Heat transfer analysis of a loop heat pipe with biporous wicks

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Heat transfer analysis of a loop heat pipe with biporous wicks

Chien-Chih Yeh, Chun-Nan Chen, Yau-Ming Chen

*

Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan, ROC

a r t i c l e

i n f o

Article history:

Received 15 October 2008

Received in revised form 23 January 2009 Accepted 18 March 2009

Available online 15 May 2009

Keywords: Loop heat pipe Evaporative heat transfer Biporous wick Monoporous wick

a b s t r a c t

Because the evaporative heat transfer of a wick structure in a loop heat pipe is exceedingly sensitive to the internal volume fractions of liquid and vapor phases, the purpose of this study was to investigate the evaporative heat transfer of various biporous wick parameters by controlling the particle size of pore for-mer, the pore former content, and the sintering temperature. A statistical experiment was carried out to analyze the evaporative heat transfer of the biporous wicks and to understand the effects of the param-eters more effectively. The statistical analysis indicated a clear and strong relationship between the effect of the pore former content and the evaporative heat transfer of a biporous wick. This is because the pore former content had a great influence on the probability of large interconnecting pores and an extended surface area for liquid film evaporation in a biporous wick. Experimental results also showed that, at the sink temperature of 10 °C and the allowable evaporator temperature of 85 °C, the evaporative heat trans-fer coefficient of the biporous wick, which reached a maximum value of 64,000 W/m2_{K, was} approxi-mately six times higher than that of the monoporous wick.

1. Introduction

The liquid ﬁlm evaporation in porous media is a very efﬁcient heat transfer method utilized in two-phase heat transport devices such as heat pipes, capillary pumped loops (CPLs), and loop heat pipes (LHPs). More recently, with the increasing demand of ther-mal management for advanced electronic cooling, the heat-dissi-pating technologies of these devices have been already more critical.

In 1994 Wolf et al. [1] pointed out that LHPs combine the advantages of both conventional heat pipes and CPLs. In addition, a LHP possesses the following advantages so this device is chosen to be the object of research in this study:

passive heat transport system – no moving parts;

a highly efﬁcient design of the inverted meniscus type evaporator;

a low thermal resistance;

ability to work reliably in operation; ability to operate against gravity; self-priming – requires no power input; ﬂexible heat transport lines;

to transport large amounts of heat over long distances with min-imal temperature drops;

A LHP was ﬁrst invented and developed in the former Soviet Un-ion in 1974[2]. These researchers have demonstrated LHPs’ effec-tiveness, reliable, and long-term operation in spacecraft thermal control. In the last several decades LHPs have been necessary and widely utilized not only in space but also in ground applications such as electronic cooling, solar heat collector, avionics cooling, air conditioner, refrigeration systems, etc.

The LHP system consists of an evaporator, a condenser, a com-pensation chamber, a vapor transport line, and a liquid transport line. A wick structure is only localized in the evaporator. A sche-matic of the LHP system can be found inFig. 1.

A LHP relies on the surface-tension force of a fine wick structure under application of heat to drive a working fluid. When heat is applied to the evaporator, the liquid is vaporized to generate the inverted menisci at the liquid–vapor interface in the wick; mean-while, the wick develops the capillary force to transfer the vapor through the vapor line to the condenser. After the vapor is con-densed, the capillary force continues to push the liquid back to the evaporator. According to the aforementioned, the main pur-pose of a wick is to develop the capillary pressure to circulate a working fluid around the loop and to generate the liquid film evap-oration. Hence, there is a close relation between the design of a wick structure and the heat transport capability of a LHP.

In recent years, miniature LHPs have been already researched more and more for passive cooling of high-power electronic and optical components. Through the analysis of the total thermal resistance for a miniature LHP, it can be also understood that the total thermal resistance is mainly inﬂuenced by the designs of the evaporator and condenser [3]. Because the design of a

*Corresponding author. Address: Department of Mechanical Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei, 10617 Taiwan, ROC. Tel.: +886 2 33662730; fax: +886 2 23631755.

E-mail address:[email protected](Y.-M. Chen).

Contents lists available atScienceDirect

International Journal of Heat and Mass Transfer

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condenser is usually determined by the different environments, it will not be discussed here. The evaporator thermal resistance mainly consists of the thermal resistance of the evaporator wall thickness, the contact thermal resistance between the wick outer surface and the evaporator wall, the thermal resistance of a vapor blanket inside the wick, and the film resistance. At high heat fluxes, formerly a monoporous wick was intolerant of boiling and easily occupied by the vapor to form a vapor blanket, leading to raise the thermal resistance. Because the thermal conductivity of a vapor blanket layer is very low, it increases the evaporator temperature. This presents a serious hurdle to using a monoporous wick for re-moval of high heat fluxes from smaller surfaces. Therefore, how to increase a wick heat flux limit by reducing a vapor blanket inside a wick will be important. To that end, the design of a wick structure is one of the major preoccupations of a miniature LHP. In general, a wick structure design can be classified into the designs of outer va-por grooves and inner wick structure parameters (effective va-pore ra-dius, porosity, and permeability). They both will affect the amount of the vapor escaped from the wick and the volume fractions of li-quid and vapor phases inside a wick. However, with the decreasing evaporator diameter of a miniature LHP, the manufacture of outer vapor grooves on a wick structure has become more difficult.

In order to avoid the foregoing problems, wick structures with bimodal pore size distributions are utilized to improve the heat transport capability of miniature LHPs. The advantages of wick structures with bimodal pore size distributions are that the large pores reduce a vapor blanket layer to impede the returning liquid ﬂow, and that the small pores continue to function as liquid supply routes and increase the evaporative surface area at the same time. In general, bidispersed wicks and biporous wicks can make the wick structures with bimodal pore size distributions.

Early heat transfer experiments of bidispersed wicks can be traced back to Vityaz et al.[4]. They utilized the surface oxidation on sintered copper wick structure to generate the bidispersed wick, which was characterized by a bimodal pore size distribution, as heat pipe wick. The bidispersed wick structure could signiﬁcantly increase the heat transport capability. Additionally, Konev et al.

[5] investigated boiling phenomenon in wick structures and

pointed out that a bidispersed wick enhances the boiling heat transfer to a greater extent than a monoporous wick. Afterwards, a biporous material was proposed by Rasor and Desplat[6]. Their K-Max consists of a solid biporous material that has exceptional heat transfer properties and is similar to a heat pipe. In addition, they also mentioned that two different types of pore sizes can be existed in a biporous wick like a bidispersed wick. The structural differentiation between a biporous wick and a bidispersed wick was described and illustrated in this literature.

Rosenfeld and North[7]indicated that a bidispersed wick takes advantage of the highly effective heat transfer intrinsic to liquid film evaporation in heat pipe operation. The evaporative character-istic of a bidispersed wick was described particularly and discussed for the potentiality of optics applications. North et al.[8]reported the liquid film evaporation from bidispersed wicks in heat pipe evaporators and explained the improvement of heat transfer due to an extended surface area for evaporating thin film from the bid-ispersed wick. Additionally, North et al.[9]proposed that the LHP’s evaporators with bidispersed wicks are effective to prevent a vapor blanket of the wick and then work at very high heat-flux densities. Nevertheless, there is very limited study on the effect of the bidi-spersed wick parameters and the relative manufacturing proce-dures of the bidispersed wick in this study.

In subsequent years Wang and Catton [10–11] carried out numerous studies about the effectiveness of bidispersed wicks for heat pipes. Semenic and Catton[12]proposed the effects of bid-ispersed wick parameters such as powder size, and cluster size, wick thickness, and liquid feed length for a heat pipe. The results indicated that a capillary pressure of small pores generated by powder size is a dominant parameter.

As reviewed and summarized previous studies, the majority of research in bidispersed wicks has focused on the behavior of vaporization heat transfer in heat pipes. A number of studies have suggested the beneﬁts of bidispersed wicks in pool boiling and heat pipes. However, few studies have been done on the procedure for making the bidispersed wick and the effect of the bidispersed wick parameters in LHPs. However, a biporous wick can provide higher porosity than a bidispersed wick. It cannot only decrease the effect of heat leak through the biporous wick to the compensa-tion chamber in the design of a LHP evaporator with the ‘‘inverted meniscus scheme”, but also can increase the surface area for liquid ﬁlm evaporation. In addition, because large pores generated by dis-solving the pore formers in biporous wicks are easier to control than those passively formed by collecting the clusters of small por-ous particles in bidispersed wicks, the effects of varipor-ous bimodal pore size distributions are demonstrated through biporous wicks in this study.

Because the heat transport capability of a LHP is exceedingly sensitive to a bimodal pore size distribution in the biporous wick, the purpose of this study was to investigate the evaporative heat transfer phenomenon of various biporous wicks in a LHP. A statis-tical method was used to analyze the evaporative heat transfer of the biporous wicks and to ﬁnd out the better biporous wick. Nomenclature

Ah heating surface area (m2)

h heat transfer coefﬁcient (W m2_K1₎

htotal aggregate value of the heat transfer coefﬁcient

(W m2_K1₎

Q heat load (W)

Rtotal total thermal resistance (°C W1)

Te evaporator temperature (°C) Tv vapor temperature (°C) Tc condenser temperature (°C) Subscripts c condenser e evaporator h heating total total v vapor Fig. 1. Schematic of a LHP.

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This investigation may lead to a better understanding of how the biporous wick parameters affect the evaporative heat transfer and be important for the related design of wick structures.

2. Experimental apparatus and procedures

2.1. LHP design and test method

All tests were examined in the same LHP system.Table 1gives the main design parameters of the LHP. The LHP test bed was placed horizontally to avoid any inﬂuence of the gravity force. The LHP evaporator was built with aluminum, and the wick structure was made from nickel powder, which was commercially available and compatible with the ammonia working ﬂuid of the LHP. Other com-ponents of the LHP system were built with stainless steels.

All tests were performed under the near ambient environment, and the condenser sink temperature was controlled to 10 ± 2 °C by a water cooler. Heat was applied to the evaporator through a cop-per heater block by a DC power supply (deviation of ±0.5%), and the heat input area was 1948 mm2_{. The thermocouple measurements}

were recorded and transferred to the computer through a GPIB card. The location of 12 T-type thermocouples (deviation of ±0.2 °C) is given inFig. 1.

For the heat transport capability of the LHP, the temperature change on the evaporator surface was measured by per 50 W, and

the heat load was increased from 50 to 570 W. In general, it is rec-ommended that the surface temperature of common electronic chips shall not exceed 85 °C[13]. It can be considered as an impor-tant reference if loop heat pipes are used in common electronic chips in the future. The heat transport capacity was taken to be a maximum if the evaporator temperature started to exceed 85 °C.

In order to examine the enhancement on the thermal perfor-mances for the different wick structures used, the calculation of the heat transfer coefficient in the evaporator will be analyzed. In the present study, the heat transfer coefficient in the evaporator is defined as:

h ¼ Q

AhðTe TvÞ ð1Þ

where Q is the heat load, and Ahdenotes the heating surface area. In

addition, Teis the evaporator temperature, and Tvis the vapor

tem-perature which is taken as the temtem-perature on the surface of the va-por outlet tube.

The total thermal resistance can be obtained by

Rtotal¼Te Tc

Q ð2Þ

where Tcis the condenser sink temperature.

An uncertainty analysis carried out on the lines suggested by Kline and McClintock[14] showed that the uncertainty involved in the estimation of the heat transfer coefficient in the evaporator Eq.(1)were ±12% at low heat fluxes and ±5% at high heat fluxes, and this involved in the estimation of the total thermal resistance Eq.(2)was within ±2.48%.

2.2. Method of manufacturing the biporous wick structure

As a rule, there are two methods to manufacture wick struc-tures with bimodal pore size distributions: consolidation of porous particles (here it is deﬁned as ‘‘bidispersed wick”) and creation of biporous materials (here it is deﬁned as ‘‘biporous wick”). The scanning electron microscopy (SEM) images of two wick structures can be gained fromFig. 2.

Because large pores generated by dissolving the pore formers in biporous wicks are easier to control than those passively formed by collecting the clusters of small porous particles in bidispersed wicks, the effects of various bimodal pore size distributions are demonstrated through biporous wicks. Biporous wicks and mono-porous wicks were made from the same nickel powder as a basic component. A schematic view of the process to produce a biporous wick is illustrated inFig. 3.

First of all, pore formers (Na2CO3) which had the suitable

parti-cle size (32–48

l

m or 74–88

l

m) and content (20% by volume or 25% by volume) were mixed uniformly with ﬁlamentary nickel powder. Then, the mixing powder ﬁlled into the mold was sintered to manufacture a biporous wick in the furnace. The smaller pores of the biporous wick could be generated by sintering the nickel

Table 1

Main design parameters of the LHP.

LHP evaporator

Total length (mm) 65

Active length (mm) 40

Outer/Inner diameter (mm) 15.5/12.5

Material Aluminum

Sintered nickel wick

Number of vapor grooves 8

Pore radius (lm) 1.5–17 Porosity (%) 70–85 Permeability (m2 ) 1012_–1013 Outer/inner diameter (mm) 12.5/9 Compensation chamber Outer/inner diameter (mm) 29/24 Length (mm) 118 Charge mass Ammonia (g) 38 Vapor line Outer/inner diameter (mm) 6.4/5 Length (mm) 470 Liquid line Outer/inner diameter (mm) 6/4 Length (mm) 583 Condenser Outer/inner diameter (mm) 6.4/5 Length (mm) 800

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powder; the larger pores of the biporous wick could be formed by dissolving the pore formers after the sintering process. By the way, pore formers were used to control the size and amount of larger pores in the wick. Finally, two different types of pore sizes could be existed in the wick at the same time. The appearance of the biporous wick can be seen inFig. 4.

2.3. Experimental design

The designs of vapor grooves and wick parameters in the evap-orator would be the key impact on the performance of a LHP. In or-der to differentiate the effects between vapor grooves and wick parameters, the eight axial vapor grooves made on the wick outer surface were ﬁxed. Then, the heat transfer coefﬁcient in the evap-orator would be analyzed by only changing the wick parameters.

A statistical experimental design was applied to increase the efﬁciency of this study and to make the conclusions be valid and objective. The study is conducted following a statistical method using a two-level factorial plan involving three variables (particle size of pore former: 32–48 and 74–88

l

m Na2CO3, pore former

content: 20% by volume and 25% by volume, and sintering temper-ature: 650 and 750 °C), as observed inTable 2. The experimental design was that of three factors such as particle size of pore former (A), pore former content (B), and sintering temperature (C), each run at two levels. This is a 23_{factorial design. The variables A, B,}

and C are deﬁned on a coded scale from 1 to +1 (the low and high levels of A–C). Furthermore, in order to consider the curvature ef-fect in the response function, the test for curvature would be per-formed by adding several center points to the 23factorial design. Finally, the regression model could be represented by the terms of coded factors. For more details, see Montgomery[15].

The heat transfer coefﬁcient change in the evaporator was mea-sured by per 50 W and the heat load was increased from 50 to 570 W. In these experimental processes, the response variable was the aggregate value of the heat transfer coefﬁcient in the evap-orator (htotal) from 50 to 570 W. This reason was to evaluate the

whole heat transfer coefﬁcient, but not the certain one. Then, the

experimental results identiﬁed and investigated by the statistical software (DESIGN-EXPERT software) were analyzed to ﬁnd the re-gion of the optimal parameters.

According to the experimental design with three independent variables (particle size of pore former, pore former content, and sintering temperature) and two levels of each variable, a 23_design

augmented with three center points yielded a total of 11 runs. The test results of eleven biporous wicks, one monoporous wick, and two conﬁrmation experiments are listed inTable 3.

3. Results and discussion

3.1. Statistical analyses of biporous wicks

The heat transfer coefﬁcient data were entered into the design matrix (Table 3) planned by the statistical software to determine the signiﬁcant variables. This method allows establishing a statis-tical relationship between experimental variables and the response (htotal). Then, a regression analysis is carried out to develop a

best-ﬁt model to the experimental data. It can be used to generate re-sponse surface plots[15].

In order to reduce the insigniﬁcant model terms, the effect estimate was ﬁrst performed to improve the model. Table 4

summarizes the effect estimates and sums of squares. The percent contribution is often effective guide to the relative importance of each model term. It is noteworthy that the main effects of A (15.59%), B (76.35%), and the AB interaction (4.19%) really dominated this process, accounting for over 96% of the total variability.

The other C, AC, BC, and ABC variables accounted for less than 4% can be ignored. The analysis of variance (ANOVA) inTable 5, which illustrates the output following removal of the nonsignifi-cant terms, may be used to confirm the magnitude of these effects and reveal the result of the test of significance of factors and inter-actions for the htotal.

When p-value (probability value) of one term is more than 0.05 (a specified significant level), indicating that this is insignificant at the 95% confidence level and so that term must be discarded. After discarding insignificant terms,Table 5illustrates that the regres-sion model was significant (F-value = 69.50, p-value < 0.05). The main effects of A, B, and the AB interaction were significant (all have small p-values); thus, A, B, and AB can be taken as significant factors at a confidence level of 95%. The curvature in the design space was not significant relative to the noise (F-value = 2.39, p-va-lue > 0.05). Therefore, the assumption of linearity over the region of exploration was adequate for the regression model.

The regression model equation describing this relationship in terms of coded factors was as follows:

htotal¼ 274:67 30:85Acodeþ 68:26Bcode 15:99AcodeBcode ð3Þ

A regression model for predicting the htotalwas established by the

statistical software, which R2_{was 0.9720 and R}2

adjwas 0.9580. These

indicated that the model would be expected to explain the experi-mental data very well.

Fig. 3. Schematic view of the process to produce the biporous wicks.

Fig. 4. The appearance of a biporous wick.

Table 2

The selected variables and experimental deign levels used.

Variables Units Symbol Coded levels

1 +1

Particle size of pore former lm A 32 48 74 88

Pore former content % B 20 25

Sintering temperature °C C 650 750

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3.2. The effects of the biporous wick parameters

From Eq.(3), one can see that the effect of the particle size of pore former (negative algebraic sign for factor A) was negative; that is, decreasing the particle size of pore former improved the htotal. On the other hand, positive trend was observed with the pore

former content (factor B). Moreover, the interaction between par-ticle size of pore former and pore former content (AB interaction) negatively affected the htotal. It is important to emphasize that

the sintering temperature (factor C) within the studied range (650–750 °C) did not obviously affect the htotal.

It can be used to generate the response surface plot according to Eq.(3).Fig. 5presents the response surface and contour plot for the htotal obtained from the regression model. The contour plot

dis-played that a direction orientation is dominated by decreasing A and increasing B, the htotalwill be higher. Obviously, the effect of

B was more than that of A. The better htotalof the biporous wick

(Sample3 or Sample7) tended to the lower level of A (32–48

l

m), the higher level of B (25% by volume), and less AB interaction. This probably indicated that the probability of large interconnecting pores in a biporous wick can be improved to form more vapor transport channels by increasing B. It will inﬂuence not only the volume fractions of liquid and vapor phases but also a higher per-meability. Besides, decreasing A can generate more number of large pores and the extended surface area for the liquid ﬁlm evap-oration in the same pore former content. This information provides a direction of the potential improvement.

According to Eq.(3), the two largest coefﬁcient estimates are A = 30.85 and B = 68.26. Although the effect of B is more than that

of A, the strength limit of a biporous wick will not allow exceeding the higher level of B (25% by volume). On the other hand, the lower level of A (32–48

l

m) can continue to be decreased to around 20– 32

l

m (the current sieve limitation). In other words, the optimal parameters of the biporous wick may be expected to be located near 25% by volume for the pore former content and 20–32

l

m for the particle size of pore former.

3.3. Conﬁrmation experiments

The experimental and predicted values were compared in order to determine the validity of the model and confirm whether the relative important factors were ignored. Hence, two confirmation experiments are planned to confirm the results inTable 6. These findings appeared that the errors between the experimental and predicted values were all less than 7%. They demonstrated the pre-dicted model was valid and adequate.

3.4. Heat transfer performances of monoporous and biporous wicks

In order to examine the heat transfer performances for the dif-ferent wick structures used, one monoporous wick (Sample14), the better and worse biporous wicks (Sample7 and Sample2) were chosen particularly to discuss here. The parameters of all wick

Table 3

Properties of the wicks tested.

Sample Experimental design variables Heat transfer coefﬁcient (kW m2

K1 ) Response Biporous wick NPS (lm) A (lm) B (%) C (°C) 50 W 100 W 150 W 200 W 250 W 300 W 350 W 400 W 450 W 500 W 550 W 570 W htotal (kW m2 K1 ) 1 3 32–48 20 650 9.51 15.11 15.41 18.02 19.76 20.28 22.76 22.83 20.10 14.85 15.61 15.17 209.40 2 3 74–88 20 650 6.94 8.71 12.43 12.68 15.47 13.52 13.03 14.37 22.89 22.33 22.25 22.52 187.13 3 3 32–48 25 650 8.56 19.02 14.54 14.27 37.77 42.81 99.88 46.70 39.85 41.42 24.57 15.66 405.04 4 3 74–88 25 650 12.23 13.17 19.26 23.35 24.23 24.08 33.29 42.81 34.50 26.48 18.23 13.07 284.69 5 3 32–48 20 750 10.27 11.17 12.04 12.84 19.17 21.40 23.97 28.15 27.85 20.55 23.54 22.18 233.13 6 3 74–88 20 750 8.03 11.17 13.06 14.47 14.43 17.12 20.20 22.83 22.66 17.59 16.24 18.19 195.98 7 3 32–48 25 750 13.52 22.33 22.01 22.33 25.68 32.10 42.81 64.21 52.53 29.86 24.57 22.52 374.48 8 3 74–88 25 750 8.86 16.57 16.75 16.57 18.09 34.24 42.81 42.81 42.03 38.33 19.09 11.35 307.48 9 3 53–62 22.5 700 9.51 13.88 16.05 19.76 21.40 24.08 29.47 35.43 27.85 23.78 19.76 19.39 260.36 10 3 53–62 22.5 700 11.67 16.57 17.12 20.55 22.14 24.46 26.83 28.54 23.11 20.55 17.23 17.22 245.99 11 3 53–62 22.5 700 11.17 16.05 17.51 21.40 24.70 25.26 23.97 32.10 28.89 23.35 24.57 21.53 270.50 Conﬁrmation experiments 12 3 20–32 25 750 17.12 16.57 16.75 20.55 27.92 34.24 41.81 68.49 53.76 38.91 28.83 26.62 391.56 13 3 124–149 25 750 12.23 14.27 15.41 18.68 21.40 17.92 17.29 17.12 15.72 15.29 14.56 15.83 195.72 Monoporous wick 14 3 – – 750 10.70 12.53 9.51 9.78 10.44 10.63 9.08 8.39 8.44 7.44

Note: NPS, nickel powder size; A, particle size of pore former; B, pore former content; C, sintering temperature.

Table 4 Effect estimate. Factor Stdized effect Sum of squares Percent contribution A-particle size of pore

former

61.69 7611.81 15.59

B-pore former content 136.52 37274.82 76.35

C-sintering temperature 6.20 76.94 0.16 AB 31.98 2045.91 4.19 AC 9.62 184.98 0.38 BC 10.09 203.44 0.42 ABC 17.06 581.96 1.19 Curvature 16.41 538.86 1.10 Table 5 Analysis of variance. Source Sum of squares Degrees of freedom Mean square F-Value p-Value Model 46932.53 3 15644.18 69.50 <0.0001 Intercept A 7611.81 1 7611.81 33.82 0.0011 B 37274.82 1 37274.82 165.59 <0.0001 AB 2045.91 1 2045.91 9.09 0.0236 Curvature 538.86 1 538.86 2.39 0.1728 Residual 1350.60 6 225.10 Lack of ﬁt 1047.32 4 261.83 1.73 0.3987 Pure error 303.28 2 151.64 Corrected total 48822.00 10 R2 0.9720 R2 Adj 0.9580

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structures are explicitly listed inTable 3. The experimental results are described below.

Sample14 (monoporous wick): the temperature difference (Te–

Tv) of Sample14 increases linearly when the heat ﬂux increases, as

shown inFig. 6. Accordingly, the heat transfer coefﬁcient of Sam-ple14 does not change very much with the increase of applied heat ﬂux and is approximate 10,000 W/m2K inFig. 7. This is due to the fact that evaporative heat transfer was dominated by conduction through the wick and evaporation from the meniscus surface area of the wick structure. Consequently, the curve of Sample14 is like a linear shape inFig. 6.

In addition,Figs. 8 and 9present that, at the sink temperature of 10 °C and the allowable evaporator temperature of 85 °C, the max-imum heat transfer capacity of Sample14 is equal to 350 W and the minimum total thermal resistance is equal to 0.22 °C/W.

Sample7 (biporous wick): heat transfer from the heater to the liquid–vapor interface in a biporous wick is a combination of con-duction, convection, boiling, and evaporation. At various heat ﬂuxes, the heat transfer performance will be dominated by the dif-ferent modes of heat transfer. The result of Sample7 reﬂected in

Fig. 6represents that the evaporative heat transfer curve is almost like an S-shape and can be divided into three different regions. This concept is a similar explanation mentioned for a bidispersed wick by Rosenfeld and North[7].

The ﬁrst region (below 128.4 kW/m2_{) reveals that there is an}

al-most linear relationship between the temperature difference and heat ﬂux. Because the evaporation phenomenon only occurs on the surface area of the wick structure at low heat ﬂuxes, the heat transfer is mainly dominated by the conductive mode. In this case,

Fig. 5. Response surfaces and contour plot of the htotal: (a) Response surface and (b) contour plot.

Table 6

Comparison of predicted and experimental values.

Sample Particle size of pore former (lm) Pore former content (vol%) Predict value of htotal(kW m2_K1₎ Experiment value of htotal(kW m2K1) Error (%) 12 20–32 25 416.52 391.56 6.37 13 124–149 25 184.56 195.72 5.70

Evaporator-to-Vapor Outlet Tube Temperature Difference/oC

Heat Flux / (Wm -2 ) 100 101 102 104 105 106

Biporous wick - Sample 2 Biporous wick - Sample 7 Monoporous wick - Sample 14

Fig. 6. Evaporator-to-vapor outlet tube temperature difference vs. applied heat ﬂux. Heat Flux / (kW m-2) Heat T ransfer Coef ficient / (Wm -2 K -1 ) 50 100 150 200 250 300 10000 20000 30000 40000 50000 60000 70000 80000 90000

Biporous wick - Sample 2 Biporous wick - Sample 7 Monoporous wick - Sample 14

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there is only a small amount of vapor generated and the large pores are still ﬁlled with the liquid, as observed inFig. 10a.

The second region (128.4–205.5 kW/m2_{) presents that the}

tem-perature difference decreases with the increase of applied heat ﬂux, and the evaporative heat transfer curve swings back. In this region the evaporative heat transfer coefﬁcient reaches rapidly a maximum value of 64,000 W/m2_{K, is higher in the whole range}

of heat ﬂuxes in Fig. 7. The result could be explained by the

liquid–vapor interface in a biporous wick. With the increase of ap-plied heat ﬂux, the vapor will preferentially occupy the large pores to form the vapor pathways. Consequently, the evaporating menis-ci in a biporous wick include two parts: inverted menismenis-ci in small and large pores. As can be seen inFig. 10b, this is due to the effect that the vapor pathways lead to an extended surface area for liquid ﬁlm evaporation, and the small pores continue to function as liquid supply routes in the biporous wick.

The third region (above 205.5 kW/m2_{) starts when vapor}

path-ways develop completely and the liquid cannot be supplied sufﬁ-ciently by the small pores. The temperature difference grows sharply with the increase of applied heat ﬂux because the dryout starts to occur in the wick inFig. 10c.

According to the aforementioned, the heat transfer coefﬁcient of Sample7, which reaches a maximum value of 64,000 W/m2_{K, is}

approximately six times higher than that of Sample14 inFig. 7. As observed inFigs. 8 and 9, the experimental results show that, at the sink temperature of 10 °C and the allowable evaporator temperature of 85 °C, Sample7 reaches 570 W and the minimum total thermal resistance is 0.10 °C/W. The heat transport capability of Sample7 is better than that of Sample14 for 350 W and 0.22 °C/W. Furthermore, it is important to emphasize that the condenser’s design in the research limits the experimental results. They can be expected to gain the higher heat transport capability if the active surface of the condenser is improved.

In order to provide a better understanding of the difference be-tween a monoporous wick (Sample14) and a biporous wick (Sam-ple7), the porous structure analysis was performed by SEM images. According toFig. 11, the porosity and permeability of Sample14 with a narrow pore size distribution are lower than those of Sam-ple7. With the increase of applied heat ﬂux, the vapor of Sample14 would accumulate gradually to form a vapor blanket between the wick and evaporator wall due to the narrow pore size distribution inFig. 11a. This not only increased the thermal resistance but also reduced the intensity of heat exchange in the evaporative zone. In contrast, Sample7 obviously has two principal pore size distribu-tions and large interconnecting pores inFig. 11b. The large pores of Sample7 not only made the vapor easily escape from the wick but also enhanced the evaporating menisci area in the small pores. Therefore, the probability of large interconnecting pores in a bipor-ous wick is of decisive importance.

Sample2 (biporous wick): the temperature difference of Sam-ple2, slight like an S-shape, almost appears to rise linearly with the increase of applied heat ﬂux as that of Sample14 in Fig. 6. The evaporative heat transfer curve of Sample2 seems to be a linear shape as that of a monoporous wick (Sample14) inFig. 7. The most obvious explanation is due to the effect of the pore former content from the statistical analysis results. With the decrease of the pore former content, the probability of large interconnecting pores in a biporous wick will be decreased. The large pores were easy to form

Heat Load / W Ev aporator T emperature / o C 0 50 100 150 200 250 300 350 400 450 500 550 600 20 40 60 80 100 120 140

Biporous wick - Sample 2 Biporous wick - Sample 7 Monoporous wick - Sample 14 Tamb=20o

C Tsink=10o C

Fig. 8. Evaporator temperature vs. applied heat load.

Heat Load / W T otal Thermal Resistance / ( o C W -1 ) 0 50 100 150 200 250 300 350 400 450 500 550 600 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55

Biporous wick - Sample 2 Biporous wick - Sample 7 Monoporous wick - Sample 14 Tamb=20o

C Tsink=10o C

Fig. 9. Total thermal resistance vs. applied heat load.

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the isolated ones in Sample2, and thus the increase of liquid ﬁlm evaporation was limited. At the same time, few amounts of the other large pores on the surface of the wick became the effect of outer vapor grooves. For this reason, the evaporative heat transfer coefﬁcient of Sample2 is better than that of a monoporous wick (Sample14) inFig. 7.

Furthermore, since the probability of large interconnecting pores for Sample7 was higher than that of Sample2, the vapor pathways of Sample7 were easy to lead to an extended surface area for liquid ﬁlm evaporation. Perhaps the results can be conjectured why the evaporative heat transfer curve of a biporous wick (Sam-ple7) is similar to that of a bidispersed wick[9–11]. Because a bid-ispersed wick is made of clusters of small porous particles, the probability of large interconnecting pores for a bidispersed wick is high between the clusters. However, the clusters must be nice spheres, or else the probability of large interconnecting pores for a bidispersed wick will be low. Further research has been pursued to examine the correlation between biporous wicks and bidi-spersed wicks.

As summarized above, the evaporative heat transfer curve of a wick structure may be determined to be like that of a monoporous wick or a biporous wick by the probability of large interconnecting pores and an extended surface area for liquid ﬁlm evaporation. This is an important relationship between a monoporous wick and a biporous wick.

On the whole, the experimental results have demonstrated that the biporous wicks can be practically implemented to increase the heat transfer coefﬁcient in the evaporator and provide adequate re-sults. With the increase of demand for high performance miniature LHPs, biporous wicks cannot only improve the heat transfer capa-bility but also be advantageous to simplify and replace the manu-facture number of outer vapor grooves on a wick structure. For passive cooling of high-power electronic and optical components, it will be an efﬁcient and simple approach.

4. Conclusions

In this paper, the experimental results showed the evaporative heat transfer characteristics of the monoporous and biporous wicks, and the statistical analysis results demonstrated that the ef-fects of various biporous wick parameters on the evaporative heat transfer coefﬁcient. Experimental results of this study lead to the following conclusions:

1. According to the statistical analysis results, the main effects of the particle size of pore former and the pore former content, and the interaction between particle size of pore former and pore former content were signiﬁcant factors. In contrast, the effect of the sintering temperature was not signiﬁcant within the studied range (650–750 °C).

2. The statistical analysis indicated that the better parameters of the biporous wick tended to the lower level of particle size of pore former (32–48

l

m) and the higher level of pore former content (25% by volume). Moreover, the optimal parameters of the biporous wick were approximately located near 20–32

l

m for the particle size of pore former and 25% by vol-ume for the pore former content.

3. It is noteworthy that there was a clear and strong relationship between the effect of pore former content and the evaporative heat transfer of a biporous wick. When the pore former content was less, the large pores were easy to form the isolated ones. Few amounts of the other large pores on the wick surface became the effect of outer vapor grooves. For this reason, the evaporative heat transfer of the biporous wick appeared to be like that of a monoporous wick. If the pore former content was more, the evaporative heat transfer of the biporous wick would be dominated by the probability of large interconnecting pores and an extended surface area for liquid ﬁlm evaporation. 4. At the sink temperature of 10 °C and the allowable evaporator temperature of 85 °C, the maximum heat transport capability is equal to 570 W for the better biporous wick and 350 W for the monoporous wick, and the minimum value of the total ther-mal resistance is 0.10 °C/W and 0.22 °C/W, respectively. In addi-tion, the evaporative heat transfer coefﬁcient of the better biporous wick, which reaches a maximum value of 64,000 W/ m2_{K, is approximately six times higher than that of the}

mono-porous wick.

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