boiling heat transfer on capillary feed copper particle sintered porous wick at reduced pressure

International Journal of Heat and Mass Transfer 63 (2013) 389–400

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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Evaporation/boiling heat transfer on capillary feed copper particle sintered porous wick at reduced pressure F.J. Hong ⇑, P. Cheng, H.Y. Wu, Z. Sun Ministry of Education Key Laboratory of Power Machinery and Engineering, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dong Chuan Road, Shanghai 200240, PR China

a r t i c l e

i n f o

Article history: Received 12 December 2012 Received in revised form 30 March 2013 Accepted 30 March 2013 Available online 2 May 2013 Keywords: Evaporation Boiling Capillary feeding Reduced pressure Heat pipe Vapor chamber

a b s t r a c t A test facility which can control the liquid level and the evaporation saturation pressure is developed to characterize the water evaporation/boiling on copper particle sintered porous wick under the conditions of capillary feeding at reduced pressures, the main factor determining the performance of a vapor chamber. Nine porous wick samples with different particle sizes, particle types and wick thicknesses are tested at the same reduced pressure. The effective heat transfer coefficient is obtained using an inverse heat transfer method. The experimental results indicate that for all of the tested samples the effective heat transfer coefficient at first increases and then decreases with the increasing of heat flux, and there is an optimum wick thickness at which the maximum effective heat transfer coefficient could be achieved when the particle size and type (or porosity) are fixed. The theoretical analysis indicates that bubble nucleation is much more difficult to occur at a reduced pressure compared to atmospheric pressure, and as a result, the boiling heat transfer may only occur when the heat flux is high enough and the liquid level has receded into the wick. Consequently, bubble nucleation normally cannot be visualized experimentally at a reduced pressure. The heat transfer model of the evaporation/boiling in thin porous wicks (<1 mm) under capillary feeding and reduced pressure conditions is also summarized and it can be used to explain all the present experimental phenomena. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction Air cooling remains the most desirable cooling method for electronic devices considering the issues of safety, system complexity and cost, provided its heat dissipation capability can still satisfy the demand. Heat pipe heat spreaders, such as traditional tube heat pipe and modern vapor chamber (it is also called vertical flat heat pipe in some references) can transport localized high heat flux within a small area using liquid–vapor phase change to the places where the heat can be dissipated to the environment using aircooled fins with large heat transfer area, and therefore mitigating the need for liquid cooling technologies. While traditional tube heat pipe has been available for more than 25 years and its applications on laptop computer have been very successful, vapor chamber represents a relatively new technology that became commercially available during the mid-1990s and is being used increasingly today. According to its working principle, a vapor chamber as shown in Fig. 1 can be considered as a 2-D heat pipe with omnidirectional vapor flows compared to the unidirectional vapor flow in traditional tube heat pipe.

⇑ Corresponding author. Tel./fax: +86 21 34206337. E-mail address: [email protected] (F.J. Hong). 0017-9310/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.03.086

The heat transfer capability of a traditional heat pipe is limited by a number of factors, i.e., the sonic limit, the viscous limit, the entrainment limit, the capillary limit and the boiling limit [1]. For the vapor chamber shown in Fig. 1, the space for vapor flow is large and the vapor flow and the liquid flow are not in the same path, so, the first three limits normally will not occur, and the capillary limit and the boiling limit are the two main factors that limit the heat transfer capability. The pressure balance among the wick and the vapor core within heat pipe devices can be expressed by Dpc = Dpl + Dpv + Dpb, where Dpc is the capillary pressure, the driven force of the liquid flow; Dpl is the pressure drop of the liquid flow in the wick; Dpv is the pressure drop of the vapor flow in the vapor channel, and the Dpb is the gravity body force. Both Dpb and Dpv can be ignored in a vapor chamber, and therefore Dpc = Dpl. With the increasing heat transfer rate, more liquid need to be vaporized, so, the liquid mass flow rate inside the wick has to increase, causing the increasing of Dpl. Therefore, the capillary radius has to become smaller to increase the pressure differential across the liquid–vapor interface Dpc. The capillary radius adjusts until the surface tension can no longer support the pressure difference and the meniscus collapses. The failure causes a rapid reduction in the heat transfer coefficient in the evaporator, driving up evaporator temperature and ultimately causing the heat pipe to stop functioning, which is the so called

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Nomenclature D g h(x) heff hfg H J(P) keff K L m00 pd pv pe Dpc Dpl Dpv Dpb Pi q00 rb rc

pore size gravity acceleration velocity the local effective heat transfer coefficient of porous wick structure the effective heat transfer coefficient of porous wick the latent heat of evaporation the liquid level difference between condensation and evaporation chambers the Jacob sensitivity matrix in inverse heat transfer simulation the effective heat conductivity of porous wick structure the permeability of porous wick the length of liquid receding into porous wick evaporation mass flux the pressure in condensation chamber vapor saturation pressure the pressure in evaporation chamber capillary pressure liquid flow resistance vapor flow resistance the pressure difference due to gravity body force the parameter vector for the construction of B-spline curve heat flux initial radius of embryo bubble meniscus radius at evaporating wick surface

‘‘capillary limit’’ [1]. Mechanically, the failure mechanism can be described as that the vapor is forced into the wick, causing the wick to dry out. The radius that can support the maximum differential pressure across the liquid–vapor interface is so called the effective capillary radius, which along with the liquid permeability (related to Dpl), determine the capillary limit of a wick. Both the effective capillary radius and liquid permeability are properties of a wick and mainly affected by the pore structure and size. The smaller pore size normally has smaller effective radius, i.e., larger maximum capillary pressure, but it at the same time reduces the permeability, i.e., increases the coefficient of flow resistance. This means that there is an optimum pore size to achieve the highest capillary limit. If the wick is saturated with liquid and the primary phase change is the evaporation at the liquid–vapor interface, a simple 1-D heat conduction model for the heat transfer from the heat pipe wall to the wick surface can be built [2]. In rectangular coordinates,

Fig. 1. The schematic of working principle of vapor chamber.

rn Rcr S(P) t TC TM Tpw Tv Twv Tw DTlv x, y, z

minimum radius for bubble growth thermal contact resistance between heating block and porous wick sample the residual function in inverse heat transfer simulation the thickness of wick structure the calculated temperatures at the measurement points the measured temperatures at the measurement points the temperature of liquid at the wick/wall interface vapor saturation temperature the temperature of liquid at wick/vapor interface the bottom center temperature of wick structure the liquid superheat at the bottom of wick structure coordinates

Greek symbols b the temperature coefficient of surface tension e stopping criteria for inverse heat transfer simulation; porosity of porous wick l damping coefficient for inverse heat transfer simulation lv vapor dynamic viscosity X the matrix used in inverse heat transfer simulation /li ðxÞ B-spline basic function with the order of l ql liquid density qv vapor density r surface tension

this heat flux in the evaporator can be expressed as q00 ¼ keff ðT pw  T wv Þ=t [3], where keff is the effective heat conductivity of the porous media, Tpw is the temperature of liquid at the heat pipe wall, Twv is the temperature of liquid at the wick/vapor interface and t is the wick thickness. For a given wick structure and working fluid, both keff and t are fixed. Therefore, the temperature difference of the liquid across the thickness of wick, Tpw  Twv, varies linearly with the evaporator heat flux. At low heat flux, the linear relationship of temperature difference and heat flux has been observed. While at high heat flux phase change occurs within the wick, the effective heat transfer coefficient defined as heff ¼ q00 =ðT w  T v Þ, where Tw is the wall temperature of the wick and Tv is the saturation temperature of the vapor, is more appropriate to describe heat transfer performance of a porous wick. It was found that the effective heat transfer coefficient sometimes increases with the increasing of heat flux but ultimately decreases and limits the maximum heat flux [4]. The decrease of effective heat transfer coefficient was often contributed to the trapping of vapor near the pipe wall, and known as the heat pipe’s boiling heat transfer limit. In recent years, several experimental researches [5–8] have been conducted to study the evaporation–boiling heat transfer in porous wicks in the condition of that the liquid level is just aligned with the top surface of the wick, or called horizontally capillary feeding condition [9], which is considered to be identical to the condition in vapor chamber as shown in Fig. 1. Hanlon and Ma [5] studied the water evaporation–boiling at atmospheric pressure in the copper particle sintered porous wicks with the particle size of 0.635 mm, the porosity of 0.43, the wick thickness of 1.9–5.7 mm, and with the heat flux ranging from 10 W/cm2 to 55 W/cm2. Their experimental results showed that the effective heat transfer coefficient decreased with the increasing of heat flux, and they contributed this to the bubble trapping inside the wick because the bubble nucleation occurred at a heat flux as low as 5 W/cm2. Li et al. [6,7] experimentally investigated the effects of wick thickness,

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porosity, and mesh size of the copper mesh sintered wick on the effective heat transfer coefficient and the critical heat flux (CHF) of the water at atmospheric pressure. The testing wicks were sintered using the copper mesh with the wire diameter of 56 lm, 114 lm, and 191 lm respectively, and had the wick thickness of 0.21–0.82 mm and the porosity of 0.409–0.698. The heat flux applied was up to 400 W/cm2. Visual observation indicated that the evaporation and boiling heat transfer occurred simultaneously when the heat flux reached a certain value, which was related to the thickness of capillary wick. Their experimental results indicated that: (1) with the increasing of heat flux, the effective heat transfer coefficient at first increased because more and more nucleation sites were actuated and then decreased due to the appearance of local dry out when heat flux was too high; (2) the smaller the mesh size, the larger was the effective heat transfer coefficient, but there was no obvious dependence on the porosity and the wick thickness; (3) the CHF increased with the wick thickness and was strongly dependent on both the mesh size and the porosity. Weibel et al. [8] investigated the effects of particle size and wick thickness on the evaporation–boiling heat transfer of water in copper particle sintered porous wick structure at atmospheric pressure. The particle sizes studied included 45–75 lm, 106–150 lm and 250–355 lm. The thickness studied included 0.6 mm, 0.9 mm and 1.2 mm, and the porosity had a small range of 0.635–0.657. The heat flux was up to 600 W/cm2. Their experimental results indicated that: (1) within the experimental range of heat flux, the thermal resistance (the reciprocal of the effective heat transfer coefficient) at first decreased, then a sharp reduction occurred due to the transitions from the evaporation on wick surface to the boiling inside the wick, and after that the thermal resistance was relatively constant; (2) at the highest flux, a little increase of thermal resistance was found due to the local dry out, which however is recoverable and characterized by the periodical growth and departure (breakup) of bubble; (3) for a given sintered powder wick thickness, the trade-off between the increased heat transfer area and the increased resistance to vapor flow out of the wick resulted in the existence of an optimum particle size which minimized the thermal resistance; (4) for all of the particle size, the maximum thermal resistance was found for the thickness of 0.9 mm, but the effect of thickness was considered to be negligible. All of the above experimental studies [5–8] were conducted at atmospheric pressure, which however is totally different from the real working condition in a vapor chamber, where the vapor pressure is far less than atmospheric pressure. Recently, Liou et al. [10] experimentally investigated the thermal resistance of a flat heat pipe made of copper mesh sintered wick on the copper plate. Different combinations of mesh wire diameters of 0.14 mm and 0.55 mm and the different wick thickness ranging from 0.26 mm to 0.8 mm were sintered on the copper substrate. Their experimental results showed that: (1) nucleate boiling is suppressed and there is only quiescent surface evaporation for all of the testing conditions and samples, even in the case of the wall superheat as large as 13 °C;

(2) with increasing heat flux, the water film (liquid level) recedes into the wick and the evaporation resistance is reduced, and the minimum evaporation resistances were found when a thin water film was sustained at the bottom of mesh layers; (3) with heat flux further increased, partial dry out appears with dry patches at the bottom mesh holes, first at the upstream end of the heated area and then expanded across the evaporator, and consequently the evaporation resistance increases. Wong [11] did a similar experiment on particle sintered wicks, with the wick thickness of 0.32 mm, sintered with full irregular particles (particle size is less than 210 lm, the porosity of wick is 0.57) or fine spherical particles (diameter is less than 75 lm, the porosity of wick is 0.37) or coarse spherical particles (diameter is 75–180 lm, the porosity of wick is 0.47). It was found that the thermal resistance at first decreases and then increases with the increasing of heat flux. Visualization experiment also confirmed that no boiling occurred in all experimental heat flux up to 170 W/ cm2. As discussed above, several research groups [5–8] had conducted studies of evaporation–boiling heat transfer in porous wicks with the configuration similar to a vapor chamber. However, different experimental phenomena on bubble nucleation and the different variations of the effective heat transfer coefficient with heat flux were found. Furthermore, these experiments [5–8] were conducted at atmospheric pressure, which is quite different from the typical working conditions in vapor chambers at reduced pressures. Experiment results obtained in a flat heat pipe working condition [10,11] revealed that the heat transfer mode at reduced pressures is different from that at atmospheric condition, for example, the nucleate boiling is absent at reduced pressure. However, in a flat heat pipe [10,11], the vapor saturation temperature could not be kept constant, but increased with the increasing of input heat flux at evaporator end [11], so it is difficult to compare the effect of wick properties on heat transfer at the same pressure. In this study, the evaporation–boiling on capillary fed copper particle sintered porous wicks are experimentally investigated at the same reduced pressure to compare the heat transfer performance of wicks with different particle size, particle type and wick thickness. 2. Experimental facility and procedure 2.1. Porous wick samples The geometric sizes of the wick samples tested in this study are summarized in Table 1, where ‘‘coarse’’ represents the particle size of 100–120 screens, or ‘‘120–150 lm’’, ‘‘fine’’ represents the particle size of 160–200 screens, or ‘‘75–96 lm’’, ‘‘electrolytic’’ represents the copper particle fabricated using electrolytic method, and ‘‘spray’’ represents the copper particle fabricated using spray method. All of the samples were provided by Delta Electronic Inc., and were sintered at the same pressure, temperature and time. So, the volumetric porosity of porous wicks is mainly relevant to the particle type and size. Fig. 2 shows the structure of electro-

Table 1 The geometric size and the copper particle types of porous wick sample. Sample no.

Volumetric porosity (%)

Thickness (mm)

Particle type

Particle size

PM1 PM2 PM3 PM4 PM5 PM6 PM7 PM8 PM9

52.85 45.38 55.50 52.85 45.38 55.50 52.85 45.38 55.50

0.35 0.36 0.37 0.41 0.48 0.67 0.46 0.59 0.81

Fine, electrolytic Fine, spray Coarse, spray Fine, electrolytic Fine, spray Coarse, spray Fine, electrolytic Fine, spray Coarse, spray

75–96 lm 75–96 lm 120–150 lm 75–96 lm 75–96 lm 120–150 lm 75–96 lm 75–96 lm 120–150 lm

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(a) electrolytic copper particle

(b) sintered wick using electrolytic copper particle

(c) spray copper particle

(d) sintered wick using spray copper particle

Fig. 2. The copper particles and their sintered wick.

lytic and spray particles and their corresponding sintered wick structures. The electrolytic particle as shown in Fig. 2(a) has somewhat tree-like micro substructures compared with spray particle, which leads to the higher volumetric porosity of porous wick sintered with the same size particles as shown in Table 1. All the wick structures were sintered to a supporting cooper substrate with the thickness of 3 mm. 2.2. Test facility The schematic of the experimental setup is shown in Fig. 3. Its working principle is similar to a loop heat pipe (LHP), but with the assistance of gravity as the additional driven force to overcome flow resistance in the liquid line. The evaporation/boiling of liquid water on the surface of porous wick in the vapor chamber produced water vapor, which entered the condensation chamber through the vapor line and condensed to liquid to accumulate at the bottom of the condensation chamber. The liquid water then returned to the vapor chamber through the liquid line to close the cycle. In the cycling of working fluid, the vapor flow was driven by the pressure difference between the vapor chamber and the condensation chamber, i.e., Dpv = pe  pd, where Dpv is the pressure drop due to vapor flow, pe is the pressure of the vapor chamber and pd is the pressure of the condensation chamber. The return of liquid flow from the condensation chamber to the vapor chamber was driven by the pressure head provided by the gravity force to overcome the pressure drop of the fluid flow through the liquid line, i.e., Dpl = qgH + pd  pe + Dpc, where H is the liquid level difference between condensation chamber and evaporation chamber and is about 0.5 m in the present experimental setup, which can provide the pressure head about 5 kPa, and Dpc is the capillary pressure of the wick. The vapor condensation is realized by the liquid cooling with the constant coolant inlet temperature from the constant temperature bath. The pressure in the condensation chamber, pd, was mainly determined by the water coolant temperature, which could be adjusted by changing the temperature of the constant temperature bath. Through adjusting the opening of the needle valve in the vapor line, the pressure drop Dpv between evaporation chamber and condensation chamber could be controlled. Therefore, the pressure in the evaporation chamber pe could be controlled as needed. When pd, pe and Dpc were fixed, the liquid le-

vel in the evaporation chamber could be adjusted to the intended position (i.e., aligned with the top surface of porous wick) by adjusting the opening of the needle valve in the liquid line to change the pressure drop in the liquid line Dpl. In practical operation, the liquid level in the vapor chamber could be monitored using the liquid leveler as shown in Fig. 3, which was carefully calibrated for each wick sample before experiment to determine the position corresponding to the top surface of the wick sample. Because all of the liquid vaporized in the evaporation chamber was finally returned as liquid, steady state conditions could be achieved in this experimental setup. Both the evaporation and the condensation chambers were cylindrical-shaped and made of stainless steel. In order to facilitate the installment of the heating and the condensation units and the replacement of the wick samples, each chamber consisting of the upper and the lower parts was connected through flange structure. The condensation unit was a homemade aluminum plate embedded with serpentine channels through which the water coolant from constant temperature bath flows. The schematic of heating unit was specifically enlarged at the right side of Fig. 3. A band heater surrounding the cylindrical part of the copper heating block was used to provide heat source. The porous wick sample was connected tightly to the top surface of the cuboidal part of the copper heating block using a specially designed structure (not illustrated to simplify the schematic), and the thermal conductive adhesive was used between them to reduce thermal contact resistance. The cylindrical part of the copper heating block and the band heater were insulated by thermal insulation cotton which was confined within a stainless cylindrical container. The side surfaces of the cuboidal part of the copper heating block were enclosed by a cuboidal Paralyene block. The bottom of copper heating block and the stainless container were supported by a cylindrical Paralyene block, which was fixed onto the bottom of the evaporation chamber. The whole heating unit was installed within the evaporation chamber and totally immersed in water during experiment. Therefore, its waterproofness was tested carefully before experiment to avoid the leakage of water into the cylindrical stainless steel container. All the valves and tubes in the liquid line, the vapor line, the vacuum line, the drainage line and the charging line were also made of stainless steel. The external surfaces of the experimental setup exposed to air were enclosed with polyurethane thermal insulation material. The pressures and temperatures in the evaporation and condensation chambers were measured by vacuum barometers and Ttype armored thermocouples with steel–sheaths. In order to get the effective heat transfer coefficient using inverse heat transfer method as will be explained later, temperatures at several locations within the copper heating block and on the bottom of the substrate of wick sample were measured by T-type wire thermocouples. These thermocouples were at first connected to a thermocouple connector that trans-through the evaporation chamber as shown in Fig. 3, and then lined to the data acquisition system. All thermocouples were calibrated with a data acquisition system and had measurement resolutions of 0.2 °C. The temperatures acquired were displayed on computer screen in situ during experiment to judge whether the steady state has been achieved. The band heater was powered by a DC source with measurement functions of voltage and electrical current. A glass window was installed on the top of wall of the vapor chamber and a CCD camera was used to monitor whether there was bubble nucleation. The glass window was covered with thermal insulation material, except when monitoring was conducted. Since the experiments were designed to be conducted at a reduced pressure, the air leakage into the experimental system was considered carefully. According to leakage testing, the pressure of the experimental system before filling water was vacuumed to about 0.1 kPa, and increased to about 2 kPa after 4 h, and then kept

F.J. Hong et al. / International Journal of Heat and Mass Transfer 63 (2013) 389–400

393

Fig. 3. The schematic of experimental system.

almost unchanged for next 12 h. Because pressures in the evaporation chamber and the condensation chamber were controlled at about 10 kPa and 3 kPa respectively (both higher than 2 kPa), the leakage of the air into the system during experiment could be neglected. Furthermore, the residual air in the system actually was accumulated in the condensation chamber during experiment and had no effect in the evaporation chamber. It was found during experiment that the measured pressure and temperature agreed well with each other according to the saturation water/vapor properties, indicating negligible contribution of the partial pressure from air. 2.3. Experimental procedure The main experimental procedure for each porous wick example is as follows: (1) After installing the wick sample and the experimental system, the system was vacuumed through vacuum line, and then the valve in the vacuum line was closed; (2) The DI water was charged into the evaporation chamber through the charging line. In order to reduce air leakage into the system during water charging, the tube of charging line before the valve was filled with water before opening the valve. The appropriate amount of water charging was determined through testing experiment, but had a relatively large flexibility because the condensation chamber in the experimental system could be used as a liquid storage tank;

(3) The heater was fully powered to heat up the system quickly for about 2 h, and then the vacuum pump was opened again for 10 min in order to further remove dissolved non-condensable air in water, which was accumulated in the condensation chamber; (4) Heating power was then set to the specified value, the opening of the vapor line valve was adjusted to control the pressure (temperature) of evaporation chamber, and the opening of the liquid line valve was adjusted to control the pressure drop between the vapor chamber and the condensation chamber to make the liquid level aligned with the top surface of the wick structure, which was monitored through the liquid leveler; (5) Once the steady state of the system was achieved (i.e., the change of temperatures at the measurement points was smaller than 0.2 °C in 30 min), all the experimental data were recorded. The average temperatures recorded during 30 min were used in data reduction. (6) Steps 4–5 were repeated until all of the heat flux testing was finished. 3. Data reduction The heat transfer performance of porous wick is characterized by the effective heat transfer coefficient defined as:

heff ¼

q00 Tw  Tv

ð1Þ

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where q00 is heat flux, Tw the center bottom surface temperature of porous wick and Tv the evaporation saturation temperature. In practice, it is impossible to measure Tw directly, so it is often estimated according to 1-D heat conduction in the heating block by measuring the temperature within the heating block close to the heating surface [12]. However, the effective heat transfer coefficient obtained in this way included the influence of the thermal contact resistance between the heating block and the wick substrate. Because the thermal contact resistance depended on many factors (such as the pressure between the substrate and the heating block when the sample is installed), and it varied from case to case and time to time. In order to get rid of the uncertainty resulting from the thermal contact resistance, some researchers soldered the substrate to the heating block [6,7], and found by doing so the effective heat transfer coefficient of porous wick improved greatly, indicating the importance of thermal contact resistance. In this paper, an inverse heat transfer method was used to obtain the local effective heat transfer coefficient of porous wick at first, and then Tw was retrieved from the numerical simulation result. In recent years, inverse heat transfer has been successfully adopted to obtain the local convective heat transfer in channel flow boiling [13] and heat exchanger [14], as well as to estimate the jet temperature in liquid jet impingement cooling [15]. The precondition for solving an inverse heat transfer problem is to define an appropriate direct heat transfer problem. The geometric size and boundary conditions of the direct heat transfer problem are shown in Fig. 4. The heat input was assumed to be uniformly distributed on the cylindrical part of heating block, and the other outer surfaces of heating block were assumed to be adiabatic due to the thermal insulation measures adopted in the experiment. In the interface of the substrate of wick sample and the heating block, a thermal contact resistance (Rcr) was assumed. When heat was conducted to the substrate of wick sample, it was expanded laterally. The side surfaces in the width direction (y-direction) of the porous wick sample were blocked just like in Ref. [5], so the liquid could only enter from the left and the right sides (x-direction), and the temperature field in the wick sample can be assumed to be 2-D and independent of y, i.e., T(x, z). The heat dissipation to the environment through the right and the left side of the wick sample was also omitted because of its small heat transfer area and low heat transfer coefficient (natural convection) to the environment. Therefore, it is assumed all the heat is dissipated through the porous wick to the vapor environment with the temperature of Tv. To avoid the modeling of heat transfer within the wick structure, which is practically infeasible considering the liquid level with the wick structure cannot be predicted, the wick structure is not included in the computational domain of the direct heat transfer problem. Instead, the heat transfer within the wick structure and to the vapor environment is modeled using

(a)

an local effective heat transfer coefficient of porous wick structure, h(x). The local effective heat transfer coefficient is a function of x coordinate, h(x), and it is assumed to be the sum of a series of basic P function /li ðxÞ, with parameters vector Pi as hðxÞ ¼ Ni¼1 Pi /li ðxÞ. Bspline function with the order l = 4 is adopted as the basic function in this study. The advantage of B-spline function is that it can reproduce various curve shapes, i.e., the distribution profile of local effective heat transfer coefficient. The detailed characteristics of Bspline function can be found in Ref. [16]. In practice, only quarter of the 3-D physical domain shown in Fig. 4 is included in the computational domain considering the symmetry of the heat transfer problem. In the experiment, six temperatures as shown in Fig. 4 were measured using thermocouples. The inverse heat transfer problem is to minimize the residual function S(P) = [TM  TC]T[TM  TC] by finding an appropriate P vector (in practice, the thermal contact resistance Rcr is added as an additional parameter in P vector, i.e., P vector has N + 1 dimensions), where TM and TC are the measured and the estimated temperatures at the locations (xi, zi), i = 1, 2, . . . , 6. The Levenberg–Marquardt Method for Parameter Estimation [17] was adopted as the inverse heat transfer algorithm as follows. The measured temperatures TM = (TM,1, TM,2, . . . , TM,I) are known, make an initial guess P0 for the vector of unknown parameters P, and choose a value for l0, say, l0 = 0.001 and set k = 0, then: P (1) Use h(x)k (obtained by hðxÞ ¼ Ni¼1 Pi /li ðxÞ) and Rkcr ðPNþ1 Þ to solve the direct heat transfer problem to get the temperature fields in the computational domain; (2) Pick out the calculated temperature at locations (xi, zi), and then compute the residual function S(Pk); h iT T (3) Compute the sensitivity matrix J k ðPÞ ¼ @T@PðPÞ and the matrix X = diag[(Jk)TJk] by using Pk; (4) Solve the linear system of algebraic equations [(Jk)TJk + lkXk]DPk = (Jk)T[TM  TC(Pk)] to get DPk; (5) Compute the new estimate vector Pk+1 = Pk + DPk; (6) Solve the direct problem again with the new estimate Pk+1 in order to find TC(Pk+1) and then computer the residual function S(Pk+1); (7) If SðPkþ1 Þ P SðP k Þ, replace l by 10l and return to step 4; If S(Pk+1) < S(Pk) replace l by 0.1l and keep the new estimate Pk+1; (8) Check the stopping criteria S(Pk+1) < e, where e is the prescribed tolerance. Stop the iterative procedure if it is satisfied, otherwise replace k by k + 1 and return to step 1. Once the correct P vector is obtained, the temperature of Tw (the center bottom temperature of the wick structure) as shown in

(b)

Fig. 4. The schematic of heat transfer model: (a) 3-D computational domain and boundary conditions (only quarter of it needs to be included in the computation considering its symmetry); (b) the geometric size and temperature measurement points.

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Fig. 4 is retrieved to estimate the effective heat transfer coefficient of the wick structure using Eq. (1). One advantage of the present method is that it can eliminate the effect of thermal contact resistance. The above numerical simulation is realized by using CFDRC-ACE software package (2008). The setup of boundary conditions and the retrieving of estimated temperature at specified locations are realized using UDF (user defined function) programed using FORTRAN language. The optimization process of P vector is realized using ‘‘Simulation Management Function’’ of CFDRC-ACE, programed using Python script language provided by CFDRC-ACE software package.

As we can see from Fig. 5(a), for the plain copper surface, the wall superheat increases almost linearly with heat flux when the heat flux is below 12 W/cm2, and then increases non-linearly when the heat flux is larger than 12 W/cm2. Correspondingly, the effective heat transfer coefficient as shown in Fig. 5(b) increases very slowly before 12 W/cm2, and increase rapidly after 12 W/cm2. This is because the heat transfer mode transits from natural convection to nucleate boiling when heat flux is larger than 12 W/cm2 and the number of nucleation sites increases with the increasing heat flux. The critical heat flux for pool boiling was not reached in the present study due to the limit of heating power. According to Fig. 5, the wall superheat for the onset of nucleate boiling (ONB) for plain copper surface is about 35 °C, which is much larger than 5 °C at atmospheric pressure as mentioned in the classical heat transfer textbook [18]. Furthermore, the effective pooling boiling heat transfer coefficient is 3000–5000 W m2 K1 at 9.6 kPa, much less than that of 10,000W m2 K1 at atmospheric pressure. These results agree well with the previous study of pool boiling heat transfer of water at sub-atmospheric pressures [19]. As for the coarse spray particle sintered porous wicks, the wall superheat – heat flux curves in Fig. 5(a) shift to left. This indicates the porous wicks can effectively lower the wall superheat for ONB as reported in previous studies [20,21]. According to Fig. 5(b), the enhancement of heat transfer (the ratio of the heat transfer coefficient of porous wick to plain surface) for the thinnest porous wick (PM3) is much smaller compared to the thicker porous wick PM6 and PM9, and the difference become larger and larger with increasing heat flux. This is because the thicker porous wicks have more potential nucleation sites for bubble nucleation, of which

4. Results and discussions To verify the experimental result and data reduction method as well as to compare with capillary feeding experiment, pool boiling experiments condition are also conducted in this study. Both the pooling boiling and capillary feeding experiments were done at the saturation vapor temperature of 45 °C, correspondingly to saturation pressure of about 9.6 kPa. 4.1. Pool boiling experimental results

25

25000

20

20000

heff (W/m /K)

15

2

2

q" (W/cm )

Fig. 5(a) and (b) shows the relationship of wall superheat (Tw  Tv) and heat flux and the variation of effective heat transfer coefficient with heat flux, respectively, for the wick PM3, PM6 and PM9 sintered using coarse spray copper particle (120– 150 lm in diameters) as well as the plain copper surface.

10 PM3-Pool boiling PM6-Pool boiling PM9-Pool boiling Plain surface pool boiling

5 0

0

5

10

15

20

25

30

35

40

Plain surface pool boiling PM3-Pool boiling PM6-Pool boiling PM9-Pool boiling

15000 10000 5000 0

45

0

5

10

15

PM2-Pool boiling PM5-Pool boiling PM8-Pool boiling

25

PM1-Pool boiling PM4-Pool boiling PM7-Pool boiling

12000

heff (W/m /K)

12000

2

20

(b) 15000

15000

9000

2

heff (W/m /K)

25

q" (W/cm )

(a)

6000

9000 6000 3000

3000 0

20

2

Tw-Tv (K)

0

0

5

10

15 2

q" (W/cm )

(c)

20

25

0

5

10

15 2

q" (W/cm )

(d)

Fig. 5. Experimental results for saturation pooling boiling at the saturation pressure of 9.6 kPa: (a) the relationship of wall superheat and heat flux for coarse spray particles sintered wick PM3, PM6, PM9 and plain surface; (b) the variation of effective heat transfer coefficient with heat flux for coarse spray particles sintered wick PM3, PM6, PM9 and plain surface; (c) the variation of effective heat transfer coefficient with heat flux for fine spray particles sintered wick PM2, PM5 and PM8; (d) the variation of effective heat transfer coefficient with heat flux for electrolytic particles sintered wick PM1, PM4 and PM7.

F.J. Hong et al. / International Journal of Heat and Mass Transfer 63 (2013) 389–400

25

20000

20

17500

heff (W/m /K)

15 PM3 PM6 PM9

10 5 0

15000

2

2

q" (W/cm )

396

12500 PM3 PM6 PM9

10000 7500

0

5

10

15

20

25

30

35

5000

40

0

5

10

15

20

25

2

Tw-Tv (K)

q" (W/cm )

Fig. 6. Experimental results for capillary feeding evaporation at saturation pressure of 9.6 kPa: (a) the relationship of wall superheat and heat flux for PM3, PM6 and PM9; (b) the variation of effective heat transfer coefficient with heat flux for PM3, PM6 and PM9.

more and more are actuated with the increasing heat flux (i.e., the nucleation sites expand towards the top surface of the wick). However, Fig. 5(b) indicates that the order of effective heat transfer coefficient is PM6 > PM9 > PM3, while the order of thickness is PM9 > PM6 > PM3 as can be seen from Table 1. This means the existence of an optimum wick thickness in pool boiling. The existence of optimum thickness for pooling boiling on porous media surfaces is well known [22,23], and is contributed to the tradeoff between the two factors: a thicker wick has larger liquid convective heat transfer area, more potential nucleation sites and larger evaporation area at the interface of liquid/vapor within wick structure when vapor core forms, and therefore is beneficial for heat transfer; on the other hand it also leads to larger thermal conductance resistance from the bottom wall to the top surface of the wick, and more importantly, the larger vapor flow resistance which will increase the saturation pressure at the bottom, i.e., the larger wall superheat. At reduced pressures as in the present study, the vapor density is much lower causing much higher vapor flow resistance for the same heat flux (because the volume flow rate at the reduced pressure is much larger), which make the appearance of optimum wick thickness much easier. The shape of heat transfer coefficient – heat flux curves for fine spray particle sintered wicks (PM2, PM5 and PM8) and fine electrolytic particles sintered wicks (PM1, PM4 and PM7) are of little difference, but they exhibit the same trend of increasing heat transfer coefficient with heat flux. Except for PM1, the heat transfer coefficient keeps almost unchanged when heat flux is larger than 7.5 W/ cm2, because the number bubble nucleation site cannot increase anymore due to its small thickness. As shown in Fig. 5(c), the opti-

mum wick thickness also exists for the fine spray particle sintered wicks, since the order of heat transfer coefficient is PM5 > PM8 > PM2, while the order of thickness is PM8 > PM5 > PM2. However, for fine electrolytic particles sintered wick PM1, PM4, and PM7, the present experiment did not find the evidence of the existence of optimum wick thinness. It may be because the thickness range of the three wick samples in this study as indicated in Table 1 (0.37–0.46 mm) is not large enough. 4.2. Capillary feeding experimental results Fig. 6(a) and (b) shows the variation of the wall superheat and the effective heat transfer coefficient with heat flux for the porous wick samples of PM3, PM6 and PM9, respectively. According to Table 1, these three sample are all sintered using coarse spray particles wick with the same particle size of 120–150 lm and have the same porosity of 55.50%, but have different thicknesses ranging from 0.37 mm to 0.81 mm, with the thickness order of PM9 > PM6 > PM3. It can be seen that for all of the three samples, the effective heat transfer coefficient at first increases and then decreases with the increasing of heat flux. For the same heat flux, the order of effective heat transfer coefficient for the three samples is PM6 > PM9 > PM3. This indicates that there is an optimum thickness to achieve the highest heat transfer coefficient when the porosity and the particle size are fixed for coarse spray particles. Note that the thickness of PM6 is not necessarily the optimum thickness, considering the limited number of samples being tested. Fig. 7(a) and (b) shows the variation of the wall superheat and the effective heat transfer coefficient with heat flux for the porous 20000

25

17500 15000

2

q" (W/cm )

20

2

heff (W/m /K)

15 PM2 PM5 PM8

10 5 0

PM2 PM5 PM8

12500 10000 7500

0

5

10

15

20

Tw-Tv (K)

25

30

35

40

5000

0

5

10

15

20

25

2

q" (W/cm )

Fig. 7. Experimental results for capillary feeding evaporation at saturation pressure of 9.6 kPa: (a) the relationship of wall superheat and heat flux for PM2, PM5 and PM8; (b) the variation of effective heat transfer coefficient with heat flux for PM2, PM5 and PM8.

397

25

20000

20

17500

PM1 PM4 PM7

15000

heff (W/m /K)

2

q" (W/cm )

F.J. Hong et al. / International Journal of Heat and Mass Transfer 63 (2013) 389–400

2

15

12500

PM1 PM4 PM7

10

10000

5 0

7500

0

5

10

15

20

25

30

35

40

(K)

5000

0

5

10

15

20

25

2

q" (W/cm )

Fig. 8. Experimental results for capillary feeding evaporation at saturation pressure of 9.6 kPa: (a) the relationship of wall superheat and heat flux for PM1, PM4 and PM7; (b) the variation of effective heat transfer coefficient with heat flux for PM1, PM4 and PM7.

wick samples of PM2, PM5 and PM8, respectively. According to Table 1, these three sample are all sintered using fine spray particle with the same particle size of 75–96 lm and have the same porosity of 45.38%, but have the different thickness ranging from 0.36 mm to 0.59 mm with the order of PM8 > PM5 > PM2. Like Fig. 6, the effective heat transfer coefficient of all three samples at first increases and then decreases with the increasing of heat flux. For the same heat flux, the order of heat transfer coefficient for the three samples is PM5 > PM8 > PM2, which again reveals that there is an optimum thickness to achieve the highest heat transfer coefficient when the porosity and the particle size are fixed. Fig. 8(a) and (b) shows the variation of the temperature difference and the heat transfer coefficient with the heat flux for the porous wick samples PM1, PM4 and PM7, respectively. According to Table 1, these three samples are all sintered using fine electrolytic particles with the same size range of 75 lm to 96 lm and the porosity of 52.85%, but with the thickness order of PM7 > PM4 > PM1. The porosity of the porous wick sintered with fine electrolytic particle is larger than that of fine spray particles although their particle sizes are in the same range of 75–96 lm, because fine electrolytic particle has tree-like structure as shown in Fig. 2. Just like Figs. 6 and 7, the effective heat transfer coefficient at first increases and then decreases with the increasing heat flux. The order of the effective heat transfer coefficient for the three samples is PM7 > PM4 > PM1, indicating that the larger is the thickness, the larger the heat transfer coefficient in the present experimental range of wick thickness. However, it should be noted that the thickness range of the wick samples made of electrolytic particles are from 0.37 mm to 0.46 mm as indicated in Table 1, far less than that of the fine sprayed particle in the range of 0.36 mm to 0.59 mm and course sprayed particles in the range of 0.37 mm to 0.81 mm. It may be the reason why no optimum wick thickness for fine electrolytic particles is found in the present experiment. Comparing experimental results of pool boiling and capillary feeding, it can be found that for both pool boiling and capillary feeding evaporation, PM5 has larger heat transfer coefficient than that of PM2 and PM8, and PM6 has larger heat transfer coefficient than that of PM3 and PM9, while for PM1, PM4, PM7, there is no evidence of optimal thickness. The difference is that in the experimental range of heat flux, the effective heat transfer coefficient at first increases and then decrease for capillary feeding evaporation, while for pool boiling the heat transfer coefficient always increases. The experimental phenomena for pool boiling have been explained above. The detailed explanation for the variation trend of heat transfer coefficient with heat flux and the existence of optimum wick thickness for capillary feeding experiments will be given in later sections along with the discussion of heat transfer model.

4.3. Does bubble nucleation occur within the wick possible at reduced pressures? The present experimental results in capillary feeding condition indicate that the effective heat transfer coefficient at first increases and then decreases with increasing heat flux for all tested samples. The same trend was reported in Li’s experiments at atmospheric pressure [6,7] and Wong and Liou’s experiments [10,11] in a flat heat pipe environment. However, Weibel’s experiment [8] at atmospheric pressure showed that the effective heat transfer coefficient at first increases and then keep almost constant with the further increasing of heat flux in their experimental range with a little decrease at the highest flux. While Hanlon and Ma’s experiment at atmospheric pressure [5] demonstrated the decreasing of effective heat transfer coefficient with heat flux. These experimental results by different researchers seem to be inconsistent and even contradictory, but actually can all be explained reasonably if the effects of wick’s geometric size (heating area) and working pressure were taken into consideration. In all of the experiments at atmospheric pressure [5–8], the bubble nucleation and growth have been reported. In Hanlon’s experiment [5], because the particle size is large (0.629 mm), the nucleation occurs very earlier (5 W/cm2), and because the wick is thick (1.9–5.7 mm), the bubble is easily to be trapped at the bottom of wick and leads to the deterioration of heat transfer with heat flux, i.e., the heat transfer coefficient decreases with the increasing of heat flux. In the studies of Li and Weibel [6–8], the wick thickness is small, around 1mm or much less than 1 mm (the bubble detachment diameter at atmospheric pressure is about 1 mm [7]), when bubble grows, it can easily reach wick’s top surface and break up, so, the boiling heat transfer (bubble nucleation) inside the wick will not deteriorate but enhance heat transfer, and the effective heat transfer increases with heat flux because of the increasing number of the nucleation sites. The difference of Weibel’s experiment [8] from Li’s experiment [6,7] is because the relatively smaller heating area of 5  5 mm in the experiments of Weibel [8] compared to that of 8  8 mm in Li’s experiment [6,7] causes the delay of capillary limit. In Li’s experiment [7], when heat flux is high enough, the capillary limit starts to play role, the liquid level recedes into the wick, at first, the nucleation of the bubble within the liquid film may still be possible, and then the nucleation will be suppressed if the film is too thin, and finally local dry out appears, causing the decrease of heat transfer coefficient. While in the experiment of Weibel [8], the receding of the liquid level into the wick and the permanent local dry out was not observed in their experimental range of heat flux due to its small heating area, i.e., no decreasing of the heat transfer coefficient due to capillary limit was found.

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Our present experiments and Wong and Liou’s experiments [10,11] were both conducted at reduced pressure, and no bubble nucleation was observed. The absence of bubble nucleation (or boiling heat transfer) can be explained using nucleation theory as follows. According to nucleation theory [24], there is a minimum radius rn for vapor bubble to grow, which is dependent on fluid properties and surface conditions. If the initial radius of the vapor bubble rb is smaller than rn, the vapor bubble will collapse and cannot grow up, otherwise the bubble growth can be sustained. The embryo bubble size rb is directly related to the liquid superheat. Supposing the liquid level is aligned with the topic surface of the wick, applying the nucleation theory to the flat surface, Williams [3] derived the heat flux at which the sustained nucleation will be initiated as:

q00 ¼

keff T v t hfg qv

  2r  Dpc rn

ð2Þ

Since evaporation heat flux can be expressed as:

q00 ¼ keff ðT pw  T wv Þ=t

ð3Þ

and the capillary pressure is:

Dpc ¼

2r rc

ð4Þ

where rc is the meniscus radius at the evaporating wick surface, suppose Twv = Tv, we can get the liquid superheat necessary for the nucleation bubble growth is:

DT lv ¼ T pw  T v ¼

  2r T v 1 1  hfg qv r n r c

ð5Þ

According to the reference [25], at saturation vapor temperature Tv = 100 °C, the saturation pressure pv ð100  CÞ ¼ 1:01  105 Pa, the water vapor density qv ð100  CÞ ¼ 0:59817 kg=m3 , the liquid density ql ð100  CÞ ¼ 958:35 kg=m3 and the latent of evaporation hfg ð100  CÞ ¼ 2156 kJ=kg, while for the saturation temperature T v ¼ 45  C; pv ð45  CÞ ¼ 0:09593  105 Pa; qv ð45  CÞ ¼ 0:06554 kg= m3 ; ql ð45  CÞ ¼ 990 kg=m3 and hfg ð45  CÞ ¼ 2582 kJ= kg. The surface tension of water normally is a linear function of temperature (the dependence of surface tension on pressure cannot be found in literature) and the temperature coefficient of surface tension b  0:16 mN=K. Considering the surface tension at room temperature rð25  CÞ ¼ 72:8 mN=m, it can be estimated that rð100  CÞ ¼ 60:8 mN=m and rð45  CÞ ¼ 69:6 mN=m. Supposing the same rn and rc and substituting all the above vapor properties values into Eq. (2), the ratio of the superheat needed for the bubble nucleation at the vapor saturation temperature of 100 °C and 45 °C is:

DT lv ð45  CÞ rð45  CÞ  ð45 þ 273:15Þ  hfg ð100  CÞ  qv ð100  CÞ ¼ DT lv ð100  CÞ rð100  CÞ  ð100 þ 273:15Þ  hfg ð45  CÞ  qv ð45  CÞ  7:4 ð6Þ That means the superheat for the nucleation at saturation temperature of 45 °C should be about 7 times of that at the saturation temperature of 100 °C, indicating the bubble nucleation is much difficult at the reduced pressure. Our experimental result on pool boiling also reveals the ONB at the saturation temperature of 45 °C is about 35 °C, which is about 7 times of 5 °C, the wall superheat for ONB at atmospheric condition. Nevertheless, ONB may still be possible if heat flux is high enough to make the wall superheat temperature satisfy the requirement. However, the heating areas of the present research (30  30 mm) and Wong’s research (11  11 mm) are large, and the long capillary pumping distance and thin wick thickness requires the receding of the liquid level into the wick structure to provide enough capillary pressure for the liquid flow in the wick.

Therefore, even bubble nucleation occurs, it cannot be observed experimentally due to the opaque of the wick material. In fact, the receding of liquid level into the wick structure will further suppress the bubble nucleation at the reduced pressure if one considers the vapor flow resistance in the wick. The exact calculation of the vapor flow resistance in the wick structure is almost impossible. However, it can be estimated roughly using 1-D analysis supposing the uniform receding of the liquid level. According to the Darcy Law, the vapor flow resistance can be calculated as:

Dpv ¼ m00 lv L=K qv

ð7Þ

where m00 ¼ q00 =hfg is the mass flow rate per area, and the permeability K ¼ D2 e3 =150ð1  eÞ2 , with D the pore size and e the porosity, and L the length of liquid level receding into wick. Supposing D = 50 lm, e = 0.5, L = 0.4 mm, q00 ¼ 20 W=cm2 , and substituting the vapor properties at the saturation temperature of 45  C; qv ð45  CÞ ¼ 0:06554 kg=m3 ; lv ð45  CÞ ¼ 10:36  106 Pa s; hfg ð45  CÞ ¼ 2582 kJ=kg, it can be estimated that Dpv = 1.176 kPa, which is in the same order of vapor saturation pressure (9.5 kPa). Furthermore, Darcy law is only valid for the low speed flow, for the high speed vapor flow (1–10 m/s) in porous wick at the reduce pressure, the additional pressure drop due to geometric factor should be considered, and will result in a higher pressure drop. The pressure drop inside wick will increases the real liquid saturation pressure at the wall, and therefore increases the wall superheat for ONB. 4.4. Heat transfer model of capillary feeding evaporation/boiling at reduced pressure Through the above comprehensive analysis of our present experimental results and those findings from previous researches, the heat transfer model on thin porous wick evaporation/boiling in the vapor chamber configuration at reduced pressure is proposed as follows. As shown in Fig. 9, the heat transfer can be divided into four regimes: Regime A: When the heat flux is small, the amount of the liquid evaporation is small and the liquid level is almost aligned with the top surface of wick. The heat transfer model in this regime is the heat conduction through wick structure and the evaporation through the liquid/vapor surface at the top surface of wick. Regime B: With the increasing of heat flux, the amount of the evaporated liquid increases, and the liquid level starts to recede into the wick structure in order to provide enough capillary pumping to feed the liquid. On one hand, the liquid receding not only reduces the heat conduction resistance through decreasing the thickness of liquid level in the wick, but also enhance the evaporation due to the distribution of the thin liquid film on particles both in vertical and horizontal direction (3-D distribution of liquid meniscus in the wick), and therefore is beneficial to heat transfer; On the other hand, the liquid receding leads to the increase of the vapor flow resistance through the wick structure to the vapor space, and therefore increases the liquid saturation pressure, which in turn increases the wall superheat. Regime C: With the heat flux further increased, the liquid superheat at the bottom of wick may be high enough to sustain the bubble growth, but because the height of liquid level is smaller than bubble departure diameter (the bubble departure diameter at reduced pressure is larger than that at atmospheric pressure), it will grow up to reach the liquid/vapor interface and break up, then the cavity will be refilled and the bubble nucleation starts again. So, in this regime, the dry out is periodical. However, as analyzed above, because at reduced pressure the nucleation is more difficult and the receding of the liquid into wick makes the nucleation even more difficult, the appearance of this regime is not necessary for

F.J. Hong et al. / International Journal of Heat and Mass Transfer 63 (2013) 389–400

(A) liquid level aligned with wick surface

399

(B) liquid level receding into wick 0

(C) periodical bubble growth and breakup

(D) perminent local dry out

Fig. 9. Heat transfer model of porous wick at reduced pressure.

all conditions but depending on the specific wick structure and working pressure. Regime D: If heat flux is too large, the capillary pumping cannot satisfy the liquid feeding for the entire region, the permanent dry out will appear first at the center and then expand laterally, leading to the rapid deterioration of heat transfer. As for the present experiment, since the heating area in this study is 30  30 mm, much larger than 5  5 mm in the experiment by Weibel et al. [8] or 8  8 mm in experiments by Li et al. [6,7], the receding of the liquid level into the wick is required to provide enough capillary pumping pressure to overcome the liquid flow resistance in the wick at low heat flux, therefore, regime A is hardly to be observed in the present study. The rapid increase of heat transfer coefficient with heat flux at 5 W/cm2 as shown in Figs. 6–8 verifies this statement. The rapid increase of heat transfer coefficient with heat flux is attributed to the increasing of evaporation area and the decreasing of the conduction resistance due to the receding of liquid level into the wick. The decreasing heat transfer coefficient can be attributed to the two possible reasons: (1) the increasing of vapor flow resistance due to the increasing of vapor flow rate and the length of vapor flow path increases due to wick receding, i.e., the heat transfer regime is still in regime B, and (2) the partial dry out of the wick. Since there is no abrupt rise of wall superheat (no abrupt decreasing of heat transfer coefficient) as shown in Figs. 6–8 and no abrupt rise of temperatures inside the heating block was monitored during experiment, the decreasing effective heat transfer coefficient in this study is more likely due to the first reason. The decreasing of effective heat transfer coefficient before the appearance of CHF (due to dry out) was also reported by the previous researches [6,7]. So, in summary, it can be concluded that regimes C and D did not appear in the present study due to the limited range of experimental heat flux. According to the above described heat transfer model, the existence of optimum wick thickness for capillary feeding condition in this study is analyzed as follows. While thicker porous wick may provide more liquid–vapor evaporation interface area when the liquid level recedes to the inside of the wick to form 3-D liquid–vapor interface, at the same time, it will increase the heat conduction thermal resistance and the vapor flow resistance though the wick. It should also be noted that when the wick is thick enough, further increase of wick thickness cannot increase evaporation heat transfer area obviously. Therefore, it is the trade-off between the cons and the pros of thicker porous wick that leads to the existence of an optimum wick thickness. 5. Conclusions A test facility which can make the liquid level aligned with the top surface of wick structure and can control the evaporation saturation pressure is developed to study the water evaporation/boil-

ing heat transfer on copper particle sintered wicks under the conditions of capillary feeding as in a vapor chamber. The effects of particle size, particle type and wick thickness on the effective heat transfer coefficient are examined at the same reduced pressure. An evaporation/boiling heat transfer model for thin porous wicks (<1 mm) under capillary feeding and reduced pressure conditions is also discussed through a comprehensive analysis of the present and the previous experimental results. The key findings and conclusions are summarized as follows: (1) With the increasing of heat flux, the effective heat transfer coefficient at first increases and then decreases. (2) There exists an optimum wick thickness to achieve maximum effective heat transfer coefficient when the particle size, type and wick porosity are fixed. (3) Comparing to atmospheric pressure, the bubble nucleation is much more difficult at reduced pressures. The liquid level may have receded into the wick when heat flux is high enough to induce boiling heat transfer, therefore, the bubble nucleation cannot be observed experimentally. This is particularly true for the case of large heating area such as in this study.

Acknowledgments This research work was supported by the National Natural Science Foundation of China through Grant No. 51036005 and Grant No. 50925624.

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