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Heat transfer performance of cylindrical heat pipes with axially graded wick at anti-gravity orientations
Applied Thermal Engineering 163 (2019) 114413
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Heat transfer performance of cylindrical heat pipes with axially graded wick at anti-gravity orientations
T
Hai Tang, Lixian Lian , Jing Zhang, Ying Liu ⁎
College of Materials Science and Engineering, Sichuan University, No. 24 South Section 1, Yihuan Road, Sichuan 610065, PR China
HIGHLIGHTS
graded wick heat pipes are manufactured to improve heat transfer performance. • Axially is made with homogeneous wick heat pipes. • Comparison tilt angles are tested: horizontal orientation and two anti-gravity orientations (30° and 90°). • Three graded heat pipes outperform homogeneous wick heat pipe in all orientations. • Axially • Increasing the wick thickness of axially graded wick heat pipe can improve heat transfer capacity notably. ARTICLE INFO
ABSTRACT
Keywords: Heat pipe Axially graded wick Anti-gravity Critical heat load
To increase the heat transfer capability at anti-gravity orientations, heat pipes with homogeneous and axially graded wicks were experimentally investigated. The homogeneous wick (0.8 mm thickness) sintered with 125–150 μm (coarse) copper powder operated at 100 W without dryout at horizontal orientation, while that sintered with 75–97 μm (fine) copper powder had lower critical heat load about 80 W. The critical heat load decreased tremendously with increasing anti-gravity angles and it was about 20 W at totally anti-gravity orientation. However, the axially graded wick, sintered with fine and coarse powder at evaporator section and the rest section of the pipe, respectively, exhibited critical heat load of 35 W, nearly 75% increment than homogeneous wick with same thickness. Further study shows that increasing the thickness of axially graded wick significantly improved the critical heat load although the thermal resistance increased simultaneously. At a tilted angle of 90°, the critical heat load increased from 35 W to 45 W when increasing thickness from 0.8 mm to 1.1 mm and it further increased to 96 W when increasing thickness to 1.35 mm. The reconciliation between the capillary force and the permeability of axially graded structure promoted the increase of the critical heat load notably.
1. Introduction The increasing heat fluxes from integrated and miniaturized electronic devices have reached levels that is hard to be transferred fastly by traditional materials [1]. Heat pipe is characterized by its high effective thermal conductivity and it can achieve a fast heat transfer over a long distance with a very small temperature drop [2]. Heat pipes with a variety of shapes have been utilized for different purposes, including heat dissipation of electronic components by cylindrical micro heat pipes [3], energy utilization of solar systems by flat heat pipes [4], temperature homogenization of reactor by annular heat pipes [5], longdistance heat transfer by loop heat pipes [6] and so on. Heat pipe which usually consists of capsule, wick and working fluid,
⁎
is a closed and highly vacuumed two-phase system and it transfers heat from heat source to heat sink with the aid of latent heat during evaporation and condensation. When the heat is applied to the evaporator, evaporation takes place at the meniscus on the wick-liquid interface and it leads to the increase of vapor pressure, which drives the vapor to travel to the condenser where the latent heat is released. The condensed liquid is sucked back to evaporator through the wick under the capillary pressure. Besides, the fluid circulates endlessly so long as the capillary pressure is big enough to overcome the total pressure loss during the heat pipe operation [7]. Though heat pipes have won admiring reputation in space applications [8,9], their performances might be discounted in terrestrial environment, where the conditions are relatively intricate. On the one
Corresponding author. E-mail address: [email protected] (L. Lian).
https://doi.org/10.1016/j.applthermaleng.2019.114413 Received 23 May 2019; Received in revised form 23 August 2019; Accepted 18 September 2019 Available online 19 September 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.
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Nomenclature Q R L T K Aw Din Dout ΔPcap δw, eff kw, eff k σ
reff θ d ε
heat load, W thermal resistance, °C/W length of the evaporator or condenser, m temperature, °C permeability, m2 area of evaporator, m2 inner diameter, m outer diameter, m capillary pressure, N/m2 wetted effective wick thickness, m effective conductivity of the wick, W/m⋅K thermal conductivity of copper, W/m⋅K surface tension, kg/s2
effective pore radius, m contact angle particle diameter, m porosity
Subscript w cap eff evap max in out
wick capillary force effective evaporator maximum inner outer
possessed smaller pores at evaporator to increase the capillary driving force and had larger pores at adiabatic and condenser section to decrease the fluid flow resistance. Moreover, the effect of tilt angle, wick structure and wick thickness on heat transfer performance were studied
hand, the wick possessing small pore can provide large capillary pressure for axial liquid suction but leading to the decrease of permeability which impedes the liquid moving back to the evaporator. Therefore, heat pipes with small pore exhibit a strong sensitivity to the total length [10]. On the other hand, the wick possessing large pore is favorable for liquid backflow but lacking enough capillary force to drive the liquid circulation. Hence, heat pipes with large pore exhibit a strong sensitivity to both the length and the orientations with respect to gravity [11]. Though extensive researches have confirmed enhancement of heat transfer performance in gravity-assisted situation [12–15], when the heat pipe worked in anti-gravity or acceleration situations, heat pipes met the capillary limit easily and thermal resistance increased [3,16–18]. For improving the heat transfer performance under antigravity situations, some strategies have been developed to weaken the effect of gravity on heat pipes. The loop heat pipes (LHP) developed by Maydanik [19] were less sensitive to the change of orientations in the gravity field [11], but some new problems like heat leak [20], temperature oscillation [21], start-up problems [22] and high cost were induced. Rui Zhou et al. [23] designed an anti-gravity loop-shaped heat pipe with a continuous graded pore-size wick for ground applications, the ideal heat load range of the heat pipe at the anti-gravity orientation was from 30 W to 90 W, but to manufacture the loop-shaped heat pipe was complicated. Y. Wang et al. [24] found that the maximum heat transfer capacity increased with increasing the wick thickness under same tilt angles, but the increase was small. Recently, Wermer et al. [25] modeled, fabricated and tested a counter-gravity heat pipe with a header and artery system. This new heat pipe system can increase the capillary limit many times compared with a conventional homogeneous wick. But to equip the header and artery was complex, especially on micro heat pipe. Therefore, designing a simple and low-cost micro heat pipe with high heat transfer capacity is indispensable when the heat source locates above the heat sink or the device experiences adverse acceleration, for example, the CPU cooler and high-speed rail. Sheleg et al. [26] conducted a numerical calculation on axially graded heat pipe which achieved 1.5 times enhancement of the heat transport capacity comparing to an optimized uniform wick. North et al. [27] also numerically optimized the axially graded heat pipe whose capillary radius was continuously varied as a function of axial position. Their results showed the optimized axially graded heat pipe can transport over 5.6 times more power than an optimal homogenous wick. However, both numerical calculations showed the capillary radius at the condenser was rather larger than that at the evaporator, for example, the latter suggested the pore size difference between condenser and evaporator was almost 100 times, which was hard to be achieved. Moreover, how to construct the axially graded structure and improve the heat transfer performance by experiment is interesting and necessary. Therefore, we manufactured axially graded heat pipes which
2. Experimentation 2.1. Preparation of heat pipes Copper pipes (≥99.9%), whose inner diameter and outer diameter were 5.2 mm and 6 mm, were cut with a length of 24.6 cm. Then one end was necked with 3.8 mm outer diameter and 2.6 mm inner diameter. The 40 mm necked length was used for secondary degas [28]. After that, the pipes and steel mandrels (diameter: 3.6 mm, 3 mm, 2.5 mm) were straightened to make sure the homogeneity of wick thickness. In addition, copper powder (≥99.9%) was tightly sieved by 100–120 mesh screens and 160–200 mesh screens, giving particle of 125–150 μm and 75–97 μm, respectively. After placing the steel mandrel in copper pipe’s central position utilizing the fixation molds, the copper powder was perfused by a funnel mold. Noted that homogeneous wick structure A and B were constructed by filling 125–150 μm and 75–97 μm powder into 200 mm length pipe, respectively. As for axially graded wicks, there were about 50 mm length to fill 75–97 μm powder and about 150 mm length to fill 125–150 μm powder. The brief models were displayed in Fig. 1. After the perfusion, the collar was fixed at the powder-filling end to compact it. Next, all the pipes were sintered at 900 °C for 1 h at pure argon (99.99 vol%) atmosphere. After the sintering process, the powder-filling end was necked again with 8 mm length, followed by argon arc welding to seal it. The distilled water (18.25 MΩ cm) was charged into the pipe by injector and the
Fig. 1. (a) homogeneous wick structure; (b) axially graded wick structure. 2
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wick was fully wetted, then a vacuum pump was used to evacuate air inside, followed by mechanical cold welding. In order to decrease the non-condensable gas (air) to the greatest extent, the secondary degassing process was implemented [29], after which the pipe was temporary sealing by cold welding and then the space where inert gases gather was cut off. Finally, the pipe was permanently sealed by argon arc welding. The detailed information of all heat pipes was shown in Table 1. For ease of the description, simplified forms of sample names were used, for example, A-0.8 represented heat pipe with a wick thickness of 0.8 mm possessing a homogeneous wick structure A.
temperature difference through the saturated wick. To calculate these thermal resistances is rather difficult, but the following Eq. (2) suggested by Chang et al. [31] can evaluate the wick thermal resistance.
Rw
The schematic of the apparatus for testing the thermal performance was shown in Fig. 2(a). The system consisted of a heating module, a cooling module and a data collecting module. The heating module included a heating copper block with a length of 50 mm and a DC power supply, whose accuracy were ± 0.01 W. The cooling module consisted of a cooling copper block with a length of 70 mm and a fan, which was fixed under the cooling copper block to dissipate the heat. During the test, the heat pipes were mounted into the grooves in the heating copper block and cooling copper block, respectively. The data collection module contained a data acquisition device, a computer and thirteen K type thermocouples, whose accuracy was ± 0.1 °C. As shown in the Fig. 2(a), T1 and T13 represented the temperature of heating and cooling copper blocks, respectively, and T2T6 indicated the upper surface temperatures of the heat pipe evaporator. T7 was the heat pipe adiabatic section temperature and T8-T12 represented the heat pipe condenser wall temperature. Silicone grease was utilized to reduce the contact thermal resistance between the copper block and the heat pipe wall. Moreover, the test apparatus was also surrounded by polymer foam to reduce the heat loss to the environment during the test. In order to evaluate the anti-gravity performance, as shown in Fig. 2(b), all heat pipes were tested at horizontal orientation and two anti-gravity orientations (evaporator was above condenser: 30° and 90°). In addition, heating power was stepwise increased in intervals of 300 s. But to protect the test unit, the highest power was not allowed to exceed 100 W.
R evap =
The equivalent circuit of thermal resistances of the test system was depicted in Fig. 3 and presented as follows [2,30]: Resistances due to thermal conduction through heating copper block (R1) and cooling copper block (R12): The thermal conduction through the two copper blocks generates the resistance R1 and R12, respectively. But the two values are small and seen as constant in our experiment due to high thermal conductivity of copper. Contact resistance (R2 and R11): These come from the gaps between heat pipe wall and copper blocks. They are inevitable though silicone grease is applied to minimize them. Thermal resistance due to radial thermal conduction (R3 and R9): Both thermal resistances are related to the inner and outer diameter of the copper pipe, the thermal conductivity of container material and the lengths of the evaporator and condenser. This can be calculated by Eq. (1) [2]. As all the heat pipes are in the same size and material, they are seen constant.
( ) Dout Din
2 kL
T1
T6
(3)
Qin
Temperature difference T1–T6 rather than T1 − (T2 + T3 + T4 + T5 + T6)/5 was used to calculate the Revap basing the experimental observation. Considering a heat pipe reaching the capillary limit, heat pipe had dried out except the position of T6, and T2, T3, T4, T5 was very close to T1. Therefore, temperature difference T1 − (T2 + T3 + T4 + T5 + T6)/5 was very small and caused to a small Revap, which was ridiculous because the heat pipe almost completely dried out. However, the difference between T1 and T6 immediately increased when the heat pipe reached capillary limit (when T2 > T3), and it adequately reflected the change of heat pipe thermal resistance during operation.
2.3. Thermal resistance model
ln
(2)
where δw, eff is the wetted effective wick thickness, kw, eff the effective conductivity of the wick, Aw the area of the evaporator. The thermal resistance due to evaporation (R5) and condensation (R7) on the liquid–vapor interface:A slight superheat and subcooling are needed to activate evaporation or condensation. These resistances can usually be neglected [2]. Resistance due to axial heat transfer (R6 and R10): The resistance along the vapor column (R6) is due to the temperature drop along the vapor column and is neglectable [32]. But the resistance along the axial tube (R10) is very large, so only a limited amount of flux will go along this path. Basing on the description of all the resistances, the axial thermal resistances (R6 and R10) and evaporation and condensation resistances (R5 and R7) are neglected. Moreover, thermal resistances R1, R2, R3, R9, R11 and R12 are regarded as constant in this experiment. Therefore, the evaporator thermal resistance is defined by the sum of R1, R2, R3 and R4 and the condenser thermal resistance is defined by the sum of R8, R9, R11 and R12. Weibel et al. [33] suggested that the behavior of the heat pipe total thermal resistance can be explained according to the behavior of the evaporator thermal resistance. Consequently, the Revap calculated by Eq. (3) was chosen as a heat transfer performance indicator in this paper.
2.2. Heat transfer performance characterization
R=
w, eff
k w, eff Aw
2.4. Uncertainty analysis Based on the thermal module, the evaporator thermal resistance is calculated by Eq. (3). The uncertainty analysis of the evaporator thermal resistance is performed as given by [34]:
R=
(
R R Qin ) 2 + ( ( T ))2 Qin ( T)
(4)
R 1 = ( T) Qin
(5)
Table 1 Specifications of heat pipes.
(1)
Where the Dout and Din are the outer and inner diameter of the copper tube, respectively. L is the length of evaporator or condenser and k is the thermal conductivity of the material. Thermal resistance in the wick (R4 and R8): R4 and R8 take account of the thermal resistance of the wick structure and include any 3
Wick structure
Wick thickness
A B C
0.8 mm 0.8 mm 0.8 mm 1.1 mm 1.35 mm
Sintered powder size Evaporator
Adiabatic and condenser section
125–150 μm 75–97 μm 75–97 μm 75–97 μm 75–97 μm
125–150 μm 75–97 μm 125–150 μm 125–150 μm 125–150 μm
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3. Results and discussion 3.1. Characteration of wick structures The scanning electron microscopy (SEM) images of wick structure A and B are shown in Fig. 4(a) and (c), respectively. Most of the pore size was 50–76 μm for wick sintered by 125–150 μm powder (Fig. 4(b)), and that of the wick sintered by 75–97 μm powder was 34–52 μm (Fig. 4(d)). Thus, the axially graded structure had the two characteristic pores—34–52 μm pore at evaporator and 50–76 μm pore at adiabatic and condenser section. The capillary force can be calculated by the Eq. (8) and the permeability of wick sintered by powder can be calculated by Eq. (9) [35,36].
Pcap =
K=
2 cos reff d2 2
c (1
)
(8) (9)
where thereff is the effective pore radius, the surface tension of liquid, the contact angle. K is the permeability of the wick, d the particle diameter, the porosity of the wick and c is related to powder sphericity. As the capillary force is inversely proportional to the pore size but the wick permeability is proportional to the pore size [1,10], the capillary force of wick structure A was smaller than that of wick structure B, while the permeability of the former was larger than that of the latter. However, for axially graded wicks, the evaporator had larger capillary pressure and the adiabatic and condenser section had larger permeability, which ensured enough fluid supply to evaporator even at anti-gravity orientations.
Fig. 2. (a) experimental set up (mm), (b) inclinations of the heat pipe.
3.2. The heat transfer performance of homogeneous wicks under different tilt angles The temperature distribution for heat pipe A-0.8 at horizontal orientation was shown in Fig. 5(a). Although a little non-condensable gas remained in the liquid might influence the temperature uniformity, nearly uniform temperature distribution was observed at all the heat loads and dryout did not occur at the power 100 W. However, as shown in Fig. 5(b), heat transfer capacity was dramatically decreased when the heat pipe was tilted at 90°. The condenser end temperature T12 (Fig. 2(a)) was significantly lower than other condenser temperature when increasing the heat load, the reason might be that gravity decreased the liquid volume fraction in evaporator wick and redundant working fluid seemed to accumulate at the condenser. A sudden increase of evaporator temperature T2 was observed at 22 W, it meant the dry patches was firstly at the upstream end of the evaporator and localized vapor blankets might cover it (partial dryout). When increasing the heat load to 30 W, T2 and T3 raised greatly, which might indicate the partial dryout was expanding with enlarging vapor blankets area. Though heat pipe still operated acceptably, the low thermal conductivity vapor blankets would enlarge until covering the complete surface of the evaporator if increased the heat load continuously (totally dryout) [33]. The evaporator thermal resistance versus heat load at different tilt angles for heat pipe A-0.8 is shown in Fig. 5(c). It was clearly that the Revap decreased gradually with increasing the power. At low heat loads, the heat was transported to the liquid surface partly by conduction through the wick and liquid and partly by natural convection, quiescent surface evaporation caused the decrease of Revap. As the heat was increased, some bubbles might form and transport some energy to the surface by vaporization and would also greatly increase convective heat transfer [2]. The intensive evaporation would reduce the effective wetted wick thickness because of the liquid layer retreat in the wick
Fig. 3. Equivalent thermal resistance network in a heat pipe.
R = Qin
T Qin 2
(6)
So, by dividing R, it can be written in following form,
R = R
(
Qin 2 ( T) 2 ) ) +( Qin T
(7)
where ΔT is the temperature difference between T1 and T6. δ(Qin) and δ(ΔT) are uncertainties of the heat load and temperature difference, respectively. At tilted angles of 0°, 30° and 90°, the maximum uncertainties for Revap of heat pipe A-0.8 were 8%, 9% and 9%, respectively. They were 8%, 9% and 9% for heat pipe B-0.8 and 9%, 10% and 10% for heat pipe C-0.8. As for C-1.1, the maximum uncertainties were approximately 9%, 9% and 8%, while they were 8%, 7% and 7% for heat pipe C-1.35. 4
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Fig. 4. SEM images and pore size distributions (a),(b) wick structure A sintered by 125–150 μm copper powder, (c) (d) wick structure B sintered by 75–97 μm copper powder.
[37,38]. It brought in a short radial heat transfer path and a large evaporation area, as a result, the Revap decreased continuously. However, noted that there was a critical heat load Qmax at which the heat pipe had a lowest Revap, for example, the lowest Revap was 0.155 °C/W at 62 W when the heat pipe was tilted at 30°. Additionally, when heat load was over the Qmax, the Revap started to increase sharply. Because partial dryout led to localized evaporator surface was covered by vapor blankets, which impeded the heat transfer and decreased the effective evaporation area. Hence, part of the increased power directly overheated the copper block, the wick and the vapor rather than transferred sufficiently by phase change [39], as a result, T1, T2 and then T3 raise up leading to the rise of Revap sharply. Since the value of Qmax was consistent with that from the temperature distribution figure, the parameter Qmax was used to judge the occurrence of dryout and to evaluate the heat pipe anti-gravity performance in this study. It was found that the Qmax might be over 100 W at horizontal orientation, but decreased to 62 W and 20 W at the inclination of 30° and 90°, respectively. Because the extra gravitational pressure loss increased with increasing anti-gravity angles. Moreover, smaller thermal resistance was found at lower heat loads when the heat pipe was tilted from 0° to 90°. This might be explained by that the working fluid volume fraction decreased with increasing adverse tilted angles, which reduced the liquid layer thickness in the wick. The temperature distribution for heat pipe B-0.8 at horizontal orientation is shown in Fig. 6(a). Nearly uniform temperature distribution below 60 W was observed, but T12 was obviously lower than T11 at 70 W, which indicated liquid gathering at the condenser. Because the intensive evaporation happen in the wick and the high-speed vapor might carry liquid to condenser at high heat load. However, the
redundant working fluid might not be delivered to evaporator timely because of the large flow resistance. Moreover, the occurrence of partial dryout was observed at 80 W as T2 started to raise up apparently. Compared with A-0.8, smaller pores of B-0.8 yielded a bigger capillary force but lower permeability, which made the heat pipe performance degradation even at horizontal orientation. At an inclination of 90°, as shown in Fig. 6(b), gravity also had an adverse effect on heat pipe B-0.8 just like heat pipe A-0.8 though the former having larger capillary force. As clearly seen from Fig. 6(c), the Qmax was 75 W at horizontal orientation, but decreased to 40 W at the inclination of 30°, and reached 20 W at totally anti-gravity orientation. In general, the Qmax was as low as 20 W at the inclination of 90° for both heat pipe A-0.8 and B-0.8, which might be the result of higher permeability but a lower capillary force for A-0.8 while the opposite for B-0.8. In conclusion, the homogeneous wick with smaller or larger pore showed a strong sensitivity to adverse tilt angles. 3.3. Heat transfer performance of axially graded wick Fig. 7 illustrates the evaporator resistance versus the heat load for three different wick structures with same wick thickness of 0.8 mm at different tilted angles. At horizontal orientation (Fig. 7(a)), it seemed that the tendency of Revap was different for different wick structures. For homogeneous wick structure A and B, the Revap almost decreased monotonically before partial dryout. However, for axially graded structure C, the decrease of Revap was stair-stepping. It might be related to the retreat process of the liquid layer in the wick. For homogeneous wick, the liquid layer became thinner and thinner with increasing heat load, the decreased liquid layer thickness and increased evaporation 5
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Fig. 5. Heat transfer performance for heat pipe A-0.8 at different angles (a) temperature distribution at 0°, (b) temperature distribution at 90°, (c) evaporator thermal resistance as a function of the power.
Fig. 6. Heat transfer performance for heat pipe B-0.8 at different angles (a) temperature distribution at 0°, (b) temperature distribution at 90°, (c) evaporator thermal resistance as a function of the power.
area promoted the decrease of Revap in the heat load 5–75 W, Eq. (2) also shows that the Revap decreases with increasing the effective thickness of wetted wick. However, the lower wick permeability of heat pipe B-0.8 limited the reduction of Revap and caused the partial dryout early. For the axially graded wick, smaller pore at evaporator produced larger capillary driving force, larger pore at adiabatic and condenser section exhibited higher permeability. Therefore, compared with homogeneous wicks, the liquid supply to evaporator for axially graded wick might be timelier at the same load, which made the liquid retreat process slowly. Thus, the decrease of Revap was also slowly in the heat load of 15–65 W. But with further increase of heat load, the liquid layer thickness might decrease abruptly because the mass of liquid evaporation was large in the heat load 70–80 W, which led to the decrease of Revap sharply. And another balance between liquid evaporation and liquid supply might be established through the synergetic effect of axially graded wick structure in the heat load of 80–100 W. Moreover, dryout did not happen at 100 W for heat pipe C-0.8, but occurred at about 75 W for B-0.8, which implied the performance improvement for
the axially graded structure heat pipe. As shown in Fig. 7(b), although the Qmax of all heat pipes decreased when heat pipes were tilted at 30°, it reached about 79 W for heat pipe C-0.8, which was nearly 1.27 times that of heat pipe A-0.8. And compared that with heat pipe B-0.8, it was increased by 100%. At totally anti-gravity orientation, as shown in Fig. 7(c), the lower thermal resistance of axially graded heat pipe than that of homogenous wick heat pipe was observed. This probably because the higher capillary force at evaporator and higher permeability at adiabatic and condenser section sustained a thinner liquid layer at the bottom of the wick, thus caused the decrease of Revap. The Qmax was 20 W for both the homogeneous wick heat pipes, but that of axially graded heat pipe was 35 W, which was 75% higher. This was to be expected because the smaller pore at evaporator exhibited larger capillary pumping ability for axial liquid suction while the larger pore at adiabatic and condenser section provided lower flow resistance passages for liquid circulation, hence the synergetic effect of axially graded wick structure promoted the increase of Qmax notably. 6
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Fig. 7. Evaporator thermal resistance as a function of the power for heat pipe with different wick structures at a thickness of 0.8 mm and at different tilted angles (a) 0°, (b) 30°, (c) 90°.
Fig. 8. Evaporator thermal resistance as function of the power for axially graded heat pipes with different wick thickness at different tilted angles (a) 0°, (b) 30°, (c) 90°.
3.4. Effect of wick thickness on the heat transfer performance of axially graded wicks
0.175–0.185 °C/W in the heat load of 60–96 W, and the Qmax reached a rather high level of 96 W for heat pipe C-1.35, which was about 170% and 100% higher compared with that of C-0.8 and C-1.1, respectively. Based on the synergetic effect of axially graded structure, thicker wick provided a wider path for liquid flow and further improved the permeability especially at the evaporator, which ensured enough liquid supply to sustain fluid circulation even at high heat load. Therefore, the Qmax was further increased dramatically for axially graded heat pipe when increasing the wick thickness.
At horizontal orientation, as shown in Fig. 8(a), it was interesting that the decreasing tendency of Revap for all axially graded heat pipes was stair-stepping, which suggested that the stair-stepping decrease trend of Revap was probably related to the axially graded wick structure. The Revap of heat pipe C-1.35 was nearly the highest because thicker wick provided a long radial path for heat transfer. Moreover, all the axially graded heat pipes operated at heat load 100 W without dryout. But the true Qmax might be much higher than 100 W for all axially graded heat pipes and other flat stages of Revap might exist at high heat load. Because two flat stages of Revap were still remained and dryout did not appear at the heat load 100 W for heat pipe C-1.1 and C-1.35 despite tilted at 30°, as shown in Fig. 8(b). However, the Qmax was 79 W at the inclination of 30° for heat pipe C-0.8, which indicated that the Qmax was enhanced by increasing the wick thickness. At the totally antigravity orientation, as shown in Fig. 8(c), it was clearly that both the Revap and Qmax increased with increasing the wick thickness, which was consistent with the results from relative studies [31,40]. The Revap was
4. Conclusion An experimental study on homogeneous and axially graded wick of copper-water micro heat pipe was performed. The effect of tilt angles, wick structures and wick thicknesses on heat transfer performance were studied. The following results were obtained: (1) Large pores are formed by sintering coarse copper powder, and small pores are formed by sintering fine copper powder. (2) The Revap decreases with increasing the tilt angle from 0° to 90° but 7
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accompany with an early occurrence of partial dryout, from which the Revap starts to increase sharply. Indeed, heat pipes with homogeneous wick show a strong sensitivity to adverse tilt angles. (3) The Qmax of axially graded heat pipe C-0.8 is increased by 75% compared with that of homogeneous wick heat pipes at the inclination of 90°. The significant increase of Qmax is due to the reconciliation between capillary force and permeability. Moreover, the tendency of Revap-Q is stair-stepping for axially graded wick, while it is monotonic for homogeneous wicks. (4) Though the thermal resistance increases with increasing the wick thickness, the sensitivity to gravity can be minimized simultaneously. Both axially graded heat pipe C-1.1 and C-1.35 can operate at heat load 100 W without the occurrence of dryout though tilted at 30°. Moreover, the axially graded structure heat pipe C-1.35 has the highest Qmax of 96 W when the heat pipe is tilted at 90°.
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We expect that the proposed axially graded structure micro heat pipe can not only have applications on anti-gravity situations, but also be applied on high heat flux occasions at horizontal orientation. Because the true Qmax of heat pipes with axially graded wick structure may be much higher than 100 W at horizontal orientation based on the change trend of Qmax and tilt angles. More work can be done to optimize the axially graded structure to maximize the heat transfer capacity. Acknowledgements This work was supported by “the Fundamental Research Funds for Central Universities (China)”. Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.applthermaleng.2019.114413. References [1] B. Zohuri, Heat pipe design and technology: modern applications for practical thermal management, 2nd ed., Springer International Publishing, Cham, 2016. [2] D.A. Reay, Heat pipes, fifth ed., Butterworth-Heinemann, 2006. [3] T. Yousefi, S.A. Mousavi, B. Farahbakhsh, et al., Experimental investigation on the performance of CPU coolers: effect of heat pipe inclination angle and the use of nanofluids, Microelect. Reliab. 53 (2013) 1954–1961. [4] S.B. Riffat, X. Zhao, P.S. Doherty, Developing a theoretical model to investigate thermal performance of a thin membrane heat-pipe solar collector, Appl. Therm. Eng. 25 (2005) 899–915. [5] Y.O. Parent, H.S. Caram, R.W. Coughlin, Tube-wall catalytic reactor cooled by an annular heat pipe, AIChE J. 29 (1983) 443–451. [6] Y. Maydanik, V. Pastukhov, M. Chernysheva, Development and investigation of a loop heat pipe with a high heat-transfer capacity, Appl. Therm. Eng. 130 (2018) 1052–1061. [7] B. Chnookaraju, P.S.V. Kurmarao, S.N. Sarada, Thermal analysis of gravity effected sintered wick heat pipe, Mater. Today Proc. 2 (2015) 2179–2187. [8] Z. Hongxing, M. Min, M. Jianyin, W. Lu, C. Yang, et al., Development and on-orbit operation of loop heat pipes on chinese circumlunar return and reentry spacecraft, J. Mech. Sci. Technol. 31 (2017) 2597–2605. [9] F. Zhou, W. Duan, G. Ma, Thermal performance of a pump-driven loop heat pipe as an air-to-air energy recovery device, Energy Build. 151 (2017) 206–216. [10] G.P. Peterson, An introduction to heat pipes: modeling, testing, and applications, Wiley, New York, 1994. [11] Y.F. Maydanik, Loop heat pipes, Appl. Ther. Eng. 25 (2005) 635–657. [12] R. Manimaran, K. Palaniradja, N. Alagumurthi, K. Velmurugan, An investigation of thermal performance of heat pipe using Di-water, Sci. Technol. 2 (2012) 77–80.
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Heat transfer performance of cylindrical heat pipes with axially graded wick at anti-gravity orientations
T
Hai Tang, Lixian Lian , Jing Zhang, Ying Liu ⁎
College of Materials Science and Engineering, Sichuan University, No. 24 South Section 1, Yihuan Road, Sichuan 610065, PR China
HIGHLIGHTS
graded wick heat pipes are manufactured to improve heat transfer performance. • Axially is made with homogeneous wick heat pipes. • Comparison tilt angles are tested: horizontal orientation and two anti-gravity orientations (30° and 90°). • Three graded heat pipes outperform homogeneous wick heat pipe in all orientations. • Axially • Increasing the wick thickness of axially graded wick heat pipe can improve heat transfer capacity notably. ARTICLE INFO
ABSTRACT
Keywords: Heat pipe Axially graded wick Anti-gravity Critical heat load
To increase the heat transfer capability at anti-gravity orientations, heat pipes with homogeneous and axially graded wicks were experimentally investigated. The homogeneous wick (0.8 mm thickness) sintered with 125–150 μm (coarse) copper powder operated at 100 W without dryout at horizontal orientation, while that sintered with 75–97 μm (fine) copper powder had lower critical heat load about 80 W. The critical heat load decreased tremendously with increasing anti-gravity angles and it was about 20 W at totally anti-gravity orientation. However, the axially graded wick, sintered with fine and coarse powder at evaporator section and the rest section of the pipe, respectively, exhibited critical heat load of 35 W, nearly 75% increment than homogeneous wick with same thickness. Further study shows that increasing the thickness of axially graded wick significantly improved the critical heat load although the thermal resistance increased simultaneously. At a tilted angle of 90°, the critical heat load increased from 35 W to 45 W when increasing thickness from 0.8 mm to 1.1 mm and it further increased to 96 W when increasing thickness to 1.35 mm. The reconciliation between the capillary force and the permeability of axially graded structure promoted the increase of the critical heat load notably.
1. Introduction The increasing heat fluxes from integrated and miniaturized electronic devices have reached levels that is hard to be transferred fastly by traditional materials [1]. Heat pipe is characterized by its high effective thermal conductivity and it can achieve a fast heat transfer over a long distance with a very small temperature drop [2]. Heat pipes with a variety of shapes have been utilized for different purposes, including heat dissipation of electronic components by cylindrical micro heat pipes [3], energy utilization of solar systems by flat heat pipes [4], temperature homogenization of reactor by annular heat pipes [5], longdistance heat transfer by loop heat pipes [6] and so on. Heat pipe which usually consists of capsule, wick and working fluid,
⁎
is a closed and highly vacuumed two-phase system and it transfers heat from heat source to heat sink with the aid of latent heat during evaporation and condensation. When the heat is applied to the evaporator, evaporation takes place at the meniscus on the wick-liquid interface and it leads to the increase of vapor pressure, which drives the vapor to travel to the condenser where the latent heat is released. The condensed liquid is sucked back to evaporator through the wick under the capillary pressure. Besides, the fluid circulates endlessly so long as the capillary pressure is big enough to overcome the total pressure loss during the heat pipe operation [7]. Though heat pipes have won admiring reputation in space applications [8,9], their performances might be discounted in terrestrial environment, where the conditions are relatively intricate. On the one
Corresponding author. E-mail address: [email protected] (L. Lian).
https://doi.org/10.1016/j.applthermaleng.2019.114413 Received 23 May 2019; Received in revised form 23 August 2019; Accepted 18 September 2019 Available online 19 September 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.
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Nomenclature Q R L T K Aw Din Dout ΔPcap δw, eff kw, eff k σ
reff θ d ε
heat load, W thermal resistance, °C/W length of the evaporator or condenser, m temperature, °C permeability, m2 area of evaporator, m2 inner diameter, m outer diameter, m capillary pressure, N/m2 wetted effective wick thickness, m effective conductivity of the wick, W/m⋅K thermal conductivity of copper, W/m⋅K surface tension, kg/s2
effective pore radius, m contact angle particle diameter, m porosity
Subscript w cap eff evap max in out
wick capillary force effective evaporator maximum inner outer
possessed smaller pores at evaporator to increase the capillary driving force and had larger pores at adiabatic and condenser section to decrease the fluid flow resistance. Moreover, the effect of tilt angle, wick structure and wick thickness on heat transfer performance were studied
hand, the wick possessing small pore can provide large capillary pressure for axial liquid suction but leading to the decrease of permeability which impedes the liquid moving back to the evaporator. Therefore, heat pipes with small pore exhibit a strong sensitivity to the total length [10]. On the other hand, the wick possessing large pore is favorable for liquid backflow but lacking enough capillary force to drive the liquid circulation. Hence, heat pipes with large pore exhibit a strong sensitivity to both the length and the orientations with respect to gravity [11]. Though extensive researches have confirmed enhancement of heat transfer performance in gravity-assisted situation [12–15], when the heat pipe worked in anti-gravity or acceleration situations, heat pipes met the capillary limit easily and thermal resistance increased [3,16–18]. For improving the heat transfer performance under antigravity situations, some strategies have been developed to weaken the effect of gravity on heat pipes. The loop heat pipes (LHP) developed by Maydanik [19] were less sensitive to the change of orientations in the gravity field [11], but some new problems like heat leak [20], temperature oscillation [21], start-up problems [22] and high cost were induced. Rui Zhou et al. [23] designed an anti-gravity loop-shaped heat pipe with a continuous graded pore-size wick for ground applications, the ideal heat load range of the heat pipe at the anti-gravity orientation was from 30 W to 90 W, but to manufacture the loop-shaped heat pipe was complicated. Y. Wang et al. [24] found that the maximum heat transfer capacity increased with increasing the wick thickness under same tilt angles, but the increase was small. Recently, Wermer et al. [25] modeled, fabricated and tested a counter-gravity heat pipe with a header and artery system. This new heat pipe system can increase the capillary limit many times compared with a conventional homogeneous wick. But to equip the header and artery was complex, especially on micro heat pipe. Therefore, designing a simple and low-cost micro heat pipe with high heat transfer capacity is indispensable when the heat source locates above the heat sink or the device experiences adverse acceleration, for example, the CPU cooler and high-speed rail. Sheleg et al. [26] conducted a numerical calculation on axially graded heat pipe which achieved 1.5 times enhancement of the heat transport capacity comparing to an optimized uniform wick. North et al. [27] also numerically optimized the axially graded heat pipe whose capillary radius was continuously varied as a function of axial position. Their results showed the optimized axially graded heat pipe can transport over 5.6 times more power than an optimal homogenous wick. However, both numerical calculations showed the capillary radius at the condenser was rather larger than that at the evaporator, for example, the latter suggested the pore size difference between condenser and evaporator was almost 100 times, which was hard to be achieved. Moreover, how to construct the axially graded structure and improve the heat transfer performance by experiment is interesting and necessary. Therefore, we manufactured axially graded heat pipes which
2. Experimentation 2.1. Preparation of heat pipes Copper pipes (≥99.9%), whose inner diameter and outer diameter were 5.2 mm and 6 mm, were cut with a length of 24.6 cm. Then one end was necked with 3.8 mm outer diameter and 2.6 mm inner diameter. The 40 mm necked length was used for secondary degas [28]. After that, the pipes and steel mandrels (diameter: 3.6 mm, 3 mm, 2.5 mm) were straightened to make sure the homogeneity of wick thickness. In addition, copper powder (≥99.9%) was tightly sieved by 100–120 mesh screens and 160–200 mesh screens, giving particle of 125–150 μm and 75–97 μm, respectively. After placing the steel mandrel in copper pipe’s central position utilizing the fixation molds, the copper powder was perfused by a funnel mold. Noted that homogeneous wick structure A and B were constructed by filling 125–150 μm and 75–97 μm powder into 200 mm length pipe, respectively. As for axially graded wicks, there were about 50 mm length to fill 75–97 μm powder and about 150 mm length to fill 125–150 μm powder. The brief models were displayed in Fig. 1. After the perfusion, the collar was fixed at the powder-filling end to compact it. Next, all the pipes were sintered at 900 °C for 1 h at pure argon (99.99 vol%) atmosphere. After the sintering process, the powder-filling end was necked again with 8 mm length, followed by argon arc welding to seal it. The distilled water (18.25 MΩ cm) was charged into the pipe by injector and the
Fig. 1. (a) homogeneous wick structure; (b) axially graded wick structure. 2
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wick was fully wetted, then a vacuum pump was used to evacuate air inside, followed by mechanical cold welding. In order to decrease the non-condensable gas (air) to the greatest extent, the secondary degassing process was implemented [29], after which the pipe was temporary sealing by cold welding and then the space where inert gases gather was cut off. Finally, the pipe was permanently sealed by argon arc welding. The detailed information of all heat pipes was shown in Table 1. For ease of the description, simplified forms of sample names were used, for example, A-0.8 represented heat pipe with a wick thickness of 0.8 mm possessing a homogeneous wick structure A.
temperature difference through the saturated wick. To calculate these thermal resistances is rather difficult, but the following Eq. (2) suggested by Chang et al. [31] can evaluate the wick thermal resistance.
Rw
The schematic of the apparatus for testing the thermal performance was shown in Fig. 2(a). The system consisted of a heating module, a cooling module and a data collecting module. The heating module included a heating copper block with a length of 50 mm and a DC power supply, whose accuracy were ± 0.01 W. The cooling module consisted of a cooling copper block with a length of 70 mm and a fan, which was fixed under the cooling copper block to dissipate the heat. During the test, the heat pipes were mounted into the grooves in the heating copper block and cooling copper block, respectively. The data collection module contained a data acquisition device, a computer and thirteen K type thermocouples, whose accuracy was ± 0.1 °C. As shown in the Fig. 2(a), T1 and T13 represented the temperature of heating and cooling copper blocks, respectively, and T2T6 indicated the upper surface temperatures of the heat pipe evaporator. T7 was the heat pipe adiabatic section temperature and T8-T12 represented the heat pipe condenser wall temperature. Silicone grease was utilized to reduce the contact thermal resistance between the copper block and the heat pipe wall. Moreover, the test apparatus was also surrounded by polymer foam to reduce the heat loss to the environment during the test. In order to evaluate the anti-gravity performance, as shown in Fig. 2(b), all heat pipes were tested at horizontal orientation and two anti-gravity orientations (evaporator was above condenser: 30° and 90°). In addition, heating power was stepwise increased in intervals of 300 s. But to protect the test unit, the highest power was not allowed to exceed 100 W.
R evap =
The equivalent circuit of thermal resistances of the test system was depicted in Fig. 3 and presented as follows [2,30]: Resistances due to thermal conduction through heating copper block (R1) and cooling copper block (R12): The thermal conduction through the two copper blocks generates the resistance R1 and R12, respectively. But the two values are small and seen as constant in our experiment due to high thermal conductivity of copper. Contact resistance (R2 and R11): These come from the gaps between heat pipe wall and copper blocks. They are inevitable though silicone grease is applied to minimize them. Thermal resistance due to radial thermal conduction (R3 and R9): Both thermal resistances are related to the inner and outer diameter of the copper pipe, the thermal conductivity of container material and the lengths of the evaporator and condenser. This can be calculated by Eq. (1) [2]. As all the heat pipes are in the same size and material, they are seen constant.
( ) Dout Din
2 kL
T1
T6
(3)
Qin
Temperature difference T1–T6 rather than T1 − (T2 + T3 + T4 + T5 + T6)/5 was used to calculate the Revap basing the experimental observation. Considering a heat pipe reaching the capillary limit, heat pipe had dried out except the position of T6, and T2, T3, T4, T5 was very close to T1. Therefore, temperature difference T1 − (T2 + T3 + T4 + T5 + T6)/5 was very small and caused to a small Revap, which was ridiculous because the heat pipe almost completely dried out. However, the difference between T1 and T6 immediately increased when the heat pipe reached capillary limit (when T2 > T3), and it adequately reflected the change of heat pipe thermal resistance during operation.
2.3. Thermal resistance model
ln
(2)
where δw, eff is the wetted effective wick thickness, kw, eff the effective conductivity of the wick, Aw the area of the evaporator. The thermal resistance due to evaporation (R5) and condensation (R7) on the liquid–vapor interface:A slight superheat and subcooling are needed to activate evaporation or condensation. These resistances can usually be neglected [2]. Resistance due to axial heat transfer (R6 and R10): The resistance along the vapor column (R6) is due to the temperature drop along the vapor column and is neglectable [32]. But the resistance along the axial tube (R10) is very large, so only a limited amount of flux will go along this path. Basing on the description of all the resistances, the axial thermal resistances (R6 and R10) and evaporation and condensation resistances (R5 and R7) are neglected. Moreover, thermal resistances R1, R2, R3, R9, R11 and R12 are regarded as constant in this experiment. Therefore, the evaporator thermal resistance is defined by the sum of R1, R2, R3 and R4 and the condenser thermal resistance is defined by the sum of R8, R9, R11 and R12. Weibel et al. [33] suggested that the behavior of the heat pipe total thermal resistance can be explained according to the behavior of the evaporator thermal resistance. Consequently, the Revap calculated by Eq. (3) was chosen as a heat transfer performance indicator in this paper.
2.2. Heat transfer performance characterization
R=
w, eff
k w, eff Aw
2.4. Uncertainty analysis Based on the thermal module, the evaporator thermal resistance is calculated by Eq. (3). The uncertainty analysis of the evaporator thermal resistance is performed as given by [34]:
R=
(
R R Qin ) 2 + ( ( T ))2 Qin ( T)
(4)
R 1 = ( T) Qin
(5)
Table 1 Specifications of heat pipes.
(1)
Where the Dout and Din are the outer and inner diameter of the copper tube, respectively. L is the length of evaporator or condenser and k is the thermal conductivity of the material. Thermal resistance in the wick (R4 and R8): R4 and R8 take account of the thermal resistance of the wick structure and include any 3
Wick structure
Wick thickness
A B C
0.8 mm 0.8 mm 0.8 mm 1.1 mm 1.35 mm
Sintered powder size Evaporator
Adiabatic and condenser section
125–150 μm 75–97 μm 75–97 μm 75–97 μm 75–97 μm
125–150 μm 75–97 μm 125–150 μm 125–150 μm 125–150 μm
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3. Results and discussion 3.1. Characteration of wick structures The scanning electron microscopy (SEM) images of wick structure A and B are shown in Fig. 4(a) and (c), respectively. Most of the pore size was 50–76 μm for wick sintered by 125–150 μm powder (Fig. 4(b)), and that of the wick sintered by 75–97 μm powder was 34–52 μm (Fig. 4(d)). Thus, the axially graded structure had the two characteristic pores—34–52 μm pore at evaporator and 50–76 μm pore at adiabatic and condenser section. The capillary force can be calculated by the Eq. (8) and the permeability of wick sintered by powder can be calculated by Eq. (9) [35,36].
Pcap =
K=
2 cos reff d2 2
c (1
)
(8) (9)
where thereff is the effective pore radius, the surface tension of liquid, the contact angle. K is the permeability of the wick, d the particle diameter, the porosity of the wick and c is related to powder sphericity. As the capillary force is inversely proportional to the pore size but the wick permeability is proportional to the pore size [1,10], the capillary force of wick structure A was smaller than that of wick structure B, while the permeability of the former was larger than that of the latter. However, for axially graded wicks, the evaporator had larger capillary pressure and the adiabatic and condenser section had larger permeability, which ensured enough fluid supply to evaporator even at anti-gravity orientations.
Fig. 2. (a) experimental set up (mm), (b) inclinations of the heat pipe.
3.2. The heat transfer performance of homogeneous wicks under different tilt angles The temperature distribution for heat pipe A-0.8 at horizontal orientation was shown in Fig. 5(a). Although a little non-condensable gas remained in the liquid might influence the temperature uniformity, nearly uniform temperature distribution was observed at all the heat loads and dryout did not occur at the power 100 W. However, as shown in Fig. 5(b), heat transfer capacity was dramatically decreased when the heat pipe was tilted at 90°. The condenser end temperature T12 (Fig. 2(a)) was significantly lower than other condenser temperature when increasing the heat load, the reason might be that gravity decreased the liquid volume fraction in evaporator wick and redundant working fluid seemed to accumulate at the condenser. A sudden increase of evaporator temperature T2 was observed at 22 W, it meant the dry patches was firstly at the upstream end of the evaporator and localized vapor blankets might cover it (partial dryout). When increasing the heat load to 30 W, T2 and T3 raised greatly, which might indicate the partial dryout was expanding with enlarging vapor blankets area. Though heat pipe still operated acceptably, the low thermal conductivity vapor blankets would enlarge until covering the complete surface of the evaporator if increased the heat load continuously (totally dryout) [33]. The evaporator thermal resistance versus heat load at different tilt angles for heat pipe A-0.8 is shown in Fig. 5(c). It was clearly that the Revap decreased gradually with increasing the power. At low heat loads, the heat was transported to the liquid surface partly by conduction through the wick and liquid and partly by natural convection, quiescent surface evaporation caused the decrease of Revap. As the heat was increased, some bubbles might form and transport some energy to the surface by vaporization and would also greatly increase convective heat transfer [2]. The intensive evaporation would reduce the effective wetted wick thickness because of the liquid layer retreat in the wick
Fig. 3. Equivalent thermal resistance network in a heat pipe.
R = Qin
T Qin 2
(6)
So, by dividing R, it can be written in following form,
R = R
(
Qin 2 ( T) 2 ) ) +( Qin T
(7)
where ΔT is the temperature difference between T1 and T6. δ(Qin) and δ(ΔT) are uncertainties of the heat load and temperature difference, respectively. At tilted angles of 0°, 30° and 90°, the maximum uncertainties for Revap of heat pipe A-0.8 were 8%, 9% and 9%, respectively. They were 8%, 9% and 9% for heat pipe B-0.8 and 9%, 10% and 10% for heat pipe C-0.8. As for C-1.1, the maximum uncertainties were approximately 9%, 9% and 8%, while they were 8%, 7% and 7% for heat pipe C-1.35. 4
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Fig. 4. SEM images and pore size distributions (a),(b) wick structure A sintered by 125–150 μm copper powder, (c) (d) wick structure B sintered by 75–97 μm copper powder.
[37,38]. It brought in a short radial heat transfer path and a large evaporation area, as a result, the Revap decreased continuously. However, noted that there was a critical heat load Qmax at which the heat pipe had a lowest Revap, for example, the lowest Revap was 0.155 °C/W at 62 W when the heat pipe was tilted at 30°. Additionally, when heat load was over the Qmax, the Revap started to increase sharply. Because partial dryout led to localized evaporator surface was covered by vapor blankets, which impeded the heat transfer and decreased the effective evaporation area. Hence, part of the increased power directly overheated the copper block, the wick and the vapor rather than transferred sufficiently by phase change [39], as a result, T1, T2 and then T3 raise up leading to the rise of Revap sharply. Since the value of Qmax was consistent with that from the temperature distribution figure, the parameter Qmax was used to judge the occurrence of dryout and to evaluate the heat pipe anti-gravity performance in this study. It was found that the Qmax might be over 100 W at horizontal orientation, but decreased to 62 W and 20 W at the inclination of 30° and 90°, respectively. Because the extra gravitational pressure loss increased with increasing anti-gravity angles. Moreover, smaller thermal resistance was found at lower heat loads when the heat pipe was tilted from 0° to 90°. This might be explained by that the working fluid volume fraction decreased with increasing adverse tilted angles, which reduced the liquid layer thickness in the wick. The temperature distribution for heat pipe B-0.8 at horizontal orientation is shown in Fig. 6(a). Nearly uniform temperature distribution below 60 W was observed, but T12 was obviously lower than T11 at 70 W, which indicated liquid gathering at the condenser. Because the intensive evaporation happen in the wick and the high-speed vapor might carry liquid to condenser at high heat load. However, the
redundant working fluid might not be delivered to evaporator timely because of the large flow resistance. Moreover, the occurrence of partial dryout was observed at 80 W as T2 started to raise up apparently. Compared with A-0.8, smaller pores of B-0.8 yielded a bigger capillary force but lower permeability, which made the heat pipe performance degradation even at horizontal orientation. At an inclination of 90°, as shown in Fig. 6(b), gravity also had an adverse effect on heat pipe B-0.8 just like heat pipe A-0.8 though the former having larger capillary force. As clearly seen from Fig. 6(c), the Qmax was 75 W at horizontal orientation, but decreased to 40 W at the inclination of 30°, and reached 20 W at totally anti-gravity orientation. In general, the Qmax was as low as 20 W at the inclination of 90° for both heat pipe A-0.8 and B-0.8, which might be the result of higher permeability but a lower capillary force for A-0.8 while the opposite for B-0.8. In conclusion, the homogeneous wick with smaller or larger pore showed a strong sensitivity to adverse tilt angles. 3.3. Heat transfer performance of axially graded wick Fig. 7 illustrates the evaporator resistance versus the heat load for three different wick structures with same wick thickness of 0.8 mm at different tilted angles. At horizontal orientation (Fig. 7(a)), it seemed that the tendency of Revap was different for different wick structures. For homogeneous wick structure A and B, the Revap almost decreased monotonically before partial dryout. However, for axially graded structure C, the decrease of Revap was stair-stepping. It might be related to the retreat process of the liquid layer in the wick. For homogeneous wick, the liquid layer became thinner and thinner with increasing heat load, the decreased liquid layer thickness and increased evaporation 5
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Fig. 5. Heat transfer performance for heat pipe A-0.8 at different angles (a) temperature distribution at 0°, (b) temperature distribution at 90°, (c) evaporator thermal resistance as a function of the power.
Fig. 6. Heat transfer performance for heat pipe B-0.8 at different angles (a) temperature distribution at 0°, (b) temperature distribution at 90°, (c) evaporator thermal resistance as a function of the power.
area promoted the decrease of Revap in the heat load 5–75 W, Eq. (2) also shows that the Revap decreases with increasing the effective thickness of wetted wick. However, the lower wick permeability of heat pipe B-0.8 limited the reduction of Revap and caused the partial dryout early. For the axially graded wick, smaller pore at evaporator produced larger capillary driving force, larger pore at adiabatic and condenser section exhibited higher permeability. Therefore, compared with homogeneous wicks, the liquid supply to evaporator for axially graded wick might be timelier at the same load, which made the liquid retreat process slowly. Thus, the decrease of Revap was also slowly in the heat load of 15–65 W. But with further increase of heat load, the liquid layer thickness might decrease abruptly because the mass of liquid evaporation was large in the heat load 70–80 W, which led to the decrease of Revap sharply. And another balance between liquid evaporation and liquid supply might be established through the synergetic effect of axially graded wick structure in the heat load of 80–100 W. Moreover, dryout did not happen at 100 W for heat pipe C-0.8, but occurred at about 75 W for B-0.8, which implied the performance improvement for
the axially graded structure heat pipe. As shown in Fig. 7(b), although the Qmax of all heat pipes decreased when heat pipes were tilted at 30°, it reached about 79 W for heat pipe C-0.8, which was nearly 1.27 times that of heat pipe A-0.8. And compared that with heat pipe B-0.8, it was increased by 100%. At totally anti-gravity orientation, as shown in Fig. 7(c), the lower thermal resistance of axially graded heat pipe than that of homogenous wick heat pipe was observed. This probably because the higher capillary force at evaporator and higher permeability at adiabatic and condenser section sustained a thinner liquid layer at the bottom of the wick, thus caused the decrease of Revap. The Qmax was 20 W for both the homogeneous wick heat pipes, but that of axially graded heat pipe was 35 W, which was 75% higher. This was to be expected because the smaller pore at evaporator exhibited larger capillary pumping ability for axial liquid suction while the larger pore at adiabatic and condenser section provided lower flow resistance passages for liquid circulation, hence the synergetic effect of axially graded wick structure promoted the increase of Qmax notably. 6
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Fig. 7. Evaporator thermal resistance as a function of the power for heat pipe with different wick structures at a thickness of 0.8 mm and at different tilted angles (a) 0°, (b) 30°, (c) 90°.
Fig. 8. Evaporator thermal resistance as function of the power for axially graded heat pipes with different wick thickness at different tilted angles (a) 0°, (b) 30°, (c) 90°.
3.4. Effect of wick thickness on the heat transfer performance of axially graded wicks
0.175–0.185 °C/W in the heat load of 60–96 W, and the Qmax reached a rather high level of 96 W for heat pipe C-1.35, which was about 170% and 100% higher compared with that of C-0.8 and C-1.1, respectively. Based on the synergetic effect of axially graded structure, thicker wick provided a wider path for liquid flow and further improved the permeability especially at the evaporator, which ensured enough liquid supply to sustain fluid circulation even at high heat load. Therefore, the Qmax was further increased dramatically for axially graded heat pipe when increasing the wick thickness.
At horizontal orientation, as shown in Fig. 8(a), it was interesting that the decreasing tendency of Revap for all axially graded heat pipes was stair-stepping, which suggested that the stair-stepping decrease trend of Revap was probably related to the axially graded wick structure. The Revap of heat pipe C-1.35 was nearly the highest because thicker wick provided a long radial path for heat transfer. Moreover, all the axially graded heat pipes operated at heat load 100 W without dryout. But the true Qmax might be much higher than 100 W for all axially graded heat pipes and other flat stages of Revap might exist at high heat load. Because two flat stages of Revap were still remained and dryout did not appear at the heat load 100 W for heat pipe C-1.1 and C-1.35 despite tilted at 30°, as shown in Fig. 8(b). However, the Qmax was 79 W at the inclination of 30° for heat pipe C-0.8, which indicated that the Qmax was enhanced by increasing the wick thickness. At the totally antigravity orientation, as shown in Fig. 8(c), it was clearly that both the Revap and Qmax increased with increasing the wick thickness, which was consistent with the results from relative studies [31,40]. The Revap was
4. Conclusion An experimental study on homogeneous and axially graded wick of copper-water micro heat pipe was performed. The effect of tilt angles, wick structures and wick thicknesses on heat transfer performance were studied. The following results were obtained: (1) Large pores are formed by sintering coarse copper powder, and small pores are formed by sintering fine copper powder. (2) The Revap decreases with increasing the tilt angle from 0° to 90° but 7
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accompany with an early occurrence of partial dryout, from which the Revap starts to increase sharply. Indeed, heat pipes with homogeneous wick show a strong sensitivity to adverse tilt angles. (3) The Qmax of axially graded heat pipe C-0.8 is increased by 75% compared with that of homogeneous wick heat pipes at the inclination of 90°. The significant increase of Qmax is due to the reconciliation between capillary force and permeability. Moreover, the tendency of Revap-Q is stair-stepping for axially graded wick, while it is monotonic for homogeneous wicks. (4) Though the thermal resistance increases with increasing the wick thickness, the sensitivity to gravity can be minimized simultaneously. Both axially graded heat pipe C-1.1 and C-1.35 can operate at heat load 100 W without the occurrence of dryout though tilted at 30°. Moreover, the axially graded structure heat pipe C-1.35 has the highest Qmax of 96 W when the heat pipe is tilted at 90°.
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We expect that the proposed axially graded structure micro heat pipe can not only have applications on anti-gravity situations, but also be applied on high heat flux occasions at horizontal orientation. Because the true Qmax of heat pipes with axially graded wick structure may be much higher than 100 W at horizontal orientation based on the change trend of Qmax and tilt angles. More work can be done to optimize the axially graded structure to maximize the heat transfer capacity. Acknowledgements This work was supported by “the Fundamental Research Funds for Central Universities (China)”. Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.applthermaleng.2019.114413. References [1] B. Zohuri, Heat pipe design and technology: modern applications for practical thermal management, 2nd ed., Springer International Publishing, Cham, 2016. [2] D.A. Reay, Heat pipes, fifth ed., Butterworth-Heinemann, 2006. [3] T. Yousefi, S.A. Mousavi, B. Farahbakhsh, et al., Experimental investigation on the performance of CPU coolers: effect of heat pipe inclination angle and the use of nanofluids, Microelect. Reliab. 53 (2013) 1954–1961. [4] S.B. Riffat, X. Zhao, P.S. Doherty, Developing a theoretical model to investigate thermal performance of a thin membrane heat-pipe solar collector, Appl. Therm. Eng. 25 (2005) 899–915. [5] Y.O. Parent, H.S. Caram, R.W. Coughlin, Tube-wall catalytic reactor cooled by an annular heat pipe, AIChE J. 29 (1983) 443–451. [6] Y. Maydanik, V. Pastukhov, M. Chernysheva, Development and investigation of a loop heat pipe with a high heat-transfer capacity, Appl. Therm. Eng. 130 (2018) 1052–1061. [7] B. Chnookaraju, P.S.V. Kurmarao, S.N. Sarada, Thermal analysis of gravity effected sintered wick heat pipe, Mater. Today Proc. 2 (2015) 2179–2187. [8] Z. Hongxing, M. Min, M. Jianyin, W. Lu, C. Yang, et al., Development and on-orbit operation of loop heat pipes on chinese circumlunar return and reentry spacecraft, J. Mech. Sci. Technol. 31 (2017) 2597–2605. [9] F. Zhou, W. Duan, G. Ma, Thermal performance of a pump-driven loop heat pipe as an air-to-air energy recovery device, Energy Build. 151 (2017) 206–216. [10] G.P. Peterson, An introduction to heat pipes: modeling, testing, and applications, Wiley, New York, 1994. [11] Y.F. Maydanik, Loop heat pipes, Appl. Ther. Eng. 25 (2005) 635–657. [12] R. Manimaran, K. Palaniradja, N. Alagumurthi, K. Velmurugan, An investigation of thermal performance of heat pipe using Di-water, Sci. Technol. 2 (2012) 77–80.
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