but natural cooling
is inefficient and only a fraction of the total heat input is transferred to the external environment. Hence, during continuous firing at a high rate of fire, the temperature of the gun barrel keeps
on rising to ultimately equal the cook-off temperature. At cook-off
temperature, the loaded charge will self-ignite given sufficient
contact time between the ammunition and the hot gun bore surface
关1兴. This premature self-ignition may result in serious damage to
the gun and injury to crew members.
Wear in gun barrels is another important consideration in gun
design. During each shot fire, the gun barrel wears as a result of
erosion. The phenomenon of gun barrel wear has been studied by
many researchers 关2–9兴. Although the mechanism of gun barrel
wear is not yet fully understood, it is known that wear is very
closely related to the maximum temperature of the bore surface.
Lawton 关10兴 demonstrated that the wear of the gun bore per cycle
is an exponential function of the maximum bore surface temperature, where a shot fire is known as a cycle. On an average, if the
maximum bore surface temperature increases by about 10%, i.e.,
from 900 K to 1000 K, then the wear per cycle increases 2.5 times
关1兴. Wear estimation is performed to predict barrel life. Assessment of wear and cook-off is only possible by accurate modeling
of gun barrel temperature history 共temperature variation over
time兲. In this work, a new scheme for computing gun barrel temperature history was proposed and accuracy of the scheme was
checked with the experimental results.
The barrel heating problem was divided in to two main parts:
共1兲 determination of the total heat transfer during a gun fire from
hot propellant gases to the gun bore surface and 共2兲 determination
of the barrel temperature distribution resulting from this heat
transfer. The code GUNTEMP8.EXE was developed for simulation of
Contributed by the Pressure Vessel and Piping Division of ASME for publication
in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received January 16,
2009; final manuscript received April 24, 2010; published online October 13, 2010.
Assoc. Editor: Ricky D. Dixon.
Journal of Pressure Vessel Technology
the total heat transfer per cycle. Heat transfer to the gun bore
surface can be approximated as an exponentially decaying heat
flux 关11兴, which was determined from the computed results of
GUNTEMP8.EXE. Subsequently a finite element model of the gun
barrel was developed in commercial finite element analysis 共FEA兲
package, ANSYS 11.0, and the exponentially decaying heat flux was
applied as a boundary condition at the gun bore surface. The finite
element model was solved to compute the gun barrel temperature
distribution for single and series of cycles.
The gun barrel heating problem has been modeled by many
researchers 关12–14兴; most of the researchers used finite difference
methods to compute the barrel temperature distribution. Wu et al.
关15兴 used exponentially decaying heat flux as a boundary condition in the finite element thermal analysis of a 155 mm midwallcooled gun barrel. However, their scheme of simulation is different as it does not incorporate internal ballistics simulation of total
heat transfer; instead a preknown experimental value of total heat
transfer was used. In contrast, the current simulation scheme facilitates generation of temperature history from the input data of
ammunition properties 共and other operational parameters兲. Moreover, in the current work, reduction in the convective heat input to
the bore surface due to the rise in the bore temperature was also
incorporated to improve the results. The current scheme is unique
as it easily couples internal ballistics simulations with the finite
element methods.
2
Formulation of Guntube Heating Problem
Figure 1 shows a schematic of the heat transfer in a gun barrel.
It was assumed that the heat conduction in the axial direction is
negligible in comparison to conduction in the radial direction 关12兴.
Friction heating between the projectile driving band and the bore
surface was neglected 关14兴. Any effect of gravitation on convection heat transfer was also neglected. The barrel was assumed to
be uniformly thick at any transverse cross section along its length.
The mathematical formulation is presented using the cylindrical
coordinate system. Based on the above assumptions, any possibility of azimuthal variation of temperature was removed and the
problem was reduced to a one-dimensional axisymmetric case.
The governing equation, Eq. 共1兲, is the diffusion equation, which
is Fourier’s conduction equation, combined with the energy equation in cylindrical coordinates.
Copyright © 2010 by ASME
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Fig. 2 Description of effective breech face
−k
Fig. 1 Schematic of heat transfer to gun barrel
冉 冊
⳵T
⳵T
1 ⳵
kr
= ␳c p
⳵r
⳵t
r ⳵r
共1兲
where r is the radius, varying from Ri to Ro; k, ␳, and c p are the
thermal conductivity, the density, and the specific heat of gun
steel, respectively. Assuming constant thermophysical properties
共k, ␳, and c p兲, Eq. 共1兲 is reduced to Eq. 共2兲, where ␣共k / ␳c p兲 is the
thermal diffusivity of the gun steel. The initial uniform barrel
temperature was 307.6 K. The boundary conditions at the bore
surface and the outside barrel surface are given by Eqs. 共4兲 and
共5兲, respectively.
⳵ T 1 ⳵T 1 ⳵T
=
+
⳵ r2 r ⳵ r ␣ ⳵ t
⳵T
= q x,
⳵r
−k
−k
t = 0,
qx =
⳵T
= hg共Tg − T兲 = qin,
⳵r
t ⬎ 0,
共7兲
␳ gC xx
␮g
共8兲
where
Rex =
E=
⳵T
= h⬁共T − T⬁兲 + e␴共T4 − T⬁4 兲 = qconv + qrad,
⳵r
共3兲
r = Ri
t ⬎ 0,
共5兲
where hg is the combined convection heat transfer coefficient between the bore surface and hot propellant gases. Heat transfer to
the bore surface by radiation is very small. It may be ignored
except in the region of the breech, where the gas velocity is usually very small or zero 关1兴. Even though being small, radiation
heat transfer was included in this work. h⬁ is the heat transfer
coefficient between the outer barrel surface and the surrounding
atmosphere. It is taken to be 6.5 W m−2 K−1. e is the emissivity
of gun steel, which is typical of oxidized steel and taken to be
0.782 and ␴ is the Stefan–Boltzmann constant 共5.669
⫻ 10−8 W m−2 K−4兲.
3
Introduction to GUMTEMP8.EXE
is an internal ballistics code developed by Lawton 关1兴. In addition to internal ballistics, the program also models
temperature fluctuation at the bore surface for a few milliseconds
and the instantaneous heat transfer at any specified position along
the length of the barrel. An explicit finite difference scheme is
followed for the computation of the bore temperature fluctuation.
For thermal calculations, Eqs. 共1兲–共3兲 are utilized as such but Eq.
共4兲 is replaced by Eq. 共6兲.
GUNTEMP8.EXE
061202-2 / Vol. 132, DECEMBER 2010
共␥ − 1兲 ⳵ V
t⬘
V ⳵t 0
t ⬘0 =
共4兲
r = Ro
共6兲
kg
关aRebx 共Tg − Tw兲 − cETw兴
x
共2兲
Ri ⱕ r ⱕ Ro
r = Ri
where qx is the instantaneous heat flux between the propellant
gases and the gun bore surface at a distance x from the effective
breech face. The definition of the effective breech face can be
understood from Fig. 2. qx is usually determined from a semiempirical equation in which the surface heat transfer coefficient is
determined from the Nusselt number 共Nu兲. The Nusselt number is
correlated with the Reynolds number 共Re兲 and the Prandtl number
共Pr兲. This is good for steady problems but does not work for
unsteady expanding flows, which exist in a gun barrel, because the
expansion of the gases distorts the temperature distribution in the
thermal boundary layer 关1兴. Lawton 关1兴 demonstrated that qx can
be computed by Eq. 共7兲.
2
T = 307.6 K,
t ⬎ 0,
冑
m cc vgd 3
V ck gC m
共9兲
共10兲
E is a dimensionless number called the expansion number. The
effect of the expansion number, E, when the gas volume is increasing, is to reduce the heat flux. E is positive for diverging gas
flow existing in gun systems. a, b, and c are constants, suitable
values being a = 0.85, b = 0.7, and c = 2000 关1兴. During gun fire, a
very large amount of heat is transferred to the gun bore surface in
a few milliseconds. Subsequently, heat penetrates into the gun
barrel and requires some time to reach the outside surface of the
gun barrel. By using the approximate analytic thermal layer
method, the depth of heat penetration at any time t can be approximately estimated to be 冑12␣t 关16兴. GUNTEMP8.EXE was run for 20
ms, during which heat penetrated 1.324 mm below the gun bore
surface. Therefore, Eq. 共5兲 never came in to consideration. The
material in the thickness of 1.324 mm was represented by 400
nodes; hence node spacing was 3.31 ␮m. For numerical stability,
the timestep of 0.8 ␮s was adopted.
4
Experimental Validation of GUMTEMP8.EXE
Experiments were performed on a 155 mm, 52 caliber gun barrel with a known charge. The temperature fluctuation and heat
transfer were measured during the experiments at 5 cm from the
commencement of rifling. Fast response, eroding type, thermocouples, available from the Swedish firm, ASEA 共Västerås, Sweden兲 , were used. A detailed description of the experimental procedure and instrumentation is available in Ref. 关17兴. The thermal
diffusivity of the thermocouple was 7.3⫻ 10−6 m2 s−1 compared
with 9.0⫻ 10−6 m2 s−1 of the typical gun steel, as mentioned in
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Table 1 Thermal properties of gun steel and thermocouple
Thermocouple
Gun steel
k
共W m−1 K−1兲
␣
共m2 s−1兲
24
35
7.3⫻ 10−6
9.0⫻ 10−6
Table 1. Therefore, the thermocouple recorded temperatures were
approximately 11% greater than those in the typical gun steel
subjected to the same heat input. Thermocouple properties were
inputted into GUNTEMP8.EXE to compare simulated results directly
with the thermocouple measurements. Measured temperature
variation was found to be in close agreement with the simulated
temperature history of GUNTEMP8.EXE, as shown in Table 2, and
Figs. 3共a兲 and 3共b兲. An error of 1.84% was observed in the simulated result of the maximum bore surface temperature. During
shot exit, propellant gases accelerate past the projectile and enclose it in a shock bottle. This sudden increase in velocity increases the rate of convective heat transfer to the gun barrel 关1兴,
which results in a slight increment in the bore surface temperature
at 12.1 ms, as shown in Fig. 3共b兲. However, this effect was not
observed in the experimental results.
5
Finite Element Model and Analysis of First Cycle
A one-dimensional, transient, thermal analysis was performed
with the FEA package ANSYS 11.0 for the first cycle. The verification of the finite element model 共FEM兲 was performed by comparing FEA results with GUNTEMP8.EXE output. The solid, quad
8node, thermal element was used throughout this work. The thermocouple properties, as listed in Table 1, were inputted into the
material model. The annulus segment, shown in Fig. 4, was used
to model the barrel cross section. When a shot is fired, almost all
of the heat transfer takes place within a few milliseconds. This
induces very acute temperature gradients near the bore surface;
hence a very fine mesh was used in that zone. Figure 4 shows a
small segment of the meshed model from near the bore surface.
Heat transfer to the gun bore surface can be approximated as an
exponentially decaying heat flux, Eq. 共11兲, and in the finite element model, this was applied as a boundary condition at the bore
surface 关11兴.
冉 冊
qx = qmax exp −
t
t0
Fig. 3 „a… Experimentally measured variation of temperature
for the first cycle. „b… Simulated temperature history of the first
cycle.
Fig. 4 Gun barrel cross section and meshed model
were same as the Eqs. 共3兲 and 共5兲 but Eq. 共4兲 was interpreted
differently as Eq. 共14兲.
共11兲
Tmax − Ti = 1.082
Equation 共11兲 was integrated from zero to t, with respect to time,
which resulted in the equation of heat transfer to the bore surface,
Eq. 共12兲.
冋 冉 冊册
H = qmaxt0 1 − exp −
t
t0
共12兲
where qmax was determined by using relation qmax ⫻ t0 = H⬁, H⬁
being the total heat transfer per unit area per cycle. Often, H⬁ is
also referred as the heat transfer per cycle. GUNTEMP8.EXE modeled the total heat transfer 共H⬁兲 and the temperature fluctuation
共Tmax − Ti兲 at the bore surface for first cycle. t0 is the time constant
that was estimated by placing Tmax − Ti and H⬁ into Eq. 共13兲. The
boundary conditions in the finite element model of the gun barrel
−k
冉 冊
H⬁
k
⳵T
t
= qmax exp −
,
⳵r
t0
冑
␣
␲t0
t ⬎ 0,
共13兲
r = Ri
共14兲
Transient thermal analysis was performed for 20 ms and the results were compared with the computed temperature history of
GUNTEMP8.EXE for validation of the finite element model. Figure 5
shows the variation of the bore surface temperature with time. The
maximum temperature was computed to be 1258.57 K, which is
very close to the maximum temperature computed by
GUNTEMP8.EXE, i.e. 1259.77 K. Figure 6 shows the temperature
history results of both Guntemp8.exe and the finite element analysis. The results are in good agreement. Moreover, it proves that an
exponentially decaying heat flux can be used as a boundary con-
Table 2 Comparison of measured and simulated results
Total heat transfer for first cycle 共K J m−2兲
Maximum bore surface temperature 共K兲
Muzzle velocity 共m s−1兲
Journal of Pressure Vessel Technology
Experimental
results
Simulated results of
963.2
1237
940
947
1259.78
938.9
GUNTEMP8.EXE
DECEMBER 2010, Vol. 132 / 061202-3
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Fig. 5 FEA result of bore surface temperature variation for the
first cycle
Fig. 7 Simulated temperature history of 9 cycles
H⬁ = H307.6
Fig. 6 Comparison of GUNTEMP8.EXE and FEA result of bore surface temperature variation for the first cycle
冉
Tr − Ti
Tr − 307.6
冊
共15兲
where H307.6 is the total heat transfer for first cycle when bore
temperature before shot fire was 307.6 K. Tr is the radiation temperature, which was estimated to be 1189.15 K for a given ammunition, and Ti is the initial bore surface temperature of a cycle.
After completion of each cycle, a new equation of exponentially
decaying heat flux was used. Heat transfer during each cycle was
computed from Eq. 共15兲, and Eqs. 共11兲–共13兲 were used to determine the exponentially decaying heat flux for each cycle. For all 9
cycles, 27 loadstep files were written and solved in ANSYS to
produce a temperature history, as shown in Fig. 7.
Experimental data of the maximum and initial bore surface
temperature are in close agreement with the simulated results
computed by finite element analysis, Fig. 8 and Table 4. The
dition to accurately model the temperature fluctuations.
6
Finite Element Analysis of Burst
In the same experiment on a 155 mm gun barrel, measurements
were made for 8 more cycles and their details are given in Table 3.
Each shot was fired at an interval of 5–6 min; however, the sixth
shot was fired 4 min after shot 5. The bore surface temperature
was measured before every shot fire and presented as the initial
bore surface temperature in Table 3. Finite element analysis of the
above-mentioned firing scenario was also performed.
Lawton 关1兴 proposed Eq. 共15兲 to compute the total heat transfer
for a particular cycle during continuous fire. It was used to incorporate the reduction in heat transfer due to an increase in the bore
temperature.
Fig. 8 Experimental and FEA results of 9 cycles
Table 3 155 mm gun barrel, experimental measurements at 5 cm from the commencement of
rifling
Shot No.
Initial bore surface
temperature 共K兲
Maximum bore surface
temperature 共K兲
Total heat transfer
共K J m−2兲
Time of fire
共min兲
1
2
3
4
5
6
7
8
9
307.6
311.4
316.9
320.7
322.4
332.9
331.1
334.7
338.8
1237
1246
1248
1250
1225
1254
1298
1269
1258
963.2
957.3
951.8
959.1
949.7
977.4
947.0
948.9
946.8
0
5
11
16
22
26
32
37
43
061202-4 / Vol. 132, DECEMBER 2010
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Table 4 Experimental and FEA results of bore surface temperature during 9 cycles
Shot No.
Experimental
measurements of initial
bore temperature 共K兲
FEA results of
initial bore
temperature 共K兲
Experimental
measurements of maximum
bore temperature 共K兲
FEA results of
maximum bore
temperature 共K兲
1
2
3
4
5
6
7
8
9
307.6
311.4
316.9
320.7
322.4
332.9
331.1
334.7
338.8
307.60
310.52
313.21
315.97
318.55
321.39
323.78
326.37
328.77
1237
1246
1248
1250
1225
1254
1298
1269
1258
1258.57
1256.64
1254.90
1253.24
1252.84
1251.01
1250.10
1248.91
1247.96
maximum error in the results was found to be 3.69%. The error in
the result for maximum temperature is expected to be reduced by
incorporating the variation of gun metal thermal properties 共c p and
k兲 with temperature in the finite element model.
7
Conclusion
In this work, a scheme of computing the gun barrel temperature
variation with time was proposed and its experimental validation
was performed. Proposed scheme can accurately simulate gun barrel temperature history; hence, improved wear calculations and
cook-off predictions can be made with it. It was also found that
exponentially decaying heat flux can be used to accurately model
gun barrel temperature variation. Finite element methods are employed by various researchers for modeling complex stress problems associated with gun barrels; moreover, complex geometries
such as midwall-cooled gun barrel can also be modeled using
finite element methods. In this direction, an important advantage
is offered by proposed scheme, as it couples internal ballistic
simulations with the finite element methods. In future, it is expected that this scheme will be used to assess thermal stresses and
the effect of midwall cooling channels on a gun barrel.
Acknowledgment
The authors are grateful to the Department of Engineering Systems and Management, Cranfield University for funding this work
and acknowledge the support of Mr. Stuart Thomson.
Nomenclature
Cm ⫽ muzzle velocity, m s−1
c p ⫽ specific heat of gun steel, J kg−1 K−1
cvg ⫽ specific heat of gas at constant volume,
J kg−1 K−1
Cx ⫽ gas velocity at position x, m s−1
d ⫽ gun bore diameter, m
E ⫽ expansion number
hg ⫽ combined convection heat transfer coefficient
between bore surface and hot propellant gases,
W m−2 K−1
h⬁ ⫽ heat transfer coefficient between the outer barrel surface and surrounding atmosphere,
W m−2 K−1
H ⫽ instantaneous total heat transfer per unit area
during a cycle, J m−2
H⬁ ⫽ total heat transfer per unit area per cycle,
J m−2
k ⫽ thermal conductivity of gun steel, W m−1 K−1
kg ⫽ thermal conductivity of propellant gas,
W m−1 K−1
mc ⫽ charge mass, kg
qconv ⫽ convection heat flux at the outer surface,
W m−2
qin ⫽ input heat flux at the bore surface, W m−2
Journal of Pressure Vessel Technology
qmax ⫽ maximum heat flux at the bore surface, W m−2
qrad ⫽ radiation heat flux at the outer surface, W m−2
qx ⫽ instantaneous heat flux at the bore surface,
W m−2
Rex ⫽ Reynolds number of propellant gas
Ri ⫽ inner radius of barrel, m
Ro ⫽ outer radius of barrel, m
Tg ⫽ average cross sectional temperature of the gas,
K
Ti ⫽ initial bore surface temperature of a cycle, K
Tmax ⫽ maximum temperature during a cycle, K
Tr ⫽ radiation temperature, K
Tw ⫽ bore surface temperature at any time t, K
T⬁ ⫽ temperature of external environment, K
t0 ⫽ time constant, s
t⬘0 ⫽ characteristic time, s
V ⫽ gas volume, m3
Vc ⫽ initial charge volume, m3
x ⫽ distance from effective breech face, m
␣ ⫽ thermal diffusivity of gun steel, m2 s−1
␥ ⫽ coefficient of adiabatic expansion
e ⫽ emissivity of gun steel
␮g ⫽ viscosity of gas, N s m−2
␳ ⫽ density of gun steel, kg m−3
␳g ⫽ density of gas, kg m−3
␴ ⫽ Stefan–Boltzmann constant, W m−2 K−4
References
关1兴 Lawton, B., and Klingenberg, G., 1995, Transient Temperature in Engineering
and Science, Oxford University Press, Oxford, Chaps. 9 and 10, pp. 444–573.
关2兴 Montgomery, R. S., 1975, “Muzzle Wear of Cannon,” Wear, 33, pp. 359–368.
关3兴 Turley, D. M., 1989, “Erosion of a Chromium-Plated Tank Gun Barrel,” Wear,
131, pp. 135–150.
关4兴 Lesquois, O., Serra, J. J., Kapsa, P., Serror, S., and Boher, C., 1996, “Degradations in a High-Speed Sliding Contact in Transient Regime,” Wear, 201, pp.
163–170.
关5兴 Chung, D. Y., Kong, H., and Nam, S. H., 1999, “A Study on the Precision
Wear Measurement for a High Friction and High Pressurized Gun Barrel by
Using a Diamond Indenter,” Wear, 225–229, pp. 1258–1263.
关6兴 Cote, P. J., and Rickard, C., 2000, “Gas–Metal Reaction Products in the Erosion of Chromium-Plated Gun Bores,” Wear, 241, pp. 17–25.
关7兴 Cote, P. J., Todaro, M. E., Kendall, G., and Witherell, M., 2003, “Gun Bore
Erosion Mechanisms Revisited With Laser Pulse Heating,” Surf. Coat. Technol., 163–164, pp. 478–483.
关8兴 Hirvonen, J. K., Demaree, J. D., Marble, D. K., Conroy, P., Leveritt, C., Montgomery, J., and Bujanda, A., 2005, “Gun Barrel Erosion Studies Utilizing Ion
Beams,” Surf. Coat. Technol., 196, pp. 167–171.
关9兴 Chung, D. Y., Shin, N., Oh, M., Yoo, S. H., and Nam, S. H., 2007, “Prediction
of Erosion From Heat Transfer Measurements of 40mm Gun Tubes,” Wear,
263, pp. 246–250.
关10兴 Lawton, B., 2001, “Thermo-Chemical Erosion in Gun Barrels,” Wear, 251共1–
12兲, pp. 827–838.
关11兴 Lawton, B., and Klingenberg, G., 1995, Transient Temperature in Engineering
and Science, Oxford University Press, Oxford, Chap. 2, pp. 61–63.
关12兴 Gerber, N., and Bundy, M. L., 1991, “Heating of a Tank Gun Barrel: Numerical Study,” Army Ballistic Research Laboratory Report No. BRL-MR-3932.
关13兴 Conroy, P. J., 1991, “Gun Tube Heating,” Army Ballistic Research Laboratory
Report No. BRL-TR-3300.
DECEMBER 2010, Vol. 132 / 061202-5
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关14兴 Gerber, N., and Bundy, M., 1992, “Effect of Variable Thermal Properties on
Gun Tube Heating,” Army Ballistic Research Laboratory Report No. BRLMR-3984.
关15兴 Wu, B., Chen, G., and Xia, W., 2008, “Heat Transfer in a 155 mm Compound
Gun Barrel With Full Length Integral Midwall Cooling Channels,” Appl.
Therm. Eng., 28共8–9兲, pp. 881–888.
061202-6 / Vol. 132, DECEMBER 2010
关16兴 Ozisik, M. N., 2002, Boundary Value Problems of Heat Conduction, Dover,
New York, Chap. 7, pp. 301–343.
关17兴 Lawton, B., 2003, “The Influence of Additives on the Temperature, Heat
Transfer, Wear, Fatigue Life and Self Ignition Characteristics of a 155 mm
Gun,” ASME J. Pressure Vessel Technol., 125共3兲, pp. 315–320.
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