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Performance of annular flow path heat pipe with a polymer insert controlling compactness for energy applications
International Journal of Heat and Mass Transfer 92 (2016) 929–939
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Performance of annular flow path heat pipe with a polymer insert controlling compactness for energy applications In Guk Kim, Kyung Mo Kim, Yeong Shin Jeong, In Cheol Bang ⇑ School of Mechanical and Nuclear Engineering, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulju-gun, Ulsan 689-798, Republic of Korea
a r t i c l e
i n f o
Article history: Received 19 July 2015 Received in revised form 13 September 2015 Accepted 15 September 2015
Keywords: Heat pipe Capillary limit Annular vapor space Compactness
a b s t r a c t This study experimentally investigates the effect of the cross-sectional area of vapor path on the heat transfer performance of a water-filled heat pipe with a polymer insert for optimizing its design. The thermal resistance and the heat transfer coefficient of the heat pipe with a screen mesh wick were measured at a saturation pressure ranging from 6.0 kPa to 12.5 kPa. It is observed that the changes of the capillary limit and the overall heat transfer coefficient come from the reduction of the vapor space. When the cross-sectional area of the vapor path is reduced to 48.3%, the capillary limit of the heat pipe is decreased by 22.9%. But the overall heat transfer coefficient of the heat pipe is slightly decreased by 3–7%. When the cross-sectional area of the vapor path is reduced to 76.8%, the capillary limit and the heat transfer coefficient of the heat pipe are decreased by 40.7% and 21.0%, respectively. Therefore, the reduction of the overall heat transfer coefficient of the heat pipe has no great effects according to the cross-sectional area of the vapor path. The experimental results suggest the direction of the optimization of the heat pipe in terms of space management for compact devices. Or, if there is enough margin in capillary limit, the optimized compact vapor path without losing heat transfer performance too much can be acquired or excess space can be used for special applications such as neutron absorber in nuclear control rods and structural supports in the electronic cooling for compactness. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction After the invention of the heat pipe by Grover et al. [1] 50 years ago, much study has been done and many applications have been created in various fields including electric cooling devices, decay heat removal systems for nuclear power plants [2–4], and energy conversion systems. A central processing unit (CPU) has a high heat flux of 67 kW/m2 [5]. It is difficult to use a heat sink that is attached to the CPU surface. A heat pipe can be used to transfer the energy away from the CPU surface to a heat sink, and it is possible to supply efficient cooling. Increases in heat flux and the power of electronic devices in a recent trend require highly integrated cooling device. To improve the capability for fully cooling the system heat, research on conventional heat pipes is focusing on advancing the working fluids, wick structure, and geometry of the heat pipes. Because of increasing demand for better cooling performance, the need for more effective cooling systems has led to various studies of heat pipes using nanoparticles and with modifications in the wick structures. Recent studies of heat pipes showed that ⇑ Corresponding author. Tel.: +82 52 217 2915; fax: +82 52 217 3008. E-mail address: [email protected] (I.C. Bang). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.09.037 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved.
the theoretical and experimental heat transport capacity of a concentric heat pipe and its capillary limits are strongly related to the properties and geometries of the wick structures and on the surface coating phenomenon of the evaporator wick. Kole and Dey [6] studied the synthesis, thermal conductivity, and thermal performance of screen-mesh-wick heat pipes using water-based copper nanofluids which was wick coating phenomenon using nanoparticle. It was found that the thermal performance of the nanofluid-based heat pipe was predominately affected by a layer of Cu nanoparticles at the evaporator section. Schampheleire et al. [7] investigated the gravity-assisted-orientation heat pipe using three different wicks: a screen-mesh wick, a sintered-powder wick, and outperforms the fiber wick. The metal-fiber wick showed the greatest potential as a wick material for high-performance heat pipes. Table 1 summarizes some experimental investigations of heat pipes of various geometries. A heat pipe is a high-heat-capacity, fully passive heat-transfer device that uses the evaporation, condensation, capillary wick structure, and working fluid in the pipe. In general, the vapor flow from the evaporation section to the condensation section is caused by a difference in vapor pressure. At the same time, the liquid flow from the condensation section to the evaporation section is produced by net forces such as capillary force and gravitational force.
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Nomenclature A g h l L _ m DP Q Q_ q00 r R T T
q e l
area [m2] acceleration of gravity [m/s2] heat transfer coefficient [W/m2 K] length [m] latent heat [J/kg] mass flow rate [kg/s] pressure difference [Pa] heat input, power [W] heat flow rate [J/s] heat flux [kW/m2] radius [m] thermal resistance [°C/W] temperature [°C] average temperature [°C] density [kg/m3] fractional void of the wick [–] dynamic viscosity [Pas]
Subscripts a adiabatic c condenser c, max maximum capillary e evaporator eff effective g gravity l liquid o overall pore effective pore v vapor v, e vapor of evaporator v, a vapor of adiabatic section v, c vapor of condenser w wick
Working fluids and wick structure modification are favorite topics for enhancing the capabilities of heat pipes, but the vapor path in concentric heat pipes is not considered owing to their low contribution. For these reasons, research on the effects of the cross-sectional area of the vapor path of heat pipe is neglected. Current researches for annular heat pipes are focused on the enhancement of the heat transfer coefficient using the additional heat transfer surface inside of heat pipe. The annular heat pipe is manufactured using two pipes having different diameters, which can be possible to heating and cooling on the inner surface. It is one of the special methods for enhancing the heat transfer. Faghri and Thomas [8] described the concentric annular heat pipe’s design, testing, and theoretical prediction of the capillary limit. The main objective was to compare the performance of the concentric annular heat pipe with that of a conventional heat pipe. The difference between the annular vapor space as well as the heat transfer area resulting from the additional surface area is seen in the two designs. The capillary limit of the annular heat pipe dramatically increased, resulting in a performance advantage. Faghri [9] indicated that the results are due to the difference in the cross-sectional shapes, with one circular and the other annular. Annular heat pipes exhibit a decreasing heat-transfer performance because of the vapor path. Kim et al. [10] used the annular heat pipe having cylindrical roll wire mesh wick for fixed wick structure at the inside surface. The thermal resistance of annular heat pipe
has lower than copper black conduction. Boo and Park [11] suggested similar geometry and experimental investigation of the annular heat pipe with various fill charge ratios was conducted. Optimized designs of annular heat pipes were suggested according to the change of the fill charge ratios. During the star-up transient, fast response was observed between heat source and annular heat pipes comparison with a copper black cooling device. For that reason, the applications for fast response heating devices were suggested. A concentric heat pipe having a medium-scale diameter (D = 10–20 mm) has a generally large vapor space compared with its wick space, so the vapor flow of the working fluid has a large enough cross-sectional area to satisfy the limits of the heat pipe. Reay and Kew [16] define the capillary limit by using the pressure difference in the heat pipe. When incompressible flow and homogeneous wicks can be assumed in a concentric heat pipe, the vapor pressure is neglected. Recent applications of the heat pipe have focused on electrical devices because heat pipes exhibit excellent performance in cooling a device per unit volume. Concentric heat pipes have excess vapor space; therefore, it is possible to decrease the volume of the heat pipe without causing degradation. The researches did not consider the vapor flow path effect because of great margin until the flow degradation [12–15]. Recent enhancement studies for conventional heat pipe are focused on the wick structures
Table 1 Review of some heat pipe experimental studies. Researchers
Working fluids
Temperature range (°C)
Wick
Geometry
Types
Faghri [8]
Water
100
Copper groove wick
Annular heat pipe
Kim et al. [10]
Water
40–160
Mesh wick (80)
Boo et al. [11] Hung and Q’bert Seng [12] Asirvatham et al. [13]
Water Water
40–180 20–100
Mesh wick (80) Groove wick
300:473:200 Diameter: 30 (mm) 60:80:60 Diameter: 25.4 (mm) N/A Diameter: 25.4 (mm) 127:246:127 Diameter: N/A
25–160 –
Copper mesh wick (100) Groove wick
50:50:80 Diameter: 10 (mm)
Yang et al. [14]
Silver nanoparticles dispersed in DI water Water
Zhang et al. [15]
d-Al2O3-R141b nanofluids
24–40
Groove wick
140:60:140 (array) 30 * 2 (mm)
N/A
Annular heat pipe Annular heat pipe Conventional heat pipe Conventional heat pipe Conventional heat pipe Flat heat pipe
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each heat pipe is discussed. To study the flow path of a heat pipe, an annular-flow-path heat pipe is used; it is shown in Fig. 1. The pipe consists of a concentric pipe and cylindrical obstacle attached by end caps, which create an annular vapor space in the heat pipe. Capillary mesh wicks are placed on the inner surface of the pipe rather than inside the structure. Annular-flow-path heat pipes have a cylindrical polymer structure of acrylonitrile butadiene styrene (ABS) owing to its low thermal conductivity.
2. Experimental setup and procedure 2.1. Experimental setup
Fig. 1. A design of annular flow path heat pipe.
and surface coating mechanism using nano-particles. Therefore, a study of the vapor path of a heat pipe is a good method for enhancing the performance of the heat pipe. The present study investigates the effects of the cross-sectional area of the vapor path and the performance of concentric heat pipes with cylindrical obstacles. A comparison is made between the heat pipes with various cross-sectional areas of their vapor paths. In addition, a theoretical and experimental analysis of the heat-transfer performance of heat pipes and the capillary limit of
The experimental heat pipe is composed of two layers of stainless steel screen wire mesh as the wick structure, with distilled water as the working fluid. The thermal performance of the heat pipe was tested at a vertical orientation at various heat loads. The stainless-steel 316L test section had an outer diameter of 12.7 mm, an inner diameter of 11.7 mm, and a length of 650 mm. The test section had an evaporator region of 200 mm that was heated by direct-current copper electrodes. The adiabatic region of 150 mm was insulated with glass wool. The condenser section was 300 mm in length. Its role was to cool the working fluid and maintain a constant temperature. Twelve thermocouples were installed to measure the wall temperature along the test section. Four thermocouples were attached to the outer wall of the evaporator region. Four thermocouples measured the outer temperature of the condenser region. Thermocouples were attached to the adiabatic region as well. The uncertainty in the measurement of temperature is 0:6 °C. Thermocouple locations and a schematic view of the experimental system are shown in Fig. 2. Before filling the system with the working fluid, all noncondensable gas was removed using a vacuum pump. The fluid charge was determined based on the void volume in the wick
Fig. 2. Schematic diagram for the experimental apparatus.
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Fig. 4. Contact angles of materials.
Table 3 Properties of ABS pellet and stainless steel 304.
3
Fig. 3. Test sections (a) conventional heat pipe, (b) annular flow path heat pipe (D = 6 mm), (c) annular flow path heat pipe (D = 8 mm).
Table 2 Initial conditions. Initial condition
Test
Filling ratio Wick size Porosity Vacuum
100% in wick 100 mesh 0.62 6.0–8.0 kPa
structure. Distilled water was added to the evaporator section at a 100% fill ratio. A pressure gage was placed at the top of the condenser section to measure the initial saturation pressure as well as the operating pressure of the steam in the heat pipe. The uncertainty of the water level owing to instrumental error was less than ±5%. The inlet temperature of the coolant was maintained at a constant level with the use of a chiller. The heat load ranged from 20 W to the limit.
2.2. Test section geometry The test section consisted of a tube made of stainless-steel 316L with a stainless-steel 304, 100 mesh wick insert. The length, outer
Density, g/cm Thermal conductivity, W/mK Specific heat, J/kg K Solubility in water Melting point, °C Contact angle, °C
ABS pellet
Screen mesh (SS304)
1.06–1.25 0.6 1100–1486 Insoluble 105 59.1
7.85–8.06 14–17 490–530 Insoluble 1400–1450 78.6
diameter, and thickness of the heat pipe were 650 mm, 12.7 mm, and 1.0 mm, respectively. Fig. 3 shows the geometry of the heat pipe test section, and Fig. 3(a) shows a conventional concentric heat pipe (CHP) with evaporation and condenser sections. Both the annular-flow-path heat pipe in Fig. 3(b) (D = 6 mm) and the annular-flow-path heat pipe in Fig. 3(c) (D = 8 mm) were cylindrical structures made of ABS using fused-deposition modeling. The length of the cylindrical structure in the heat pipes are 650 mm. The conditions of the heat pipes are summarized in Table 2. 2.3. Material ABS is a thermoplastic polymer that results in a plastic with a lustrous and impervious surface. ABS is easy to fabricate because of its low melting point (approximately 105 °C). Fig. 4 shows the water-wetting surface with the contact angle. The ABS pellet had a contact angle of approximately 59.1°. The main reasons for using the ABS material were its low thermal conductivity and simple manufacture. The occupying region of the ABS is a vapor flow region, which means that ABS material has no effect on the boiling heat transfer. The contact angle of screen wire mesh wick was approximately 78.6°. The material properties of the ABS materials and screen wire mesh are summarized in Table 3.
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Fig. 5. Temperature response to heat load of (a) conventional heat pipe, (b) annular flow path heat pipe (D = 6 mm), (c) annular flow path heat pipe (D = 8 mm).
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3. Results and discussion 3.1. Temperature distributions The temperature response to the heat load of the three heat pipes is shown in Fig. 5. From Fig. 5(a), the heat input power at the evaporator section was increased incrementally from 20 to the limit in steps of 20 W. The temperatures of the evaporator and the condenser remained unchanged at each heat load. When a heat power of 260 W was applied, temperature oscillations began in the evaporator region, and temperature peaks resulting from the capillary limit were observed. Adiabatic temperatures increased
Fig. 6. Temperature distribution of tested heat pipes according to position (a) conventional heat pipe, (b) annular flow path heat pipe (D = 6 mm), (c) annular flow path heat pipe (D = 8 mm).
Fig. 7. (a) Capillary rise in the evaporator section of the screen mesh wick heat pipes (b) illustration of evaporator section with capillary phenomenon: (left) conventional heat pipe (right) annular vapor path heat pipe.
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slightly because of internal pressure changes in the heat pipe. The initial pressure of the heat pipes was 6 kPa, 7 kPa, and 8 kPa, and the heat pipes had an operating pressure that ranged from 6.0 kPa to 12.5 kPa. The vapor temperature range during the operation was from 35 °C to 52 °C. The temperature difference between the evaporator sections was approximately 1.5 °C because of heat conduction through the stainless steel structure. The results in Fig. 5(b) and (c) were similar to conventional heat pipe behavior except for the capillary limit. Annular-flow-path heat pipes had low values of capillary limits owing to small vapor space. The temperature distribution of the three heat pipes at a 100% filling ratio is shown in Fig. 6. When the heat input of the copper electrode heater was increased, the temperature difference between the evaporator and the condenser section wall also increased. For all power ranges, the annular-flow-path heat pipe (D = 8 mm) had the poorest performance. Vaporization in the evaporator section was not enough to transport the working fluid from the evaporator to the condenser at the tested temperature range. Additionally, the capillary pumping power of the wick structure is not sufficient to transfer the working fluid from the evaporator to the condenser. The vapor space of the annular-flow-path heat pipe was smaller than that of the conventional heat pipe. According to the relationship between pressure drop and driving force,
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the cross-sectional area of the vapor path directly affected the capillary pumping power. The vapor pressure drop made the capillary force of the heat pipe decrease. 3.2. Visualized capillary and condensation phenomenon Fig. 7 shows the visualization images for the 100 mesh screen wick structure with capillary rise at the evaporator section. This can be explained that the surface tension of the working fluid in the screen mesh wick provided a capillary pressure. The effects of decrease of vapor path are (1) increasing the interfacial friction at the adiabatic region and (2) increasing the pressure difference between evaporation section and condensation section. The pressure drop across a curved liquid interface is defined with surface tension and radius.
DP ¼
2r R
ð1Þ
The radius of the curved liquid can reflect the effective radius of the mesh wick and contact angle. Therefore, it is possible to define the pressure at the evaporator and condenser.
DP e ¼
2r cos he r
ð2Þ
Fig. 8. Sequential images of the condenser section with liquid droplet in the screen mesh wick heat pipe (b) illustration of condensation phenomenon with droplet growth.
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DP c ¼
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2r cos hc r
ð3Þ
The capillary force from the pressure difference leads to the liquid flow between condenser and evaporator sections. Therefore, total capillary driving pressure with gravitational force is,
DPc ¼ DP e DPc þ DPg
ð4Þ
The decrease of vapor path means that total volume of the annular vapor path heat pipe is decreased. Therefore, the expansion from the vaporization of working fluid (water) has the relatively large effect of pressure in comparison with the conventional heat pipe. The driving force of the heat pipe is the pressure difference between the heat pipe ends and annular vapor path heat pipe has high pressure at the evaporator section, which make a driving force of the heat pipe decrease. Therefore, capillary pressure of annular flow path heat pipe can be defined as,
DPc0 ¼ DPe0 DPc þ DP g DP e 0 P DP e
ð5Þ ð6Þ
to the heat flux. In Fig. 10, the overall heat transfer coefficient of the experimental heat pipes is plotted as function of heat flux with various operation temperatures. The heat transfer coefficient values from 80 W/m2 °C to 860 W/m2 °C for the conventional heat pipe, and the values of heat transfer coefficient of annular flow path heat pipes are reduced by 12–21% with various heat fluxes. Heat flux inputs range from 2.0 kW/m2 to 32 kW/m2. The thermal resistance and the heat transfer coefficient can be determined by
Ro ð C=WÞ ¼
T e T c Qe
q00 ho ðW=m2 CÞ ¼ e Te Tc
ð7Þ
ð8Þ
The maximum error of the input power is approximately 0.5%. The uncertainties in overall resistance and the heat transfer coefficient are calculated by
DRo ¼ Ro
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DQ in 2 DðDTÞ 2 þ Q in DT
Dho ¼ ho
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi Dq00in 2 DðDTÞ 2 þ q00in DT
ð9Þ
Fig. 8 shows the sequential images of the condensation phenomena at the condenser section. Several drops form on the open site of the screen wire (Fig. 8 and the drops growth are observed according to the time sequence (Fig. 8a(B–E)). Liquid drops formed by condensation are moved to the evaporator section at bottom site of heat pipe by a gravity assisted capillary force.
The estimated maximum uncertainties in thermal resistance and the heat transfer coefficient are 6.4% and 5.1%, respectively.
3.3. Thermal resistance and heat transfer coefficients
3.4. Capillary limit
Fig. 9 shows the overall thermal resistance that is plotted as function of the heat input with various operation temperatures. The thermal resistance of the heat pipes shows a trend similar to the experimental results presented by Asirvatham et al. [13] and Shukla et al. [18]. The heat pipes show a decreasing thermal resistance with an increase in the heat input. The reduction in thermal resistance of screen-mesh-wick heat pipes is a result of the activation of a larger number of nucleation sites in the evaporator surface, which increases the regime of nucleate boiling according
In this section, a simple analysis to predict the annular-flowpath heat pipe limit will be presented. The analysis shows the effect of the cross-sectional area of vapor and the correlating modification to the suggested geometry of the heat pipe. The operation limits of the heat pipe are developed using a one-dimensional approach. Using a schematic of a concentric annular-flow-path heat pipe, a heat load is applied to the bottom of the heat pipe, and a heat sink is applied to the top of the heat pipe. Vaporization occurs in the evaporator section because of the heat load, and vapor is transferred to the condenser section. The vapor is condensed to fluid and is absorbed by the wick structure, which is highly porous media. The condensed working fluid returns to the evaporator section by the capillary wicking of the wick structure. The driving force for the working fluid is affected by capillary and gravitational forces. For correct operation of the heat pipe, we calculate the following:
DPc;max P DPl þ DPv þ DPg
ð10Þ
ð11Þ
If the capillary pressure is smaller than the overall pressure drop in the heat pipe, the wick will drop out in the evaporation region and the heat pipe will not work. The capillary limit is defined as the maximum allowable heat flux when the heat pipe does not operate. The pressure drop, DP c;max , is the capillary limit from the wick structure. A gravity-assisted heat pipe has a hydrostatic head of liquid that can be positive or negative, depending on the relative positions of the condensation section and evaporation section. The bottomheated concentric heat pipe has a negative value because of the angle / between the heat pipe and the horizontal. The pressure difference from the hydrostatic head is determined by
DPg ¼ ql gl sin / Fig. 9. Overall heat resistance of heat pipes according to the heat load at saturation temperature of 40 °C.
ð12Þ
The void fraction of the mesh wick is used as the fluid flow path of the working fluid. The total-flow cross-sectional area Af is defined by
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Af ¼ pðr2w r 2v Þe
ð13Þ
If the working fluid in the heat pipe is of a constant viscosity and incompressible conditions at a given working temperature, the mass flow rate of the liquid flow is described by the Hagen–Poiseuille equation [16].
_ l ¼ qpr 2 v ¼ m
pðr2w r2v Þer2pore ql DPl 8l l leff
ð14Þ
Heat transport occurs from the heated liquid to the vapor phase during the operation of the heat pipe. Then, heat and mass flow are defined as a relationship between the latent heat of vaporization and the mass flow rate.
_ Q_ ¼ mL
ð15Þ
Rearranging Eq. (5),
DP l ¼
_ eff S1 lQl pðr2w r2v Þer2e ql L
ð16Þ
The vapor pressure difference is defined as the sum of heat pipe sections.
DPv ¼ DPv ;e þ DP v ;a þ DPv ;c
ð17Þ
_ eff _ _ a lQl plv ml m þS þS pðr2w r2v Þer2pore ql L 2 qv A2v 3 qv A2v þ ql gl sin /
DPc;max ¼ S1
ð20Þ
The capillary limit determines the maximum allowable heat flux from the pressure drop in the heat pipe. Using Darcy’s law and rearranging the equations, we obtain
DPc;max P S1
_ _ a ll leff m_ plv ml m þ S2 þ S3 þ ql gl sin / ql KAw qv A2v qv A2v
ð21Þ
0 1 h 1 fg A Q_ ¼ mmax hfg ¼ ð2rl cos h ql glre sin /Þ@ l l S2 þS3 ll la l eff re q KAw þ S q A2 l
1
ð22Þ
v v
The experimentally determined capillary limits of heat pipes were compared with the analytical predictions. Analytical operation limits were determined for adiabatic temperatures from the temperature distribution. The operation limits of the water-based heat pipe, which are shown in Fig. 11, were highly related to the viscous limit, capillary limit, and boiling limit. Major differences between the heat pipes are the crosssectional area of the vapor space and that the pressure drop in
If the pressure drop of the vapor is incompressible and has a laminar flow, the vapor pressure drop of the heat pipe can be modeled by an equation presented by Cotter and Busse [17]. This equation considered the pressure drop in the vapor phase of a long concentric heat pipe; therefore, it is necessary to modify the correlation. The cross-section of the annular flow path of a heat pipe is defined by
Av ¼ p r 2v r2c
ð18Þ
This suggests a modified correlation for the annular-flow-path heat pipe that is shown in Eq. (11).
D P v ¼ S2
_ m
qv A2v
þ S3
_ a plv ml qv A2v
ð19Þ
The capillary limit for the annular-flow-path heat pipe is given by the following equation:
Fig. 11. Operation limit of conventional heat pipe.
Fig. 10. Overall heat transfer coefficient of heat pipes according to the heat flux at saturation temperature 40 °C.
Fig. 12. Comparison of theoretical capillary limit and experimental results of heat pipes.
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Fig. 13. The design guide for effectiveness of vapor space of heat pipe having screen mesh wick.
the vapor was dominant for the capillary limit. A comparison of the theoretical capillary limit and experimental results is shown in Fig. 12. The theoretical capillary limit of an annular-flow-path heat pipe was slightly lower than that of a conventional heat pipe, and both predictions underestimated the experimental results. The capillary limits were experimentally determined with saturation pressure 7.5 kPa, 10.0 kPa and 12.5 kPa. The maximum reductions of 32.5% and 43.7% were determined in the capillary limit of the heat pipes with cylindrical structure D = 6 mm and D = 8 mm, respectively, while the cross-sectional area of the vapor path decreases 48.3% and 76.8% at a saturation temperature of 40 °C. The design guide for effectiveness of vapor space of heat pipe having screen mesh wick is shown in Fig. 13. It is observed that the changes of the capillary limit and the overall heat transfer coefficient come from the reduction of the vapor space. When the crosssectional area of the vapor path is reduced to 48.3%, the capillary limit of the heat pipe is decreased by 22.9%. But the overall heat transfer coefficient of the heat pipe is slightly decreased by 3–7%. When the cross-sectional area of the vapor path is reduced to 76.8%, the capillary limit and the heat transfer coefficient of the heat pipe are decreased by 43.7% and 11.5%, respectively. Therefore the reduction of the overall heat transfer coefficient of the heat pipe is no great effect according to the cross-sectional area of the vapor path. The experimental results suggest the direction of the optimization of the heat pipe in terms of space management for compact devices. Or, if there is enough margin in capillary limit, the optimized compact vapor path without losing heat transfer performance too much can be acquired or excess space can be used for special applications such as neutron absorber in nuclear control rods and structural supports in the electronic cooling for compactness.
provides the best performance compared with the annular-flowpath heat pipes. The annular-flow-path heat pipes exhibited heat transfer reduction. The reduced rate of heat transfer coefficient was quite small in comparison with the conventional heat pipe that means the heat pipes had a good heat transfer capability under the capillary limit. The heat pipes were analyzed, maximum heat transfer coefficients, and capillary limits were determined with saturation pressure 7.5 kPa, 10.0 kPa and 12.5 kPa. The reductions of 21.0% and 43.7% were determined in the maximum heat transfer coefficient and capillary limit, respectively, while the cross-sectional area of vapor path decreases 76.8% at a saturation temperature of 40 °C. The annular flow path made the vapor space and the pressure difference decrease. The heat transfer coefficient of the conventional heat pipe was relatively high compared with that of the annular-flow-path heat pipe for an equivalent heat flux. Major differences between the heat pipes are the cross-sectional area of the vapor space and that the pressure drop in the vapor was dominant for capillary limit. Therefore, the cross-sectional area of the vapor space had a significant effect on the heat pipe dry-out phenomenon. The reduction of the overall heat transfer coefficient of the heat pipe is no great effect according to the cross-sectional area of the vapor path. The experimental results suggest the direction of the optimization of the heat pipe in terms of space management for compact devices. Or, if there is enough margin in capillary limit, the optimized compact vapor path without losing heat transfer performance too much can be acquired or excess space can be used for special applications such as neutron absorber in nuclear control rods and structural supports in the electronic cooling for compactness. Acknowledgements
4. Conclusion An experimental study of three 12.7-mm O.D. heat pipes was performed. The working fluid was distilled water, the wick and container material was stainless steel, and the length of the heat pipe was 650 mm. Thermal analyses of the annular flow path through the heat pipes were discussed. The objective was to investigate the effects of the inner structure of the heat pipe on the heat-transfer performance with a cross-sectional area of vapor path. An ABS pellet was used as the cylindrical structure. The thermal performance of each heat pipe was measured experimentally and the results indicated that the conventional heat pipe
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[11] J.H. Boo, S.Y. Park, An experimental study on the thermal performance of a concentric annular heat pipe, J. Mech. Sci. Technol. 19 (4) (2005) 1036–1043. [12] Y.M. Hung, Q. Seng, Effects of geometric design on thermal performance of star-groove micro-heat pipes, Int. J. Heat Mass Transfer 54 (2011) 1198–1209. [13] L.G. Asirvatham, R. Nimmagadda, S. Wongwises, Heat transfer performance of screen mesh wick heat pipes using silver–water nanofluid, Int. J. Heat Mass Transfer 60 (2013) 201–209. [14] X. Yang, Y.Y. Yan, D. Mullen, Recent developments of lightweight, high performance heat pipes, Appl. Therm. Eng. 33 (2012) 1–14. [15] J. Zhang, Y.H. Diao, Y.H. Zhao, X. Tang, W.J. Yu, S. Wang, Experimental study on the heat recovery characteristics of a new-type flat micro-heat pipe array heat exchanger using nanofluid, Energy Convers. Manage. 75 (2013) 609–616. [16] D.A. Reay, P.A. Kew, Heat Pipes, Elsevier, New York, 2006. [17] C.A. Busse, Pressure drop in the vapour phase of long heat pipes, in: Thermionic Conversion Specialists Conference, Palo Alto, Calif, October, 1967, pp. 391–398. [18] K. Shukla, A. Solomon, B. Pillai, B. Singh, S. Kumar, Thermal performance of heat pipe with suspended nano-particles, Heat Mass Transfer 48 (2012) 1913– 1920.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Performance of annular flow path heat pipe with a polymer insert controlling compactness for energy applications In Guk Kim, Kyung Mo Kim, Yeong Shin Jeong, In Cheol Bang ⇑ School of Mechanical and Nuclear Engineering, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulju-gun, Ulsan 689-798, Republic of Korea
a r t i c l e
i n f o
Article history: Received 19 July 2015 Received in revised form 13 September 2015 Accepted 15 September 2015
Keywords: Heat pipe Capillary limit Annular vapor space Compactness
a b s t r a c t This study experimentally investigates the effect of the cross-sectional area of vapor path on the heat transfer performance of a water-filled heat pipe with a polymer insert for optimizing its design. The thermal resistance and the heat transfer coefficient of the heat pipe with a screen mesh wick were measured at a saturation pressure ranging from 6.0 kPa to 12.5 kPa. It is observed that the changes of the capillary limit and the overall heat transfer coefficient come from the reduction of the vapor space. When the cross-sectional area of the vapor path is reduced to 48.3%, the capillary limit of the heat pipe is decreased by 22.9%. But the overall heat transfer coefficient of the heat pipe is slightly decreased by 3–7%. When the cross-sectional area of the vapor path is reduced to 76.8%, the capillary limit and the heat transfer coefficient of the heat pipe are decreased by 40.7% and 21.0%, respectively. Therefore, the reduction of the overall heat transfer coefficient of the heat pipe has no great effects according to the cross-sectional area of the vapor path. The experimental results suggest the direction of the optimization of the heat pipe in terms of space management for compact devices. Or, if there is enough margin in capillary limit, the optimized compact vapor path without losing heat transfer performance too much can be acquired or excess space can be used for special applications such as neutron absorber in nuclear control rods and structural supports in the electronic cooling for compactness. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction After the invention of the heat pipe by Grover et al. [1] 50 years ago, much study has been done and many applications have been created in various fields including electric cooling devices, decay heat removal systems for nuclear power plants [2–4], and energy conversion systems. A central processing unit (CPU) has a high heat flux of 67 kW/m2 [5]. It is difficult to use a heat sink that is attached to the CPU surface. A heat pipe can be used to transfer the energy away from the CPU surface to a heat sink, and it is possible to supply efficient cooling. Increases in heat flux and the power of electronic devices in a recent trend require highly integrated cooling device. To improve the capability for fully cooling the system heat, research on conventional heat pipes is focusing on advancing the working fluids, wick structure, and geometry of the heat pipes. Because of increasing demand for better cooling performance, the need for more effective cooling systems has led to various studies of heat pipes using nanoparticles and with modifications in the wick structures. Recent studies of heat pipes showed that ⇑ Corresponding author. Tel.: +82 52 217 2915; fax: +82 52 217 3008. E-mail address: [email protected] (I.C. Bang). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.09.037 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved.
the theoretical and experimental heat transport capacity of a concentric heat pipe and its capillary limits are strongly related to the properties and geometries of the wick structures and on the surface coating phenomenon of the evaporator wick. Kole and Dey [6] studied the synthesis, thermal conductivity, and thermal performance of screen-mesh-wick heat pipes using water-based copper nanofluids which was wick coating phenomenon using nanoparticle. It was found that the thermal performance of the nanofluid-based heat pipe was predominately affected by a layer of Cu nanoparticles at the evaporator section. Schampheleire et al. [7] investigated the gravity-assisted-orientation heat pipe using three different wicks: a screen-mesh wick, a sintered-powder wick, and outperforms the fiber wick. The metal-fiber wick showed the greatest potential as a wick material for high-performance heat pipes. Table 1 summarizes some experimental investigations of heat pipes of various geometries. A heat pipe is a high-heat-capacity, fully passive heat-transfer device that uses the evaporation, condensation, capillary wick structure, and working fluid in the pipe. In general, the vapor flow from the evaporation section to the condensation section is caused by a difference in vapor pressure. At the same time, the liquid flow from the condensation section to the evaporation section is produced by net forces such as capillary force and gravitational force.
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Nomenclature A g h l L _ m DP Q Q_ q00 r R T T
q e l
area [m2] acceleration of gravity [m/s2] heat transfer coefficient [W/m2 K] length [m] latent heat [J/kg] mass flow rate [kg/s] pressure difference [Pa] heat input, power [W] heat flow rate [J/s] heat flux [kW/m2] radius [m] thermal resistance [°C/W] temperature [°C] average temperature [°C] density [kg/m3] fractional void of the wick [–] dynamic viscosity [Pas]
Subscripts a adiabatic c condenser c, max maximum capillary e evaporator eff effective g gravity l liquid o overall pore effective pore v vapor v, e vapor of evaporator v, a vapor of adiabatic section v, c vapor of condenser w wick
Working fluids and wick structure modification are favorite topics for enhancing the capabilities of heat pipes, but the vapor path in concentric heat pipes is not considered owing to their low contribution. For these reasons, research on the effects of the cross-sectional area of the vapor path of heat pipe is neglected. Current researches for annular heat pipes are focused on the enhancement of the heat transfer coefficient using the additional heat transfer surface inside of heat pipe. The annular heat pipe is manufactured using two pipes having different diameters, which can be possible to heating and cooling on the inner surface. It is one of the special methods for enhancing the heat transfer. Faghri and Thomas [8] described the concentric annular heat pipe’s design, testing, and theoretical prediction of the capillary limit. The main objective was to compare the performance of the concentric annular heat pipe with that of a conventional heat pipe. The difference between the annular vapor space as well as the heat transfer area resulting from the additional surface area is seen in the two designs. The capillary limit of the annular heat pipe dramatically increased, resulting in a performance advantage. Faghri [9] indicated that the results are due to the difference in the cross-sectional shapes, with one circular and the other annular. Annular heat pipes exhibit a decreasing heat-transfer performance because of the vapor path. Kim et al. [10] used the annular heat pipe having cylindrical roll wire mesh wick for fixed wick structure at the inside surface. The thermal resistance of annular heat pipe
has lower than copper black conduction. Boo and Park [11] suggested similar geometry and experimental investigation of the annular heat pipe with various fill charge ratios was conducted. Optimized designs of annular heat pipes were suggested according to the change of the fill charge ratios. During the star-up transient, fast response was observed between heat source and annular heat pipes comparison with a copper black cooling device. For that reason, the applications for fast response heating devices were suggested. A concentric heat pipe having a medium-scale diameter (D = 10–20 mm) has a generally large vapor space compared with its wick space, so the vapor flow of the working fluid has a large enough cross-sectional area to satisfy the limits of the heat pipe. Reay and Kew [16] define the capillary limit by using the pressure difference in the heat pipe. When incompressible flow and homogeneous wicks can be assumed in a concentric heat pipe, the vapor pressure is neglected. Recent applications of the heat pipe have focused on electrical devices because heat pipes exhibit excellent performance in cooling a device per unit volume. Concentric heat pipes have excess vapor space; therefore, it is possible to decrease the volume of the heat pipe without causing degradation. The researches did not consider the vapor flow path effect because of great margin until the flow degradation [12–15]. Recent enhancement studies for conventional heat pipe are focused on the wick structures
Table 1 Review of some heat pipe experimental studies. Researchers
Working fluids
Temperature range (°C)
Wick
Geometry
Types
Faghri [8]
Water
100
Copper groove wick
Annular heat pipe
Kim et al. [10]
Water
40–160
Mesh wick (80)
Boo et al. [11] Hung and Q’bert Seng [12] Asirvatham et al. [13]
Water Water
40–180 20–100
Mesh wick (80) Groove wick
300:473:200 Diameter: 30 (mm) 60:80:60 Diameter: 25.4 (mm) N/A Diameter: 25.4 (mm) 127:246:127 Diameter: N/A
25–160 –
Copper mesh wick (100) Groove wick
50:50:80 Diameter: 10 (mm)
Yang et al. [14]
Silver nanoparticles dispersed in DI water Water
Zhang et al. [15]
d-Al2O3-R141b nanofluids
24–40
Groove wick
140:60:140 (array) 30 * 2 (mm)
N/A
Annular heat pipe Annular heat pipe Conventional heat pipe Conventional heat pipe Conventional heat pipe Flat heat pipe
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each heat pipe is discussed. To study the flow path of a heat pipe, an annular-flow-path heat pipe is used; it is shown in Fig. 1. The pipe consists of a concentric pipe and cylindrical obstacle attached by end caps, which create an annular vapor space in the heat pipe. Capillary mesh wicks are placed on the inner surface of the pipe rather than inside the structure. Annular-flow-path heat pipes have a cylindrical polymer structure of acrylonitrile butadiene styrene (ABS) owing to its low thermal conductivity.
2. Experimental setup and procedure 2.1. Experimental setup
Fig. 1. A design of annular flow path heat pipe.
and surface coating mechanism using nano-particles. Therefore, a study of the vapor path of a heat pipe is a good method for enhancing the performance of the heat pipe. The present study investigates the effects of the cross-sectional area of the vapor path and the performance of concentric heat pipes with cylindrical obstacles. A comparison is made between the heat pipes with various cross-sectional areas of their vapor paths. In addition, a theoretical and experimental analysis of the heat-transfer performance of heat pipes and the capillary limit of
The experimental heat pipe is composed of two layers of stainless steel screen wire mesh as the wick structure, with distilled water as the working fluid. The thermal performance of the heat pipe was tested at a vertical orientation at various heat loads. The stainless-steel 316L test section had an outer diameter of 12.7 mm, an inner diameter of 11.7 mm, and a length of 650 mm. The test section had an evaporator region of 200 mm that was heated by direct-current copper electrodes. The adiabatic region of 150 mm was insulated with glass wool. The condenser section was 300 mm in length. Its role was to cool the working fluid and maintain a constant temperature. Twelve thermocouples were installed to measure the wall temperature along the test section. Four thermocouples were attached to the outer wall of the evaporator region. Four thermocouples measured the outer temperature of the condenser region. Thermocouples were attached to the adiabatic region as well. The uncertainty in the measurement of temperature is 0:6 °C. Thermocouple locations and a schematic view of the experimental system are shown in Fig. 2. Before filling the system with the working fluid, all noncondensable gas was removed using a vacuum pump. The fluid charge was determined based on the void volume in the wick
Fig. 2. Schematic diagram for the experimental apparatus.
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Fig. 4. Contact angles of materials.
Table 3 Properties of ABS pellet and stainless steel 304.
3
Fig. 3. Test sections (a) conventional heat pipe, (b) annular flow path heat pipe (D = 6 mm), (c) annular flow path heat pipe (D = 8 mm).
Table 2 Initial conditions. Initial condition
Test
Filling ratio Wick size Porosity Vacuum
100% in wick 100 mesh 0.62 6.0–8.0 kPa
structure. Distilled water was added to the evaporator section at a 100% fill ratio. A pressure gage was placed at the top of the condenser section to measure the initial saturation pressure as well as the operating pressure of the steam in the heat pipe. The uncertainty of the water level owing to instrumental error was less than ±5%. The inlet temperature of the coolant was maintained at a constant level with the use of a chiller. The heat load ranged from 20 W to the limit.
2.2. Test section geometry The test section consisted of a tube made of stainless-steel 316L with a stainless-steel 304, 100 mesh wick insert. The length, outer
Density, g/cm Thermal conductivity, W/mK Specific heat, J/kg K Solubility in water Melting point, °C Contact angle, °C
ABS pellet
Screen mesh (SS304)
1.06–1.25 0.6 1100–1486 Insoluble 105 59.1
7.85–8.06 14–17 490–530 Insoluble 1400–1450 78.6
diameter, and thickness of the heat pipe were 650 mm, 12.7 mm, and 1.0 mm, respectively. Fig. 3 shows the geometry of the heat pipe test section, and Fig. 3(a) shows a conventional concentric heat pipe (CHP) with evaporation and condenser sections. Both the annular-flow-path heat pipe in Fig. 3(b) (D = 6 mm) and the annular-flow-path heat pipe in Fig. 3(c) (D = 8 mm) were cylindrical structures made of ABS using fused-deposition modeling. The length of the cylindrical structure in the heat pipes are 650 mm. The conditions of the heat pipes are summarized in Table 2. 2.3. Material ABS is a thermoplastic polymer that results in a plastic with a lustrous and impervious surface. ABS is easy to fabricate because of its low melting point (approximately 105 °C). Fig. 4 shows the water-wetting surface with the contact angle. The ABS pellet had a contact angle of approximately 59.1°. The main reasons for using the ABS material were its low thermal conductivity and simple manufacture. The occupying region of the ABS is a vapor flow region, which means that ABS material has no effect on the boiling heat transfer. The contact angle of screen wire mesh wick was approximately 78.6°. The material properties of the ABS materials and screen wire mesh are summarized in Table 3.
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Fig. 5. Temperature response to heat load of (a) conventional heat pipe, (b) annular flow path heat pipe (D = 6 mm), (c) annular flow path heat pipe (D = 8 mm).
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3. Results and discussion 3.1. Temperature distributions The temperature response to the heat load of the three heat pipes is shown in Fig. 5. From Fig. 5(a), the heat input power at the evaporator section was increased incrementally from 20 to the limit in steps of 20 W. The temperatures of the evaporator and the condenser remained unchanged at each heat load. When a heat power of 260 W was applied, temperature oscillations began in the evaporator region, and temperature peaks resulting from the capillary limit were observed. Adiabatic temperatures increased
Fig. 6. Temperature distribution of tested heat pipes according to position (a) conventional heat pipe, (b) annular flow path heat pipe (D = 6 mm), (c) annular flow path heat pipe (D = 8 mm).
Fig. 7. (a) Capillary rise in the evaporator section of the screen mesh wick heat pipes (b) illustration of evaporator section with capillary phenomenon: (left) conventional heat pipe (right) annular vapor path heat pipe.
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slightly because of internal pressure changes in the heat pipe. The initial pressure of the heat pipes was 6 kPa, 7 kPa, and 8 kPa, and the heat pipes had an operating pressure that ranged from 6.0 kPa to 12.5 kPa. The vapor temperature range during the operation was from 35 °C to 52 °C. The temperature difference between the evaporator sections was approximately 1.5 °C because of heat conduction through the stainless steel structure. The results in Fig. 5(b) and (c) were similar to conventional heat pipe behavior except for the capillary limit. Annular-flow-path heat pipes had low values of capillary limits owing to small vapor space. The temperature distribution of the three heat pipes at a 100% filling ratio is shown in Fig. 6. When the heat input of the copper electrode heater was increased, the temperature difference between the evaporator and the condenser section wall also increased. For all power ranges, the annular-flow-path heat pipe (D = 8 mm) had the poorest performance. Vaporization in the evaporator section was not enough to transport the working fluid from the evaporator to the condenser at the tested temperature range. Additionally, the capillary pumping power of the wick structure is not sufficient to transfer the working fluid from the evaporator to the condenser. The vapor space of the annular-flow-path heat pipe was smaller than that of the conventional heat pipe. According to the relationship between pressure drop and driving force,
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the cross-sectional area of the vapor path directly affected the capillary pumping power. The vapor pressure drop made the capillary force of the heat pipe decrease. 3.2. Visualized capillary and condensation phenomenon Fig. 7 shows the visualization images for the 100 mesh screen wick structure with capillary rise at the evaporator section. This can be explained that the surface tension of the working fluid in the screen mesh wick provided a capillary pressure. The effects of decrease of vapor path are (1) increasing the interfacial friction at the adiabatic region and (2) increasing the pressure difference between evaporation section and condensation section. The pressure drop across a curved liquid interface is defined with surface tension and radius.
DP ¼
2r R
ð1Þ
The radius of the curved liquid can reflect the effective radius of the mesh wick and contact angle. Therefore, it is possible to define the pressure at the evaporator and condenser.
DP e ¼
2r cos he r
ð2Þ
Fig. 8. Sequential images of the condenser section with liquid droplet in the screen mesh wick heat pipe (b) illustration of condensation phenomenon with droplet growth.
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DP c ¼
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2r cos hc r
ð3Þ
The capillary force from the pressure difference leads to the liquid flow between condenser and evaporator sections. Therefore, total capillary driving pressure with gravitational force is,
DPc ¼ DP e DPc þ DPg
ð4Þ
The decrease of vapor path means that total volume of the annular vapor path heat pipe is decreased. Therefore, the expansion from the vaporization of working fluid (water) has the relatively large effect of pressure in comparison with the conventional heat pipe. The driving force of the heat pipe is the pressure difference between the heat pipe ends and annular vapor path heat pipe has high pressure at the evaporator section, which make a driving force of the heat pipe decrease. Therefore, capillary pressure of annular flow path heat pipe can be defined as,
DPc0 ¼ DPe0 DPc þ DP g DP e 0 P DP e
ð5Þ ð6Þ
to the heat flux. In Fig. 10, the overall heat transfer coefficient of the experimental heat pipes is plotted as function of heat flux with various operation temperatures. The heat transfer coefficient values from 80 W/m2 °C to 860 W/m2 °C for the conventional heat pipe, and the values of heat transfer coefficient of annular flow path heat pipes are reduced by 12–21% with various heat fluxes. Heat flux inputs range from 2.0 kW/m2 to 32 kW/m2. The thermal resistance and the heat transfer coefficient can be determined by
Ro ð C=WÞ ¼
T e T c Qe
q00 ho ðW=m2 CÞ ¼ e Te Tc
ð7Þ
ð8Þ
The maximum error of the input power is approximately 0.5%. The uncertainties in overall resistance and the heat transfer coefficient are calculated by
DRo ¼ Ro
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DQ in 2 DðDTÞ 2 þ Q in DT
Dho ¼ ho
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi Dq00in 2 DðDTÞ 2 þ q00in DT
ð9Þ
Fig. 8 shows the sequential images of the condensation phenomena at the condenser section. Several drops form on the open site of the screen wire (Fig. 8 and the drops growth are observed according to the time sequence (Fig. 8a(B–E)). Liquid drops formed by condensation are moved to the evaporator section at bottom site of heat pipe by a gravity assisted capillary force.
The estimated maximum uncertainties in thermal resistance and the heat transfer coefficient are 6.4% and 5.1%, respectively.
3.3. Thermal resistance and heat transfer coefficients
3.4. Capillary limit
Fig. 9 shows the overall thermal resistance that is plotted as function of the heat input with various operation temperatures. The thermal resistance of the heat pipes shows a trend similar to the experimental results presented by Asirvatham et al. [13] and Shukla et al. [18]. The heat pipes show a decreasing thermal resistance with an increase in the heat input. The reduction in thermal resistance of screen-mesh-wick heat pipes is a result of the activation of a larger number of nucleation sites in the evaporator surface, which increases the regime of nucleate boiling according
In this section, a simple analysis to predict the annular-flowpath heat pipe limit will be presented. The analysis shows the effect of the cross-sectional area of vapor and the correlating modification to the suggested geometry of the heat pipe. The operation limits of the heat pipe are developed using a one-dimensional approach. Using a schematic of a concentric annular-flow-path heat pipe, a heat load is applied to the bottom of the heat pipe, and a heat sink is applied to the top of the heat pipe. Vaporization occurs in the evaporator section because of the heat load, and vapor is transferred to the condenser section. The vapor is condensed to fluid and is absorbed by the wick structure, which is highly porous media. The condensed working fluid returns to the evaporator section by the capillary wicking of the wick structure. The driving force for the working fluid is affected by capillary and gravitational forces. For correct operation of the heat pipe, we calculate the following:
DPc;max P DPl þ DPv þ DPg
ð10Þ
ð11Þ
If the capillary pressure is smaller than the overall pressure drop in the heat pipe, the wick will drop out in the evaporation region and the heat pipe will not work. The capillary limit is defined as the maximum allowable heat flux when the heat pipe does not operate. The pressure drop, DP c;max , is the capillary limit from the wick structure. A gravity-assisted heat pipe has a hydrostatic head of liquid that can be positive or negative, depending on the relative positions of the condensation section and evaporation section. The bottomheated concentric heat pipe has a negative value because of the angle / between the heat pipe and the horizontal. The pressure difference from the hydrostatic head is determined by
DPg ¼ ql gl sin / Fig. 9. Overall heat resistance of heat pipes according to the heat load at saturation temperature of 40 °C.
ð12Þ
The void fraction of the mesh wick is used as the fluid flow path of the working fluid. The total-flow cross-sectional area Af is defined by
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Af ¼ pðr2w r 2v Þe
ð13Þ
If the working fluid in the heat pipe is of a constant viscosity and incompressible conditions at a given working temperature, the mass flow rate of the liquid flow is described by the Hagen–Poiseuille equation [16].
_ l ¼ qpr 2 v ¼ m
pðr2w r2v Þer2pore ql DPl 8l l leff
ð14Þ
Heat transport occurs from the heated liquid to the vapor phase during the operation of the heat pipe. Then, heat and mass flow are defined as a relationship between the latent heat of vaporization and the mass flow rate.
_ Q_ ¼ mL
ð15Þ
Rearranging Eq. (5),
DP l ¼
_ eff S1 lQl pðr2w r2v Þer2e ql L
ð16Þ
The vapor pressure difference is defined as the sum of heat pipe sections.
DPv ¼ DPv ;e þ DP v ;a þ DPv ;c
ð17Þ
_ eff _ _ a lQl plv ml m þS þS pðr2w r2v Þer2pore ql L 2 qv A2v 3 qv A2v þ ql gl sin /
DPc;max ¼ S1
ð20Þ
The capillary limit determines the maximum allowable heat flux from the pressure drop in the heat pipe. Using Darcy’s law and rearranging the equations, we obtain
DPc;max P S1
_ _ a ll leff m_ plv ml m þ S2 þ S3 þ ql gl sin / ql KAw qv A2v qv A2v
ð21Þ
0 1 h 1 fg A Q_ ¼ mmax hfg ¼ ð2rl cos h ql glre sin /Þ@ l l S2 þS3 ll la l eff re q KAw þ S q A2 l
1
ð22Þ
v v
The experimentally determined capillary limits of heat pipes were compared with the analytical predictions. Analytical operation limits were determined for adiabatic temperatures from the temperature distribution. The operation limits of the water-based heat pipe, which are shown in Fig. 11, were highly related to the viscous limit, capillary limit, and boiling limit. Major differences between the heat pipes are the crosssectional area of the vapor space and that the pressure drop in
If the pressure drop of the vapor is incompressible and has a laminar flow, the vapor pressure drop of the heat pipe can be modeled by an equation presented by Cotter and Busse [17]. This equation considered the pressure drop in the vapor phase of a long concentric heat pipe; therefore, it is necessary to modify the correlation. The cross-section of the annular flow path of a heat pipe is defined by
Av ¼ p r 2v r2c
ð18Þ
This suggests a modified correlation for the annular-flow-path heat pipe that is shown in Eq. (11).
D P v ¼ S2
_ m
qv A2v
þ S3
_ a plv ml qv A2v
ð19Þ
The capillary limit for the annular-flow-path heat pipe is given by the following equation:
Fig. 11. Operation limit of conventional heat pipe.
Fig. 10. Overall heat transfer coefficient of heat pipes according to the heat flux at saturation temperature 40 °C.
Fig. 12. Comparison of theoretical capillary limit and experimental results of heat pipes.
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Fig. 13. The design guide for effectiveness of vapor space of heat pipe having screen mesh wick.
the vapor was dominant for the capillary limit. A comparison of the theoretical capillary limit and experimental results is shown in Fig. 12. The theoretical capillary limit of an annular-flow-path heat pipe was slightly lower than that of a conventional heat pipe, and both predictions underestimated the experimental results. The capillary limits were experimentally determined with saturation pressure 7.5 kPa, 10.0 kPa and 12.5 kPa. The maximum reductions of 32.5% and 43.7% were determined in the capillary limit of the heat pipes with cylindrical structure D = 6 mm and D = 8 mm, respectively, while the cross-sectional area of the vapor path decreases 48.3% and 76.8% at a saturation temperature of 40 °C. The design guide for effectiveness of vapor space of heat pipe having screen mesh wick is shown in Fig. 13. It is observed that the changes of the capillary limit and the overall heat transfer coefficient come from the reduction of the vapor space. When the crosssectional area of the vapor path is reduced to 48.3%, the capillary limit of the heat pipe is decreased by 22.9%. But the overall heat transfer coefficient of the heat pipe is slightly decreased by 3–7%. When the cross-sectional area of the vapor path is reduced to 76.8%, the capillary limit and the heat transfer coefficient of the heat pipe are decreased by 43.7% and 11.5%, respectively. Therefore the reduction of the overall heat transfer coefficient of the heat pipe is no great effect according to the cross-sectional area of the vapor path. The experimental results suggest the direction of the optimization of the heat pipe in terms of space management for compact devices. Or, if there is enough margin in capillary limit, the optimized compact vapor path without losing heat transfer performance too much can be acquired or excess space can be used for special applications such as neutron absorber in nuclear control rods and structural supports in the electronic cooling for compactness.
provides the best performance compared with the annular-flowpath heat pipes. The annular-flow-path heat pipes exhibited heat transfer reduction. The reduced rate of heat transfer coefficient was quite small in comparison with the conventional heat pipe that means the heat pipes had a good heat transfer capability under the capillary limit. The heat pipes were analyzed, maximum heat transfer coefficients, and capillary limits were determined with saturation pressure 7.5 kPa, 10.0 kPa and 12.5 kPa. The reductions of 21.0% and 43.7% were determined in the maximum heat transfer coefficient and capillary limit, respectively, while the cross-sectional area of vapor path decreases 76.8% at a saturation temperature of 40 °C. The annular flow path made the vapor space and the pressure difference decrease. The heat transfer coefficient of the conventional heat pipe was relatively high compared with that of the annular-flow-path heat pipe for an equivalent heat flux. Major differences between the heat pipes are the cross-sectional area of the vapor space and that the pressure drop in the vapor was dominant for capillary limit. Therefore, the cross-sectional area of the vapor space had a significant effect on the heat pipe dry-out phenomenon. The reduction of the overall heat transfer coefficient of the heat pipe is no great effect according to the cross-sectional area of the vapor path. The experimental results suggest the direction of the optimization of the heat pipe in terms of space management for compact devices. Or, if there is enough margin in capillary limit, the optimized compact vapor path without losing heat transfer performance too much can be acquired or excess space can be used for special applications such as neutron absorber in nuclear control rods and structural supports in the electronic cooling for compactness. Acknowledgements
4. Conclusion An experimental study of three 12.7-mm O.D. heat pipes was performed. The working fluid was distilled water, the wick and container material was stainless steel, and the length of the heat pipe was 650 mm. Thermal analyses of the annular flow path through the heat pipes were discussed. The objective was to investigate the effects of the inner structure of the heat pipe on the heat-transfer performance with a cross-sectional area of vapor path. An ABS pellet was used as the cylindrical structure. The thermal performance of each heat pipe was measured experimentally and the results indicated that the conventional heat pipe
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