Contents lists available atScienceDirect
Applied Thermal Engineering
journal homepage:www.elsevier.com/locate/apthermengPhase change heat transfer characteristics of an additively manufactured
wick for heat pipe applications
Davoud Jafari
a,⁎, Wessel W. Wits
b, Bernard J. Geurts
caFaculty of Engineering Technology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands bThales Nederland B.V., P.O. Box 42, 7550 GD Hengelo, The Netherlands
cFaculty of Electrical Engineering, Mathematics and Computer Science, Multiscale Modeling and Simulation, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
H I G H L I G H T S
•
An additively manufactured wick forflat heat pipes is fabricated and examined.•
Sintered powder on the wick surface enhances heat transfer performance due to multi-scale features.•
Optimum operation of the examined system is evaluated and discussed.•
A thermal network model accurately predicts the operating temperature. A R T I C L E I N F O Keywords: Porous structure Evaporation Condensation Additive manufacturing Heat pipe A B S T R A C TThis study presents the phase change heat transfer characteristics of an additively manufactured wick for heat pipe applications. For this study, aflat heat pipe is considered that is made of stainless steel 316L utilizing a fabrication process that yields a wick structure with multi-scale features. Using laser powder bed fusion, rela-tively large pore structures, similar to screen-mesh structures, are laser molten with micro-scale laser-sintered features on top of this– we refer to these as multi-scale features in this paper. To characterize the phase change processes at heat pipe operating conditions, an experimental facility was developed. For this aim, a test cell with an internal volume of 40 × 20 × 6 mm3was fabricated. Different filling ratios with water as working fluid and heat inputs ranging from 0.75 to 82.5 kW/m2were tested. Additionally, a thermal network model to predict the overall heat transfer performance of an additively manufacturedflat heat pipe is presented. The model is based on the heat conduction through the wick and wall in both axial and radial directions. Validation by comparison to experimental data shows an excellent agreement for the operating temperature (adiabatic or vapour tem-perature). The fabricated wick structure exploits enhanced evaporation heat transfer; thinfilm evaporation occurs due to the multi-scale sintered powder features on top of the fabricated wick surface. Additionally, the optimalfilling ratio for which the device has maximal thermal performance is determined. The evaporation superheat is determined and discussed for different filling ratios. Experimental results show the optimum thermal performance of theflat heat pipe for a filling ratio of 110%. Compared to conventional wick structures, additively manufactured wick design exhibits improved thermal performance at higher heatfluxes. The ex-perimental results suggest that additive manufacturing is a promising technology to fabricate freeform porous structures for heat pipes in general.
1. Introduction
Many types of heat pipes (HPs) are nowadays part of relevant in-dustrial thermal solutions, including capillary-driven HPs, capillary pumped loop HPs, vapour chambers, and many more[1–3]. Such de-vices have been considered as effective cooling dede-vices which provide a
very high effective thermal conductivity, thereby yielding a high heat transfer rate with negligible temperature drop. HPs operate by utilizing the latent heat of an internal workingfluid[4]. Aided by capillary ac-tion of the wick as the heart of HPs, the liquid workingfluid is circu-lated in its liquid phase. The wick structure is also used as an eva-poration enhancement structure to release the workingfluid in its phase
https://doi.org/10.1016/j.applthermaleng.2019.114890
Received 5 June 2019; Received in revised form 25 November 2019; Accepted 29 December 2019 ⁎Corresponding author.
E-mail address:davoud.jafari@utwente.nl(D. Jafari).
Available online 31 December 2019
1359-4311/ © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
of vaporisation or capture the working fluid during condensation. Continuous miniaturization of electronic components with high heat dissipation requirements, motivates thermal engineers tofind solutions for realizing a high heatflux within a restricted space[5,6]. HPs play an important role in reaching the desired form factors and performance targets. Therefore, the development of new wick structures is an im-portant engineering goal.
Flat heat pipes (FHPs) are desired to carry higher heat loads without an increase in size. Moreover, their overall thickness should be reduced, which allows for a more compact design. The additively manufactured wick structure is a promising alternative relying on recent develop-ments in 3D prototyping. This method offers multi-scale feature sizes in a variety of shapes. Additive manufacturing (AM) gives freedom in defining the shape-optimized wicks and graded structures. In this paper, we investigate experimentally the thermal performance of an additively manufactured wick that operates as a part of FHPs, for the first time. The main question that is addressed in this study is how AM helps to improve thermal performance of a FHP, and howfilling ratio and heatflux affect its evaporation and condensation effectiveness.
AM is a promising and fast-growingfield that provides freedom of design and opens up many advantageous possibilities at the level of system architecture. It can directly produce complex 3D parts[7,8]. AM enables the efficient manufacture of complex, customized layer-by-layer products directly from the digital CADfile. There are many dif-ferent types of AM processes, each with its own benefits and dis-advantages. The AM process is able to create an integrated wick structure and solid material as well as external heat exchanges/heat sinks within one part. Laser-based power bed fusion (LPBF) processes, such as selective laser melting (SLM), are a good option for heat pipe applications as hermetic metal structures can be fabricated.
The key challenging part of HPs to be manufactured, besides the external geometry, is the capillary wick structure. Screen mesh, grooves, and sintered powder are most commonly used types of wick structures. The main benefit of AM wick structure lies in the ability to (i) fabricate a freeform structure with a controlled porosity and pore size, and (ii) integrate flexibly as a single manufactured HP without introducing additional interfaces. We believe that the multi-scale fea-tures of the sintered-like powder feafea-tures on the surface of an additively manufactured wick may enhance the evaporating/condensing heat transfer by providing a larger surface area covered with a thinfilm of the workingfluid. Moreover, fabrication of a relatively large pore size like in a screen mesh, provides a large dimensionflow paths, avoiding a reduction in permeability. This results in a significant improvement of the heat pipe’s heat removal rate at the evaporator end.
The heat transfer performance of the HP is linked to material properties of wick, workingfluid, the composition of wick, amount of workingfluid and operating conditions, i.e., operating temperature and inclination angle. To understand the effect of the filling ratio, Chen and Chou[9]showed best thermal performances of a grooved wick for a filling ratio of 25% (the ratio of liquid volume to channel volume). Lips et al.[10]examined the thermal performance of grooved wick FHPs with different filling ratios and heat fluxes. They demonstrated that the optimumfilling ratio ranges between 100 and 200% (the ratio of liquid volume to effective volume of the wick). Li et al. [11] studied the thermal performance of FHPs with composite wick structures for dif-ferentfilling ratios. At filling ratios of 70–80% (the ratio of liquid vo-lume to effective vovo-lume of the wick), they showed maximum heat transport capacity. The details of some studies regarding FHPs with different wicks (screen mesh, sintered and grooves) are summarized in Table 1. From above examples, it is demonstrated that determining the optimalfilling ratio is not trivial but essential in FHP performance, and depends on the applied heatflux and type of wick. Although effects of filling ratio on the thermal performance of conventional capillary wicks have been studied, the heat transfer behaviour of additively manu-factured wicks has been rarely addressed.
Liquid-vapour phase transitional heat transfer in capillary wick Table
1 Summery of literature research evaluating FHPs. Type of wick/material Working fl uid Filling Ratio (%) Heat fl ux (W/cm 2) Performance indicator Investigated parameters Ref. Sintered/Copper Water – 16 –170 Thermal resistance [13] Sintered/Copper Water 50 i 1– 11 Maximum heat transfer, thermal resistance Evaporation and condensation lengths [27] Sintered, screen mesh/copper Water 2– 2.5 i 16 –100 Maximum heat transfer, thermal resistance Wick thickness, fi lling ratio [14] Sintered-grooved/Copper Water 30 –80 ii 0.8 –1.6 Maximum heat transfer, thermal resistance Filling ratio [11] Screen mesh & grooved/copper Methanol 10 –20 i 0.01 –0.4 Thermal resistance Tilt angles, condenser location [28] Grooved/copper n-pentane 0– 80 i 2– 6.3 Thermal resistance Filling ratio; vapour thickness [10] Grooved/aluminium Isopropyl alcohol 0– 30 iii 2– 5.3 Thermal resistance Filling ratio [29] Grooved/Copper Water 20 i 10 –160 Maximum heat transfer, thermal resistance Evaporation and adiabatic lengths [30] Grooved/aluminium Water – 0– 80 Maximum heat transfer, thermal resistance – [31] Grooved/aluminium Acetone 5– 50 i 0.2 –2.4 Maximum heat transfer, thermal resistance Filling ratios [9] Grooved/copper Water, methanol, acetone 260 iii 8– 20 Thermal resistance Working fl uid [32,33] i The ratio of liquid volume to total volume of HP. ii The ratio of liquid volume to eff ective volume of the wick. iii The ratio of liquid volume to volume of grooves.
structures is a topic of significant activity for a wide variety of appli-cations [2,3]. An important part of HP research is the evaporation/ boiling evaluation through the wick. Lips et al.[12]observed nucleate boiling at the evaporator section of a grooved FHP for relatively small heatfluxes (30 kW/m2), while others[13,14]did not observe nucleate boiling even for high heatfluxes (600 kW/m2) for FHPs made of sin-tered screen meshes. Scholars have shown that the phenomenon of nucleate boiling improves the thermal performance for grooved wick [12] and screen mesh [15] HPs. From the above findings, nucleate boiling in some cases is reported even at low heatfluxes and in some cases it is not observed even at high heatfluxes. This complex situation is likely due to the fact that the evaporation/boiling process is influ-enced by many parameters, including the wall material, wick structure (the type, thickness, porosity and permeability), workingfluid and its charge amount, input heat load, etc. The evaporation/boiling process that will actually be present in an additively manufactured wick for FHPs has not been investigated so far.
Understanding physical phenomena of HP operations is an im-portant addition to experimental research. Simulations typically require input parameters such as wick properties (thickness, porosity, and permeability), material properties (thermal conductivity, density, etc.), workingfluid properties, geometry, and operating conditions[16]. The HP thermal performance can be simulated according to a thermal re-sistance network in which temperature distribution is the main para-meter. Researchers have used these network models as suitable for modeling transient temperatures because of their simplicity and rapid predictions[17,18]. In this approach, HP performance is generally in-vestigated based on an analogy between the HP operation and an electric network. We employ a thermal network model to simulate the operating temperature of our fabricated FHP with parameters taken from the thermal network approach develop by Zuo & Faghri[18]for a cylindrical HP.
In recent years, AM has been explored to produce customized de-vices for heat transfer applications[19,20]. Limited studies are avail-able reporting AM for fabricating porous structures to enhance eva-poration/boiling heat transfer[21,22], performing their experiment in atmospheric pressure and not under HP conditions. They have shown an improvement of up to 70% in heat transfer and an increase of 76% in critical heat flux compared to a plain surface[21]. Esarte et al.[23]
presented an additively manufactured wick for a loop HP. They char-acterized the wick structure in terms of permeability, capillary pumping and thermal conductivity, and have shown a 10% increase in heat transfer rate compared to a conventionally produced version. Ameli et al.[24]considered an aluminium additively manufactured wick for HPs with ammonia as workingfluid. However, they did not report any thermal performance tests. Recently, we[25]fabricated and tested a stainless steel additively manufactured wick, and showed that the ef-fective thermal conductivity of the particular wick was 3 W/m K for ethylene glycol and 6 W/m K for water as tested workingfluid. Hence, a high sensitivity of the thermal conductivity to the interstitialfluid was established. Moreover, we[26]examined the capillary performance of an additively manufactured wick structure. We concluded that the de-signed additively manufactured wick enhances capillary performance compared to sintered powder, screen mesh, and composite wicks re-ported in literature.
In this paper, the emphasis is on experimentally verifying the thermal performance of an additively manufactured wick structure as a part of FHPs. Compared to conventionally available metal wicks that tend to have a coarse pore structure, random pore size distribution and interconnectivity issues between the wick and wick-wall, AM can pro-duce complex wicks with controllable repeating unit cells. A serie of experiments is conducted to determine the evaporation and condensa-tion thermal resistances for different amounts of working fluid and heat loads. The experiments were performed using a custom-built FHP in-strumented with thermocouples within the vapour core and along the wall. In order to evaluate heat transfer mechanisms, temperature dif-ferences and effective thermal conductivity of the system were analysed using a thermal network model and compared to experimental data. The benefit of multi-scale sintered features compared to the screen mesh-like wick structure is discussed in term of heat transfer en-hancement relative to conventional screen mesh structures. The em-ployed thermal network model is presented inSection 2, the experi-mental facilities are described inSection 3, followed by a discussion of the results inSection 4and conclusions from this study inSection 5.
2. Thermal network model
In this study, a fast thermal network model has been employed to provide a qualitative understanding of the HP performance. This thermal network is adapted from[18]for FHPs.Fig. 1shows the FHP thermal network model for six serial and parallel heat conductors. Vapour and liquidflows were assumed to have negligible effects on the transfer of heat from the HP[18]. The heat transfer rate into the system (Qe), and the convective cooling heat transfer and temperature are given as hfand Tf, respectively. Heat conductors with a cross sectional area of Ai, a thickness ofδiand a thermal conductivity of kiare shown as well. It should be noticed that the effective thermal conductivity of the additively manufactured wick structure is not known. We showed, however, that the effective thermal conductivity is between the upper and lower Maxwell models for such structures. In this case, the effective thermal conductivity was chosen to be 6.0 W/m K for water as working fluid[25].
Details of the treatment of the system as a thermal network model is presented in Appendix A. By this model, we can predict the wall and wick temperature at the evaporator, adiabatic and condenser sections, thus, overall thermal resistance and effective thermal conductivity can be determined and compared to experimental data.
3. Experimental set-up
To determine reliable information on heat transfer mechanisms of additively manufactured wicks, an experimental set-up to represent FHP operation was developed. In this section, the wick structure and experimental set-up are described, capable of quantifying evaporation and condensation thermal resistances as well as effective thermal Fig. 1. A HP thermal network model. ksis thermal conductivity of solid wall,
keffis the effective thermal conductivity of the wick, A is the surface area, W is the width of the HP,δwickandδware the thickness of the wick and wall, La, Le and Lcare the length of adiabatic, evaporator and condenser sections, respec-tively.
conductivity of the FHP. The experimental procedure and an estimate of the experimental uncertainty are presented at the end of this section.
3.1. Fabrication of the additively manufactured wick
An additively manufactured wick was designed from a repeating octahedral unit cell, manufactured using an Mlab Cusing 90 SLM ma-chine. The dimensions of the wick are 1 × 20 × 40 mm3 with a measured average pore size of 216μm[26]. The wick was printed di-rectly onto a 2 mm thick stainless-steel 316L plate for thermal perfor-mance measurement.Fig. 2shows a photograph of the sample as well as its CAD model and scanning electron microscopic image. Specifica-tions of the SLM machine and the additively manufactured wick are given in Table 2andTable 3, respectively. The details of the manu-facturing process are reported in[26,34].
3.2. Experimental apparatus
Experiments were performed using a custom-built FHP. A glass chamber was tightened to the stainless-steel substrate plate onto which the additively manufactured wick was fabricated as a single part. A gasket was used to seal the contact surfaces between the glass and plate. The internal dimensions of theflat heat pipe are 6 × 20 × 40 mm3.
The evaporator and condenser sections were heated and cooled using aflat heater and cooler, respectively. The 10 × 20 mm2 eva-porator surface was connected to a surface kept at a uniform tem-perature heated by a rod via a layer of thermal paste (thermal con-ductivity of 2.9 W/m K) to reduce the contact thermal resistance. The heating rod (a block of 10 × 20 × 100 mm3), electrically heated with a 300 W cartridge heater, was enclosed by a box of polycarbonate in-sulating material. Power to the heating rods was supplied by an AC power supply. Four T-type thermocouples were connected onto the surface of the heating rod at a uniform separation distance of 10 mm
(seeFig. 3).
It was observed from the thermocouple signals that the heatflow through the heating rod was well approximated as one-dimensional for all measurements. The measured linear temperature gradient can therefore be used to calculate the heatflux supplied. The condenser section of the system was cooled using waterflow through an acrylic jacket. The heat sink area was 18 × 20 mm2onto which inlet cooling water at 25 °C was inserted. Cooling water entered and exited the jacket with a massflow rate of 0.02 kg/s. The cooling water was supplied from a thermal bath (Haake SC150) to provide a uniform and constant temperature under different heat loads. A magnetic flow meter (SM8000, ifm electronic) was used to measure the waterflow level, located at the inlet port of the acrylic jacket. Two T-type stainless steel thermocouples were used to measure the inlet and outlet temperatures of the cooling water.
Eight 0.25 mm T-type thermocouples were used to measure the FHP wall temperature distribution (Omega, Inc.), shown schematically in Fig. 3. The thermocouples were embedded along grooves on the outer surface of the wall. The internal distribution of the vapour temperature was measured using four stainless steel, 1 mm diameter, T-type ther-mocouples inserted through holes drilled through the glass chamber prior to charging. The thermocouples were positioned in the centreline of the vapourflow.
3.3. Experimental procedure
The FHP and workingfluid were firstly degassed to eliminate any non-condensable gases. Non-condensable gases were evacuated using Fig. 2. Photo of the additively manufactured wick as well as its CAD model and scanning electron microscopic image (a) and pore shape and size compared to conventional screen mesh wicks (b).
Table 2
Specifications of SLM machine and process.
SLM machine Concept laser Mlab cusing 90
Laser system
Yttriumfibre laser, W 100
Wavelength,μm 1.07
Beam radius,μm 40
Layer thickness,μm 50
Hatch distance, mm 1.3
Protective gas Nitrogen
Table 3
Design summary of the additively manufactured FHP including integrated wick properties.
Parameter
Wall and wick material Stainless steel 316L Heat pipe dimensions, mm3 40 × 20 × 6
Evap. Area, mm2 10 × 20
Cond. Area, mm2 18 × 20
Adiabatic area, mm2 12 × 20
Workingfluid Water
Filling ratio (Vl/Vw), % 50, 80, 110, 130 and 150 Wick dimensions, mm3 40 × 20 × 1
Pore size (average),μm 216
Porosity,– 0.46
vacuum pumps placed in a heated container. The FHP was charged with different amounts of degassed de-ionized water through a fill tube di-rectly after evacuation down to a pressure of 10−4mbar using an ultra-vacuum pump. Thefilling ratio of working fluid is defined as:
= ×
FR V
V 100
l
w (1)
where Vlis the volume of the liquid and Vwis the effective volume of the wick obtained by multiplying the bulk volume of the porous structure by its porosity. The porosity of the wick structure was mea-sured according to the Archimedes approach [25]as 0.46. Thefluid charge range was initially determined by estimating the volume offluid required to saturate the wick. Measurements were performed at workingfluid charges that correspond to 50%, 80%, 110%, 130% and 150% of the amount offluid required to saturate the wick.
The experiments were conducted horizontally using a series of tests for heat inputs to the evaporator section ranging from 7.5 to 82 kW/m2 with an increment of 15 kW/m2. The test facility was allowed to reach the equilibrium state before recording any test data, defined as the point at which temperature readings for any thermocouple varied less than 0.2 K over a five-minute period. After a measurement at
equilibrium, the power was changed stepwise and a new equilibrium state was allowed to settle in. Using Superwool® fiber insulation ma-terial, the sample was thermally insulated to reduce experimental errors caused by heat loss to the environment.
The thermal performance of a FHP can be characterized by the thermal resistance and effective thermal conductivity. Based on the measured temperature values, the overall thermal resistance (Rt), eva-poration thermal resistance (Re) and condensation thermal resistance (Rc) are obtained as follows:
= − R T T Q t we wc (2) = − R T T Q e we ve (3) = − R T T Q c wc vc (4) where, Tweis average evaporator wall temperature of the two thermo-couples in the evaporator section, Twcis the average temperature of the two condenser wall thermocouples, Tveand Tvcare vapour temperature of evaporator and condenser sections, respectively, and Q is the average Fig. 3. Experimental set-up for thermal performance evaluation of the additively manufactured FHP (a) as well as positioning of the thermocouples attached to the bottom plate (b), an image of heat pipe showing the thermocouples in the vapour passage (c), and a picture of test facility (d).
input (Qin) and output (Qc) heat transfer of the system given as: = − Q k A x T T Δ in h h h4 h1 (5) = − Qc mC Ṫ p( c out, Tc in, ) (6) where, khand Ahare the thermal conductivity and surface area of the heating block, respectively,ṁ and Cpare massflow rate of the cooling water and its specific heat, respectively, and Tc,out, Tc,in, Th1, Th4andΔx are indicated inFig. 3. The effective thermal conductivity of the FHP can be estimated as follows:
= k L R Wδ eff eff t (7)
where W andδ are the width and thickness of FHP, respectively, and Leff is its effective length defined as:
= + +
L L L L
2 2
eff e a c (8)
3.4. Uncertainty analysis
Uncertainties in the estimated parameters (heatflux and thermal resistance) arises from measurements of the temperatures and FHP and heating bock dimensions. An uncertainty analysis was employed based on a universally accepted approach, the root of sum of squares (RSS) method, given by[35]. Recordings from the thermocouples were col-lected through a data acquisition module (Keysight 34972A). The un-certainty associated with the temperature measurement was de-termined to be ± 0.5 °C. Uncertainty in the input heatflux and thermal resistance was calculated with the RSS method as:
= ⎡ ⎣ ⎢⎛⎝ ⎞⎠ + ⎛⎝ ⎞⎠ + ⎛⎝ ⎞⎠ + ⎛⎝ ⎞⎠⎤ ⎦ ⎥ δQ Q δk k δA A δ x x δ T T Δ Δ Δ in in 2 2 2 2 (9) ⎜ ⎟ = ⎡ ⎣ ⎢⎛⎝ ⎞⎠ + ⎛⎝ ⎞⎠ ⎤ ⎦ ⎥ δR R δQ Q δ T T Δ Δ in in 2 2 (10) The thermal conductivity of aluminium alloy was assumed to have a ± 2% uncertainty. The dimensional uncertainty was estimated from the digital calliper′s resolution used for the measurements. The distance uncertainty between thermocouples, Δx, and cross sectional area, A, was estimated to be ± 0.1 mm and ± 0.01 mm2, respectively. Accordingly, the uncertainty of input heatflux and thermal resistance ranges between 11% and 3% and 22% to 13%, respectively, for input heatfluxes of 7.5 to 82.5 kW/m2.
4. Results and discussion
This section presents the heat transfer measurements of the addi-tively manufactured wick structure, representing FHP operation. The section is divided into two parts. The first part is to present the ex-perimental temperate profile analysis, and temperature differences and the effective thermal conductivity of the FHP with a filling ratio of 110%, and compare this to the presented thermal network model. The second part is the evaluation of the effect of filling ratio on the thermal performance of the custom-built FHP.
4.1. Temperature profile analysis and thermal network model validity The typical external wall temperature distributions are shown in Fig. 4for a measurement with a constant condenser wall temperature of 25 °C,filling ratio of 110% and different heat inputs in the horizontal position. The wall temperatures are the average of two thermocouples for each axial position (seeFig. 3). As shown, the adiabatic section of the FHP has an almost uniform temperature distributions for different
heatflux values. There is a very small temperature gradient, indicating a small axial heat conduction contribution estimated at less than 6% of the total heat transfer. The lower the heat flux, the better the tem-perature uniformity. At the maximum applied heatflux, q = 82.7 kW/ m2, the maximum temperature does not exceed 349.5 K, and the maximum temperature difference is less than 8 K between the eva-porator and condenser wall temperatures.
Fig. 5compares the experimentally and theoretically determined results for the operating temperature as well as wall temperature dif-ferences (Twe-Twc, Twe-Twaand Twa-Twc). Compare to the network model, Fig. 5a shows that the adiabatic surface temperature is accurately predicted: the maximum difference is less than 2%, suggesting that the thermal network model approach is valid to predict the operating temperature of an FHP utilizing an integrated additively manufactured wick structure.
Fig. 5b shows that the temperature differences between the eva-porator, adiabatic and condenser areas are highly dependent on the input power. The difference between predicted and experimental re-sults increases as heat transfer rate increases. The steady-state tem-perature increments from evaporator to condenser (Twe-Twc) computed by the network model are below the experimental results by approxi-mately 1 K for a low heatflux and above the experimental results by approximately 6.5 K for a high heat flux. Progressively lower tem-perature differences between evaporator and adiabatic, and adiabatic and condenser areas were measured compared to the model as well. Thus, the effect of neglecting evaporation/condensation interface re-sistances is not significant at low heat fluxes, while for high heat fluxes the discrepancy can be attributed to the effect of heat transfer en-hancement of the system.
To discuss above observations, effective thermal conductivity is considered as a thermal performance enhancement indicator. The ef-fective thermal conductivity is defined as the relation between the surface temperature difference and energy passing through the system at steady-state operation (Eq.(7))– combined conduction through the wall and wick structure, and phase change behaviour.Fig. 6shows the measured and predicted effective thermal conductivity as a function of input heatflux. The figure shows that the effective thermal conductivity predicted by the thermal network model is about 400 W/m K. Experi-mentally the FHP shows a significantly higher value of 858 W/m K. Conductivity values increase with input power for the additively manufactured wick. This increase in effective conductivity results from a larger portion of the applied energy going into vaporization latent heat[36]. The reduction in effective thermal conductivity after peaking at 67.5 kW/m2 is also noticeable, after which stable operation Fig. 4. Experimental (markers) and corresponding theoretical (lines) variation of wall temperature at different heat inputs.
continued around 821 W/m K. It is believed that the liquid/vapour interface receded into the wick; however, the large pores of the wick structure allow continued vapour departure easily from the wick. Hence, the additively manufactured wick avoided much decrease in performance. Considering the fact that the thermal conductivity of stainless steel is approximately 15 W/m K, the FHP performs as a system with a heat transfer capacity more than 55 times higher than that of a stainless steel bar of the same size.
We believe that the multi-scale features of sintered powder onto a screen mesh-like additively manufactured wick (seeFig. 2) effectively increase the evaporative and condensation surface areas. Hence, there is a higher number of evaporating menisci at the interface between li-quid and vapour, thereby minimizing temperature losses due to eva-poration and condensation heat transfer. The large internal pores also offer a low-resistance flow delivery path, resulting in a high-perfor-mance FHP.
Compared to the network model which does not consider these ef-fects the measurement results clearly have a performance advantage. While a detailed study of evaporation heat transfer enhancement of the additively manufactured wick was not carried out, information from literature strongly supports this theory. Researchers have evidenced increased thinfilm evaporation due to a decrease in pore size and a higher density of evaporative menisci at the interface between liquid and vapour[37,38].
4.2. Effect of filling ratio on the thermal performance of an additively manufactured FHP
This section presents the effect of filling ratio on the distribution of the wall temperature along the length of the FHP, the evaporation and condensation thermal resistances as well as the superheat wall tem-perature. Thefilling ratio is defined as the liquid volume divided by the effective volume of the wick, see Eq. 16. Filling ratios of 50%, 80%, 110%, 130% and 150% were analysed.
Fig. 7compares the distribution of wall temperatures at a heatflux of 52.5 kW/m2for different filling ratios. At low filling ratios of 50 and 80%, a high evaporator wall temperature is observed and the lowest evaporator temperature is observed at a filling ratio of 110%. The adiabatic section, however, remained at about 327 K at an almost constant temperature. Finally, the wall temperature of the condenser section using the highestfilling ratio is slightly lower at the same input power than for otherfilling ratios. This may be due to the additional workingfluid remaining at the end of the condenser section.
Fig. 8a shows the evaporation thermal resistance versus applied heatflux for different filling ratios. The evaporation thermal resistance Fig. 5. Comparison of the predicted outer wall temperature with the
experi-mental data for adiabatic surface (a) and temperature differences between adiabatic, condenser and evaporator surfaces (b).
Fig. 6. Comparison of the predicted effective thermal conductivity of additively manufactured FHP with the experimental data.
Fig. 7. Experimental variation of wall temperature at different filling ratios and afixed heat flux.
is computed by the difference in temperature between Tweand Tve, and applied heat flux (Q). In all cases, the thermal resistances decrease sharply as the heat transfer rate is increased– this is commonly ob-served in literature on HPs as well[39]. From 7.5 kW/m2to 37.5 kW/ m2heatflux, a sharp decrease in thermal evaporation resistance from about 1.2 K/W and above to about 0.4 K/W was observed. It is expected that the decrease in evaporation thermal resistance from 7.5 kW/m2to 37.5 kW/m2is attributed to system start-up problems – start-up pro-blems for two-phase devices are common [40]. There is insufficient energy at low heat input to initiate phase change. The reduction in the evaporation thermal resistance is therefore due to the proper operating of the system, essentially at the higher heat loads.
For higher heatfluxes, the thermal resistances approach a threshold value, except forfilling ratios of 50 and 80%. The volume of working fluid above 80% does not impact the non-linearity of the thermal re-sistance. For filling ratios of 50% and 80%, the thermal resistance is lower than for otherfilling ratios at a low heat flux of 7.5 kW/m2. For heat fluxes above 37.5 kW/m2, since the working fluid no longer completely saturates the wick, the thermal resistance increases rapidly. Filling ratios less than 110% may lack liquid supply and dry-out locally, leading to a higher evaporator wall temperature. The two curves for filling ratios of 130% and 150% are very close to each other. A filling ratio of 110% presents the best thermal performance, as low as 0.21 K/ W at a heatflux of 82.5 kW/m2. For higherfilling ratios, e.g. at 130% and 150%, the surplus liquid hinders efficient release of vapour.
Therefore, there is a need to determine the optimalfilling ratio for each configuration and operational conditions.
A typical condensation thermal resistance is shown inFig. 8b for different filling ratios. As shown also the condensation thermal re-sistance depends strongly on thefilling ratio. The increase of the heat flux does not affect the condenser thermal resistance much. This mostly depends on the percentage of area that is liquidflooded, except for the lowestfilling ratio.
It is shown that the thermal resistance of condensation at lower filling ratios – 50%, 80% and 100% – is lower than that of higher filling ratios. A lower condensation thermal resistance is primarily attributed to the fact that the condensation of thefilm starts at the sintered-like structure of the additively manufactured wick. Thus, the condensation heat transfer is improved due to a higher surface area, resulting in a lower thermal resistance in the condenser section. The thickness of the liquidfilm greatly affects system performance – we observe a higher condensation thermal resistance at a higherfilling ration. The liquid clogging phenomenon affects thermal condensation resistance for a higherfilling ratio as well. Working fluid accumulates at the condenser section and a thickerfilm results in larger condensation thermal re-sistances. Hence also here, there exists an optimal filling ratio that optimises the thermal performance, i.e. that minimizes the condensa-tion thermal resistance.
The heatflux versus superheat wall temperature is an interesting relation to analyse evaporation/boiling heat transfer.Fig. 9provides the evaporation/boiling heat transfer characteristics of the additively manufactured wick through the measured heatflux versus superheat relation. At heatflux values below 37.5 kW/m2, all cases, except for a filling ratio of 50% show identical performance. This confirms that heat transfer is dominated by evaporation from the liquid spreading layers and is not strongly influenced by the amount of working fluid[41]. The measured data deviates at higher heatfluxes and the filling ratio starts to play an increasingly important role. This suggests that evaporation/ boiling heat transfer behaviour of the additively manufactured wick is roughly independent on the filling ratio above a certain threshold value. However, when boiling occurs, wick structures withfilling ratios below this threshold value dry-out locally.
Afilling ratio of 80% shows even better performance for lower heat fluxes prior to boiling. Local dry-out occurs with heat fluxes above 37.5 kW/m2atfilling ratios below 80%. When the superheat reaches about 3.6 K for thefilling ratios of 130 and 150% and 2.7 K for the filling ratio of 110%, and the heat flux increases from 37.5 to 52.5 kW/ m2, minimal changes to the evaporator superheat occur. This improves the performance of heat transfer, as discussed before, which can be attributed to the receding liquid menisci and hence decreasing average Fig. 8. Variation of evaporation (a), condensation (b) thermal resistance versus
heatflux at different filling ratios.
Fig. 9. Heatflux as function of temperature difference between evaporator wall and evaporator vapour temperature for different filling ratios.
liquid layer thickness.
In order to justify the advantage of employing AM for producing enhanced wick structures, Fig. 10 compares the superheat wall tem-perature of this study to other results from literature. Due to a lack of research on stainless steel FHPs as well as the variety of operational conditions, little data was available to perfectly match the structure and operating conditions of the current study. Data was collected for the most similar conditions using water as the workingfluid, operating at a horizontal orientation with the coolant temperature at 25 °C and heat fluxes ranging from 5 to 100 kW/m2. In order to exclude the effect of the heater size, the superheat wall temperature is plotted in relation to the heatflux. Compared to those reported in the literature, the addi-tively manufactured wick structure outperforms conventional wick structures in all cases. It is expected that a conventional screen mesh wick with pore sizes approaching our additively manufactured wick would decrease the number of evaporating menisci, and hence, increase the superheat temperature. Conversely, the multi-scale features on our wick structure and direct attachment to the wall result in an improve-ment of evaporation and condensation heat transfer rates.
In summary, the mechanism of the multi-scale features (hybrid sintered-like powder features on the screen mesh-like structure) of the additively manufactured wick structure can be explained by an en-hancement of the surface area for thinfilm evaporation/condensation. We have observed enhancement of evaporation performance particu-larly at optimumfilling ratio and/or higher heat loads fluxes in which attributed to larger surface area due to sinter-like features. To further explore the internalflow behaviour within the additively manufactured wick structure, we aim to visualize theflow regimes of the fluid flow similar to that of[42,43]. This work is being performed and will be reported in the future.
5. Conclusions
The evaporation and condensation heat transfer of a stainless steel
additively manufactured wick structure operating as an integrated part of aflat heat pipe is characterized by measuring the vapour and wall temperature distributions at different filling ratios and heat fluxes. This study determined the optimal charging amount of workingfluid and evaluated the evaporation thermal resistances at heat fluxes ranging from 7.5 to 82.7 kW/m2. The optimal workingfluid charge was found to be 110%. For lowerfluid charges, local dry-out resulted in an in-crease of the evaporator thermal resistance.
A quick-to-compute and efficient thermal network model capable of estimating the operating temperature of aflat heat pipe utilizing an additively manufactured wick structure is proposed. Hereto, the system is split into coupled thermal conductors and evaporation/condensation interfaces are neglected. It was found that the adiabatic temperature predicted by the present model is in good agreement with the experi-mental results with an approximately 2% difference, while a difference is observed for the evaporator and condenser wall temperatures. To better predict the temperature response of evaporator and condenser sections, a detailed consideration of evaporation and condensation in-terfaces considering multi-scale sintered powder features on the wick structure is required.
The additively manufactured wick fabricated in this study showed improved heat pipe performances compared to conventional wick structures previously reported in literature. This thermal performance enhancement is believed to be attributed to an increase in the eva-porating meniscus density at the liquid–vapour interface due to the presence of sintered powder features. Moreover, the presence of rela-tively large pores of the addirela-tively manufactured wick seems to si-multaneously provide a high liquid permeability. In addition, additive manufacturing allows for an integral attachment to the HP wall as well. We conclude that the use of additive manufacturing technology for fabricating heat pipes allows thermal management systems to operate with lower temperature differences between the hot and cold interfaces with an identical operating temperature as confirmed by the compar-ison to the thermal network model. For industrial applications, more efficient electronics cooling systems will lower component tempera-tures, thereby meeting stringent design goals and improving reliability. The presented data in this paper provides guidance and confidence for engineers and researchers to develop novel structures for additively manufactured heat pipes for electronics cooling applications. Moreover, the fabricated porous structures can be beneficial for other applications areas as well.
Declaration of Competing Interest
The authors declare that they have no known competingfinancial interests or personal relationships that could have appeared to influ-ence the work reported in this paper.
Acknowledgement
The Science Based Engineering (SBE) institute at University of Twente is gratefully acknowledged.
Appendix A. Thermal network model of theflat heat pipe
In this method, as shown inFig. 1, the system is described as a thermal resistance network system. Assuming Tiis the temperature of the middle of the heat conductor i, and Ti,1and Ti,2are temperature of two ends of the heat conductor i, the following energy balance equations can be given:
= −
ρ A δ C dT
dt Q Q
i i i p i, i i,1 i,2
(A-1) Fig. 10. Comparison of the superheat temperature as a function of heatflux for
the present study (filled marker) and the literature: grooved/copper[12], sin-tered/copper[44], screen mesh/stainless steel[45]and screen mesh/copper [15].
= − Q kT T δ/2 A i i i i i i ,1 ,1 (A-2) = − Q kT T δ/2 A i i i i i i ,2 ,2 (A-3) Rearrangement of the above equations is given by:
= + − dT dt α δ T T T 2 ( 2 ) i i i i i i 2 ,1 ,2 (A-4) By solving energy balances on each temperature node, the heat conductors 1–6 associated with the various element temperatures can be obtained. The evaporator wall temperature is given by:
= + − + + + + dT dt α δ T T T T 2 [(Δ Γ 2) Δ Γ Γ Ψ] 1 1 12 12 1 1 21 2 5 5 6 6 (A-5) The evaporator wick is given by:
= + + − + dT dt α δ T T T 2 [Δ (Δ Δ 2) Δ ] 2 2 22 12 1 21 23 2 32 3 (A-6) Similarly, the condenser wick temperatures is represented by:
= + + − + dT dt α δ T T T 2 [Δ (Δ Δ 2) Δ ] 3 3 32 23 2 32 34 3 43 4 (A-7) The condenser wall temperature is given by:
= + + − + + + dT dt α δ T T T T 2 [Δ (Δ Γ 2) Γ Γ Φ] 4 4 42 34 3 43 4 4 Ấ 5 5 Ấ 6 6 (A-8) The adiabatic wick temperature is obtained by:
= + + + − + + + + dT dt α δ T T T T 2 [Γ Γ (Γ Γ 2) (Γ Γ ) Ψ Φ] 5 5 52 1 1 Ấ 4 4 5 Ấ 5 5 6 Ấ 6 6 (A-9) Finally, the adiabatic wall temperature is given by:
= + + + + + − + + dT dt α δ T T T T 2 [Γ Γ (Γ Γ ) (Γ Γ 2) Ψ Φ] 6 6 62 1 1 Ấ 4 4 5 Ấ 5 5 6 Ấ 6 6 (A-10) In(5)–(10), the parametersΔij,Γi, ′ Γ i,Ψ and Φ are: = + k A δ k A δ k A δ Δ / / / ij i i i i i i j j j (A-11) = + + k A δ k A δ k A δ k A δ Γ / / / / i i i i 1 1 1 5 5 5 6 6 6 (A-12) = + + + k A δ k A δ k A δ k A δ h A Γ / / / / /2 i i i i f c ' 4 4 4 5 5 5 6 6 6 (A-13) = + + Q k A δ k A δ k A δ Ψ /2 / / / 1 1 1 5 5 5 6 6 6 (A-14) = + + + ∞ h A T k A δ k A δ k A δ h A Φ /2 / / / /2 c f f c 4 4 4 5 5 5 6 6 6 (A-15)
(A-5)-(A-10) arefirst-order, linear, ordinary differential equations which have been solved by the fourth order Runge-Kutta method.
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