Experimental Study on Thermal Performance of a Loop Heat Pipe with Different Working Wick Materials

Abstract

In loop heat pipes (LHPs), wick materials and their structures are important in achieving continuous heat transfer with a favorable distribution of the working fluid. This article introduces the characteristics of loop heat pipes with different wicks: (i) sintered stainless steel and (ii) ceramic. The evaporator has a flat-rectangular assembly under gravity-assisted conditions. Water was used as a working fluid, and the performance of the LHP was analyzed in terms of temperatures at different locations of the LHP and thermal resistance. As to the results, a stable operation can be maintained in the range of 50 to 520 W for the LHP with the stainless-steel wick, matching the desired limited temperature for electronics of 85 °C at the heater surface at 350 W (129.6 kW·m⁻²). Results using the ceramic wick showed that a heater surface temperature of below 85 °C could be obtained when operating at 54 W (20 kW·m⁻²).

1. Introduction

Loop heat pipes use a passive two-phase heat transport device in which advantageous characteristics are offered, such as operation against the gravity through the capillary effect and flexible characteristics. They have been widely used in energy applications, spacecraft thermal control, electronic device cooling, and commercial radiators [1]. Zhou [2] fabricated a plate-type loop heat pipe (LHP) and investigated the effect on the heat transfer performance of the LHP with multilayer metal foams as a wick structure. Their flat evaporator’s experimental results show that multilayer copper foams have better performance than nickel foam because of higher thermal conductivity and smaller pore size. Siedel [3] presented a numerical simulation, comparing it with the experimental data of a flat disk-shaped evaporator. The results showed that the larger effective thermal conductivity of wick has an influence on the overall thermal performance of the LHP. However, other researchers, Maydanik [4] and Hoang [5], suggested the wick material, with its lower effective thermal conductivity, to handle the problem of heat leakage. In addition, the hydrophilic effect on the ceramic wick structure is higher than that of stainless steel [6]. Therefore, the performances of stainless-steel wicks and ceramic wicks in LHPs are compared in this study, of which the ceramic wick has much lower thermal conductivity and a higher hydrophilic effect [7,8]. In an LHP system, the porous wicks’ structure is essential because it provides the capillary force for working fluid circulations, a liquid flow path, and a place for phase change heat transfer. Moreover, the porosity effect of the wick materials inside the evaporator is necessarily considered for improving the overall performance of LHPs [9]. Therefore, the porosity, pore diameter, and thermal conductivity of the wicks were measured. The influence of the different wicks on the performance of LHPs is tested with the designed evaporator. Although this is a simple case study of an arrangement with different wicks, the appropriate engineering approach of the calculation procedure related to applying the designed evaporator is presented in this paper. It may improve the understanding of the problems that exist in the LHP evaporator and future LHP systems.

The LHP has some similar operation principles with conventional HPs. The phase changing process is happened in the LHP system and the capillary force is used as the motivation for the operation. Figure 1 demonstrates the scheme of the analytical LHP and an operation cycle diagram.

At first, the system is not supplied with heat load. In this case, the liquid stays at Level A–A as an assumption. The liquid found at the evaporator zone (Point 1) and the compensation chamber evaporates from the wick when heat is supplied to the evaporator. The vapor from the evaporator flows. Then, it approches to the heating wall. As a result, the vapor pressure reduces. Simultaneously, the temperature rises a little (Point 2) and is higher than the vapor located at the compensation chamber. In this situation, the wick behaves as a thermal barrier. The vapor which is superheated condition in the evaporator zone cannot pass the compensation chamber through the wick which is saturated due to the force of capillary that keeps the liquid inside. Then, the hydraulic lock is happened in the wick. Afterwards, the vapor continuously flow to the condenser’s inlet (Point 3). When vapor flows from Point 2 to Point 3, both temperature and pressure decrease. The de-superheat, condensation, and subcooled processes happen from Point 3 to Point 5. In this case, there is no pressure loss from Point 3 to Point 5 as an assumption. Because of the pressure loss and the hydrostatic resistance caused by friction, the pressure difference ∆P₅₆ includes the pressure loss. Afterward, the liquid located at Stage 6 flows into the chamber for compensation. Moreover, some parts of the heat load are provided to the evaporator at the expense of the working fluid. This condition is heated to temperature T₇. The progress from Point 7 and Point 8 are relative to the filtration of the liquid through the wick into the evaporation place. In this way, the liquid may prove to be superheated. However, its boiling-up does not happen because of its short duration in such a state. The state of the working fluid in the vicinity of the evaporating menisci is represented by Point 8. Pressure loss (dP_1–8) corresponds to the total value of pressure losses in all the working-fluid circulation sections. From the above analysis, the function of the LHP is considered in three conditions. At first, the capillary condition is the condition for conventional HPs for an operation.

$$\mathsf{∆}{P}_c\ge \mathsf{∆}{P}_v+\mathsf{∆}{P}_l+\mathsf{∆}{P}_g$$

(1)

where

∆P_v is the working fluid’s pressure loss during the vapor state’s motion.

∆P_l is the working fluid’s pressure loss during the liquid state’s motion.

∆P_g is the pressure loss because of the hydrostatic of the liquid column.

∆P_c is the wick capillary pressure.

The second condition is just for the LHP. At the LHP’s startup, it ensures that the liquid is exhibited from the evaporating zone to the compensation chamber.

$${\frac{\partial P}{\partial T}|}_{T_v}\mathsf{\Delta }{T}_{1-7}=\mathsf{\Delta }{P}_{EX}$$

(2)

where

∂P/∂T is the derivative of the saturated line’s slope. T_v is the mean temperature between T₁ and T₇.

ΔP_EX is the total pressure loss in all the sections of the working fluid’s circulation except the wick.

At the third condition, the liquid is prevented from steaming in the liquid line because of the ambient pressure loss and heating.

$${\frac{\partial P}{\partial T}|}_{T_v}\mathsf{\Delta }{T}_{4-5}=\mathsf{\Delta }{P}_{5-6}$$

(3)

where

∂P/∂T is the derivative of the saturation line’s slope. T_v is the mean temperature between T₄ and T₅.

ΔP_5–6 is the pressure loss in total from State 5 to State 6.

The working fluid should own a high value of dP/dT to minimize the temperature difference ΔP_1–7 and ΔP_4–6 from the second condition.

The purpose of the tested LHP in this study is the cooling of electronics such as processors located at Data Centers (DCs). Therefore, the evaporator surface which is heated needs to be flat to improve the evaporator and electronics’ contact quality. Moreover, it will make the heat flux q and distribution of temperature on the active surfaces uniform and eliminate the occurrence of mounting blocks at the evaporator. The investigated evaporator design belongs to the evaporator group with opposite replenishment (EOA). In this design, liquid flows from the top to the bottom surface of the wick structure, as shown in Figure 2a. Figure 2b shows the evaporator with longitudinal replenishment (ELR). The liquid from ELR is provided from the compensation chamber which is located behind the wick. Otherwise, the liquid flows perpendicular to the heat flow rate. The evaporator with opposite replenishment own a simple structure and the liquid absorption surface is large. However, the evaporator can become thicker because the compensation chamber is located above the capillary system. Moreover, the heat leak from the evaporator to the compensation chamber through the wick will be more severe because of the large cross-section of the wick.

The investigated evaporator has two parts: the vapor collector and the wick’s space and compensation chamber. The copper plate is used for the separation between two elements. The brazing method is used to fix them. Additionally, to install the thermocouples, a hole with a 1-mm diameter and 22.5 mm for the length was fabricated at the evaporator’s base. The heating block’s top surface and the evaporator’s bottom surface have the same area: 27 cm² (45 × 60 mm). This dimension was considered based upon the specifications of some processors, as presented in

Table 1. Processor specifications.

No.	Modern	Thermal Power Design (W)	Case Dimensions (mm × mm)	Heat Flux (W/cm2)
1	Core i7 5960X	140	52.5 × 45	5.9
2	Core i7 5930K	140	52.5 × 45	5.9
3	Core i7 4960X	130	52.5 × 45	5.48
4	Core i7 4930X	130	52.5 × 45	5.48
6	Core i7 3790X	150	52.5 × 45	6.3
7	Xeon E7 8891 v3	165	52 × 45	7.05
8	Xeon E7 8880 v3	150	52 × 45	6.41
9	Xeon E7 8890 v2	155	52 × 45	6.62
10	Itanium 9300	185/155/130	48.5 × 40.25	9.47/7.94/6.66
11	Itanium 9500	170/130	48.5 × 40.25	8.71/6.66

. Different LHP technologies focussing on various designs of the LHP’s evaporator and other types of LHPs such as miniature LHPs, micro LHPs, evaporator with longitudinal replenishment (ELR) LHPs, and LHPs with parallel condensers are compared and summarized in

Table 2. Different LHP technologies from the literature.

No.	References	Specifications of LHPs from the Literature	Objects and Results
1.	K. Fukushima—2017 [11] Keywords: Capillary force, heat transport, LHP, porous PTFE	Flat—rectangular evaporator New-fashioned flat evaporator structure, micro-LHP (Evaporator 20 × 10 × 3 mm, 200 mm in length transport line) Porous polytetrafluorethylene wick 17 × 9 × 2 mm (PTFE) (50%, 2.2 μm, 6.48 × 10−14 m2, 0.25 W/m·K) Working fluid: ethanol.	Objects: A wick with a liquid core is proposed. An experimental and computational investigation was conducted. The temperature distribution inside the evaporator and the heat load’s break down from the mathematical model are obtained. Results: Minimum RLHP is 1.2 K/W and maximum Q = 11 W, from the experiment.
2.	M. Nishikawara—2017 [12] Keywords: Capillary evaporator, capillary pumped loop, evaporator HTC, LHP, optimized wick shape, 3-phase contact line	PTFE wick (bulk thermal conductivity = 0.25 W/m·K). Stainless steel case (k = 16 W/m·K) Machined widths (minimum): 0.3 (circumferential groove) and 0.4 mm (axial groove) Increasing axial grooves will reduce the number of circumferential grooves. Three wicks were fabricated for experimental examination: Ltri = 3150/m (4 axial × 71 circumferential) Ltri = 2630/m (16 axial × 56 circumferential) Classical wick with only 16 axial grooves and 1 mm width of the groove	Objects: It presents a method for the wick shape optimization via calculation and experiment. Using only the three-phase contact line’s length, the hevap is maximized (q = 2 W/cm2). Effects of the case, wick material, and the working fluid, are discussed. Results: The effect of the three-phase contact line (TPCL) on the groove pressure loss (by calculation) is shown. Comparison between evaporator heat-transfer coefficient (HTC) obtained using Equation (9) and that obtained through the experiments (ethanol) is presented. The heat transport’s contribution at TPCL was estimated at 0.87 when fitting to experiment results and 0.63 in simulation. Comparison of various working fluids and wick materials, htri increased with wick’s thermal conductivity. The value of htri was higher for ammonia due to the changes in interfacial HTC.
3.	Jinliang Xu—2014 [13] Keywords: LHP, evaporator, heat transfer, modulated porous wick	Flat-disk shape evaporator. Tilt angles: −90°, −60°, −30°, 0°, 90° (“−”: antigravity) Forced convective air cooling (Ta = 22 to 24 °C) Water as working fluid There are three layers of porous materials, primary layer (as shown in table), secondary copper table (2 mm–149μm), and third absorbent wool layer (2 mm–rpore = 20 μm) Evaporator: ϕ80 × 10 (without CC thickness); Aheating = 5 cm2 Vapor line: ID6/OD8 × 550 mm Liquid line: ID6/OD8 × 300 mm Condenser: 130 × 130 × 25 CR = 38.5%, 51.3%; 64.1%, 64.1%, 76.9% Sintering process: oven temperature 900 °C for 4 h.	Objects: It is to enhance heat transfer of pool boiling using the modulated porous wick sintered on the heater wall. Three types of evaporators: MWE (microchannel/wick evaporator), MME (modulated monoporous wick evaporator), and MBE (modulated biporous wick evaporator) were fabricated. Results: MBE LHP reduces the startup time and achieves more stable operation than MWE. At heat flux of 40 W/cm2 (heater heat flux), the MBE LHP can operate when Tc is around 63 °C; (Rt = 0.12 K/W) Optimum CR = 51.3%. Operation antigravity condition is better than others with the MBE LHP’s proper design. Best fin’s geometric parameters: h = 1.5 mm; p = 1.5 mm; w = 3 mm; best particle size: 88 μm
4.	S.C. Wu—2014 [14] Keywords: Wick structure, LHP, evaporator area, grooves	LHP with cylindrical stainless-steel evaporator (ϕ16 × 65) Water cooling Wick material: nickel (ID/OD = 9/12.5); largest rpore = 1.9 − 2.5 μm; K = 1.3 − 3.25 × 10−13 m2, porosity: 63–67%. Vapor line: ID5/OD6 × 470 Liquid line: ID4.5/OD6 × 585 Condenser: ID5/OD6.4 × 800 Ammonia as working fluid.	Objects: The effects of increasing the number of grooves on a wick’s surface on LHP performance were investigated. Results: The wick with 16-groove was quickly damage. The other wicks have similar properties, such as porosity, pore radius, K. Sintering condition: 45 min at 600 °C. Increasing the groove number increases the LHP’s performance (Q = 500 W, Rt = 0.14 K/W). An optimal number of grooves fabricated on the wick surface is presented.
5.	Jeehoon Choi—2013 [15] Keywords: Miniature LHP, evaporator, sintering, contact conductance, thermal resistance	Flat-disk shape evaporator. Wick material = Nickel (ϕ42 × 3), particles size: 3 μm, Pcapillary= 401. kPa, K = 0.99·10−11 m2, porosity = 64%, keff = 9 W/K·m CC: stainless-steel (ϕ46 × 7) Vapor line: ID4.95/OD6.35 × 250 (made by copper) Liquid line: ID4.95/OD6.35 × 300 (made by stainless-steel) Forced convective air cooling Working fluid: water Horizontal orientation Heater surface area: 30 × 30 mm2	Objects: For fabricating the LHP’s evaporator, a low-cost sintering method is explored. The porous material partially fills the vapor collection channel embedded in the evaporator’s base; two evaporators were fabricated. A sintering procedure is used to fabricate the evaporator shown in Figure (b). It is presented in Section 2.2 of the paper. Results: The startup of LHP with the second evaporator was shorter in time and more stable than one with the traditional LHP. By using the evaporator with the interpenetrated wick, the temperature on the CC reduced significantly which is 34 °C. Traditional LHP operated at 30–165 W; 80–141 °C; 1.81–0.71 K/W LHP using interpenetrated wick/base plate: 30–180 W; 47–102 °C; 0.76–0.43 K/W The lower temperature of the CC was due to the design of the second evaporator. It helped the wick and evaporator base contact excellently. It reduced heat loss to the CC through the evaporator’s wall.
6.	Randeep Singh—2008 [16] Keywords: LHP, heat transfer, thermal performance, miniature LHP, flat evaporator, thermal control	Miniature LHP using flat disk-shaped copper evaporator (ϕ30 × 10 mm) Working fluid: water Nickel wick (thickness = 3 mm, rpore = 3–5 μm; porosity: 75%) Condenser using Air forced cooling (Ta = 22 ± 2 °C) Copper Vapor line: ϕ2 × 150 mm Copper Liquid line: ϕ2 × 290 mm Heater surface area: 25 × 25 mm Condenser: ϕ2 × 50 mm	Objects: For the thermal control of small electronic equipment, it addresses the thermal characteristics of mLHP using a flat disk-shaped evaporator. Results: Startup condition at different heat loads, Q = 5–70 W, RmLHP = 5.66–0.17 K/W. The evaporator wall’s temperature was lower than 100 °C. Oscillating behavior was found when Q was between 10 and 20 W. This oscillation occured due to the fluctuation of heat loss from the evaporator to the CC and the subcooled liquid temperature.
7.	M.A. Chernysheva—2014 [17] Keywords: LHP, supercomputer, cooling system, operating temperature, thermal resistance	Flat-oval evaporator (longitudinal replenishment evaporator) 80 × 42 × 7 mm, Aactive = 32 × 42 mm2 12 Vapor grooves ϕ1.8 × 33 Copper wick (porosity 43%, rpore = 27 μm) Vapor line: (1) ID4/OD5 × 305 mm, (2) ID3/OD4 × 305 mm Liquid line: ID3/OD4 × 810 mm Condenser: ID4/OD5 × 160 mm	Objects: A cooling system with an LHP for a supercomputer’s thermal control is presented. Copper loop heat pipes with different vapor pipe IDs (4 and 3 mm each) were fabricated. The test was carried out with a heat load from 20 to 600 W during the cooling water’s temperature was changed from 20 to 80 °C. Results: LHP’s operating temperature varied slightly when the condenser cooling temperature changed in the range below 40 °C (called as variable conductance mode). It is more applicable to use copper-water LHPs when cooling temperatures of condenser is above 50 °C.
8.	Guohui Zhou—2016 [18] Keywords: Miniature LHP, ultrathin, thermal resistance, mobile electronics	Flat evaporator (thickness, δ = 1.2 mm), vapor line, liquid line, and condenser line (δ = 1 mm) Evaporator: 60 × 23 × 1.2 mm Aactive: 15 × 9 mm Primary porous material (inside evaporator): sintered from 10 layers of 500 mesh copper wire mesh (50 × 21 × 0.8 mm) (porosity: 65.2%) Secondary wick (in liquid line) sintered from 4 layers of 150 mesh copper wire mesh (δ = 0.43 mm) Liquid line: 105 mm, vapor line: 105 mm. Condenser: 125 mm (Natural cooling) LHP’s inclination: horizontal, anti-, and assisted gravity. Water as working fluid	Objects: mLHP for mobile electronics. Results: Startup of LHP happened at 2 W with evaporator temperature 43.9 °C. When Q is at 11 W, RLHP = 0.11 K/W There is no noticeably different performance with different orientations. For cooling mobile electronics: a tablet or smartphone, this mLHP achieves a promising thermal management solution.
9.	Takeshi Shioga—2015 [19] Keywords: Micro LHP, thermal resistance, heat leak, operation orientation	Micro loop heat pipe Chemical-etching and diffusion bonding process for fabrication Evaporator: 20 × 17 × 0.6 mm Vapor line: (1) 5.6 × 0.4 and (2) 1 × 75 mm in length Liquid line 4 × 0.4 × 120 mm Condenser (1) 5.6 × 0.4 and (2) 1 × 110 mm in length Working fluid: water	Objects: This micro LHP was fabricated for mobile electronic devices. The effect of vapor and condenser thickness on μLHP performance was investigated. Results: The μLHP could not operate with vapor line and condenser line thickness at 0.4 mm. When Q is at 5 W, RLHP = 0.8 K/W, Tevaporator = 50.5 °C. When Q = 15 W, RLHP = 0.32 K/W. Heat loss was estimated at around 11%. Based on the operating orientation, the LHP’s performance was slightly changed.
10.	Ji Li—2013 [20] Keywords: LED cooling, LHP, parallel condensers, thermal resistance	Evaporator: 30 × 30 × 15 (in mm). Gravity assisted LHP Connecting line: ID 5 mm Wick material is copper (porosity 50%, rpore = 65 μm, K = 6 ×10−11 m2) A Heater = 25 × 25 mm2 Condenser size: 120 × 80 × 50 mm	Objects: The investigation of copper-water LHP using dual parallel condensers was conducted primarily for LED illumination applications with high-power. Results: At Q = 300 W, the value of R is 0.4 °C/W; with Tair = 15 °C, Q = 0–100 W, Tjunction < 75 °C. At low heat loads, the condenser’s unpredictable nonuniform performance caused the unstable behavior of the LHP.

.

2. Experimental Setups and Data Reduction

2.1. Description of Test LHP

The elevation difference between the evaporator and condenser is 350 mm in this experiment. Cartridge heaters were used and inserted into the copper heating block at the evaporator base. The heat is rejected at the water-cooled condenser. The mass flow rate and inlet temperature of cooling water were around 7.5 × 10⁻³ kg s⁻¹ and 27.5 °C, respectively. The power supplied to the evaporator was adjusted and measured by a volt slider and a digital power meter, respectively. The thermal contact resistance between the heating block and the evaporator is minimized by thermal grease, which was filled in the interface and fixed with screws. Pressure transducers and four thermocouples were inserted directly into the path of the working fluid at different positions of the LHP, such as at evaporator outlet T_eo, condenser inlet T_ci, condenser outlet T_co, and the inlet of compensation chamber T_cci. These temperature transducers detect the temperature distribution inside the LHP. Therefore, the characteristics of circulation, as well as phase distribution, can be evaluated. Pressure transducer P_e was installed at the outlet of the evaporator. Figure 3 and Figure 4 and

Table 3. Main parameters of the LHP.

Evaporator Body	Values
Material	Copper
Length (mm)	80
Width (mm)	70
Height (mm)	24.5
Active area (mm2)	60 × 45
Fin geometry
Cross area (mm2)	2 × 2
Height (mm)	1.5
Fin pitch (mm)	4
Wick structure
Material	Stainless steel
Bulk volume (mm3)	50 × 41 × 5
Material	Ceramic
Bulk volume (mm3)	50 × 41 × 5
Vapor line
OD/ID (mm)	6.35/4.35
Length (mm)	800
Condenser line
OD/ID (mm)	6.35/4.35
Length (mm)	600
Liquid line
OD/ID (mm)	3.2/1.7
Length (mm)	1300
Working fluid
Water
Amount (mL)	33

show the schematic diagram, photo of the real experimental setup, and the main specifications of the LHP.

Thermocouples T₁, T₂, T₃ were installed, as shown in Figure 3b, to consider the temperature gradient caused by the heat flux and the temperature on the top surface of heating block T_s1, and the correct values of heating power and heat flux supplied to the evaporator were accessed. In the evaporator base, thermocouple T₄ was inserted to estimate the temperature at the evaporator’s bottom surface; T_s2 measures the temperature at the base of fin T_bf. The heat released from the condenser, Q_c, is obtained from the temperature difference of cooling water T_wa-i, T_wa-o, and the mass flow rate of cooling water. All measured data were collected and recorded by the KEITHLEY 2701 data acquisition system. Moreover, the level of liquid inside the compensation chamber can be observed by the polycarbonate evaporator cover.

Table 4. Uncertainty values.

Parameters	Uncertainty
T1, T2, T3	0.06 °C
T4	0.07 °C
Teo	0.06 °C
Tci	0.06 °C
Tco, Tcci	0.1 °C
Twa-i	0.1 °C
Twa-o	0.06 °C
Pressure transducer	1.5 kPa
Mass flow meter	0.18% of reading

describes the uncertainties of the mass flow meter and thermocouples (obtained from the calibration process in which a Pt100 thermometer (Chino Co. Model—R900-F25AT) was used as the standard source). Figure 5 and Figure 6 demonstrate the structure of the evaporator and the geometry of the evaporator’s inner surface.

Furthermore, the experimental uncertainty analysis of the computed heat transfer coefficients is given by the following equation (Equations (4)–(13)).

The experimental result R is assumed to be calculated from a set of measurements using a data interpretation program presented by [21].

R = R(X₁, X₂, X₃, …, X_N)

(4)

Each measurement uncertainty’s effect on the calculated result if only that one measurement were in error would be

$$\delta R_{Xi}=\frac{\partial R}{\partial X_i}\delta X_i$$

(5)

The partial derivative of R with respect to X_i is the sensitivity coefficient for result R with respect to measurement X_i. The single terms are combined by a root-sum-square method when respective independent variables are used in function R.

$$\delta R_{Xi}={\left\{{\displaystyle \sum }_{i=1}^N{\left(\frac{\partial R}{\partial X_i}\delta X_i\right)}^2\right\}}^{\frac{1}{2}}$$

(6)

Then, the parameter ΔT₁₂ can be defined as,

$$\mathsf{\Delta }{T}_{12}=T_1-T_2$$

(7)

The uncertainty for ΔT₁₂ is shown in Equation (8).

$$\delta \left(\mathsf{\Delta }{T}_{12}\right)={\left(\delta T_1^2+\delta T_2^2\right)}^{\frac{1}{2}}$$

(8)

where

ΔT₁₂ is the temperature difference between T₁ and T₂ at the heating block.

The parameter ΔT₂₃ can be defined as,

$$\mathsf{\Delta }{T}_{23}=T_2-T_3$$

(9)

The uncertainty for ΔT₂₃ is shown in Equation (10).

$$\delta \left(\mathsf{\Delta }{T}_{23}\right)={\left(\delta T_3^2+\delta T_2^2\right)}^{\frac{1}{2}}$$

(10)

where

ΔT₂₃ is the temperature difference between T₂ and T₃ at the heating block.

The parameter ΔT₁₃ can be defined as,

$$\mathsf{\Delta }{T}_{13}=T_1-T_3$$

(11)

The uncertainty for ΔT₁₃ is shown in Equation (12).

$$\delta \left(\mathsf{\Delta }{T}_{13}\right)={\left(\delta T_1^2+\delta T_3^2\right)}^{\frac{1}{2}}$$

(12)

where

ΔT₁₃ is the temperature difference between T₁ and T₃ at the heating block.

The parameter q can be defined as,

$$q=k\frac{\mathsf{∆}{T}_{12}}{{\delta }_1}$$

(13)

The uncertainty for q is shown in Equation (14).

$$\delta q=\frac{k}{{\delta }_1}\delta \left(\mathsf{∆}{T}_{12}\right)$$

(14)

where

q is the heat flux; k is the thermal conductivity of copper.

δ₁ is the distance between the heating block’s thermocouples.

The parameter T_bf can be defined as,

$$T_{bf}=T_4-\frac{q{\delta }_2}{k}$$

(15)

The uncertainty for T_bf is shown in Equation (16).

$$\delta \left(T_{bf}\right)={\left({\left(\delta T_4\right)}^2+{\left(\frac{{\delta }_2}{k}\delta q\right)}^2\right)}^{\frac{1}{2}}$$

(16)

where

T_bf is the evaporator fin’ base temperature.

T₄ is the evaporator’s base temperature.

The parameter h_e can be defined as,

$$h_e=\frac{q}{T_{bf}-T_{eo}}$$

(17)

The uncertainty for h_e is shown in Equation (18).

$$\delta \left(h_e\right)={\left({\left(\frac{\delta q}{T_{bf}-T_{eo}}\right)}^2+{\left(\frac{q\delta T_{eo}}{{\left(T_{bf}-T_{eo}\right)}^2}\right)}^2+{\left(\frac{q\delta T_{bf}}{{\left(T_{bf}-T_{eo}\right)}^2}\right)}^2\right)}^{\frac{1}{2}}$$

(18)

where

h_e is the heat transfer coefficient of the evaporator.

T_eo is the evaporator outlet temperature.

The parameter h_esat can be defined as,

$$h_{esat}=\frac{q}{T_{bf}-T_{esat}}$$

(19)

The uncertainty for h_esat is shown in Equation (20).

$$\delta \left(h_{esat}\right)={\left({\left(\frac{\delta q}{T_{bf}-T_{esat}}\right)}^2+{\left(\frac{q\delta T_{sat}}{{\left(T_{bf}-T_{esat}\right)}^2}\right)}^2+{\left(\frac{q\delta T_{bf}}{{\left(T_{bf}-T_{esat}\right)}^2}\right)}^2\right)}^{\frac{1}{2}}$$

(20)

where

h_esat is the heat transfer coefficient of the evaporator, calculated from the saturation temperature.

T_esat is the saturation temperature accessed from vapor pressure.

2.2. Description of the Wick’s Thermal Conductivity Measuring System

The wick materials’ thermal conductivity was measured by the transient hot-wire method. Figure 7 shows a schematic diagram of the thermal conductivity measuring device and sensor unit. It consists of a power supply device, a measuring device, a sensor unit, and a recording device (Personal Computer, PC). At the time of measurement, a constant current is applied from the power supply to the sensor. In addition, the voltage drop of the sensor unit is measured by a measuring device at regular intervals and recorded by a recording device.

The basic equation for thermal conductivity measurement is expressed by the following equations (Equations (21)–(24)).

The thermal conductivity of the wicks (Equation (21)) [22],

$${\lambda }_2=\frac{q^{*}}{2\pi } \frac{d ln t}{d \mathsf{\Delta }T}-{\lambda }_1$$

(21)

where

λ₂ is the thermal conductivity of the wick sample.

λ₁ is the thermal conductivity of the insulator.

q* is the amount of heating per wire length.

t is the time taken.

ΔT is the temperature change from t = 0 s.

Resistance of thin wire at a certain temperature,

$$R=R_o\left(1+\alpha \mathsf{\Delta }T\right)$$

(22)

where

R_o is the initial electrical resistance.

α is the temperature coefficient of resistance.

From Equation (22) and Ohm’s Law,

$$\mathsf{\Delta }T=\frac{1}{\alpha } \left(\frac{V\left(t\right)}{I{R}_o}-1\right)$$

(23)

where

V is the voltage drop on the thin wire.

I is the current.

By substituting ΔT into Equation (21),

$$\frac{d V\left(t\right)}{d ln t}=\frac{\alpha I^3{R}_o^2}{2\pi \left({\lambda }_1+{\lambda }_2\right)}=Constant$$

(24)

Then, the wick materials’ thermal conductivity can be obtained from the slope of the relationship between the voltage drop of the thin wire and the logarithm of the heating time. The measured thermal conductivity of the tested wicks and the comparison with literature data [7,8] are presented in

Table 5. Thermal conductivity of wicks.

Present Study		Value from References
Wick	λ2 [W (m K)−1]	Wick	λ2 [W (m K)−1]
Stainless Steel	6.4	SP-Sintered [8]	11.87
Ceramic	3.5	Ceramic [7]	4

.

2.3. Description of Condenser

In this study, the condenser is a double-pipe heat exchanger with a counter flow arrangement. Cooling water from the constant temperature pump flows in the annular area while the vapor condenses inside the copper tube. The condenser structure is described in Figure 8 and

Table 6. Specification of the condenser.

Parameters	Inner Tube	Outer Tube
Material	Smooth Copper tube	Poly-carbonated resin
Length, mm	600 mm	600 mm
OD/ID, mm	6.35/4.35	13/9

.

Furthermore, the same copper smooth tube is used for the vapor pipe and liquid pipe of the LHP, whose OD/ID is 6.35/4.35 and 3.2/1.5 mm, respectively.

2.4. Data Reduction

From Figure 3b, the values of heat flux q, heat transfer coefficient h_e, and thermal resistances R_e, R_c, and R_ct can be estimated by the following equations (Equations (25)–(36)): A = 27 cm², δ₁ = 5 mm, δ₂ = 2.5 mm.

Heat flux flowing from the heating block to the evaporator’s active area is calculated by Fourier’s Law of heat conduction as

$$q^{\mathsf{·}}=k\frac{T_1-T_2}{{\delta }_1}=k\frac{T_2-T_3}{{\delta }_1}=k\frac{T_1-T_3}{2{\delta }_1}$$

(25)

where

$q^{\mathsf{·}}$ is the heat transfer rate per unit heating block’s surface area.

k is the thermal conductivity of the copper heating block.

T₁ to T₃ is the heater temperature.

δ₁ is the distance between the thermocouples inside the heating block.

Then, the mean of $q^{\mathsf{·}}$ can be expressed by Equation (26).

$$q=\frac{1}{3}\left(k\frac{\mathsf{\Delta }{T}_{12}}{{\delta }_1}+k\frac{\mathsf{\Delta }{T}_{23}}{{\delta }_1}+k\frac{\mathsf{\Delta }{T}_{13}}{2{\delta }_1}\right)$$

(26)

$$Q=q*A$$

(27)

Additionally, the temperature of the heating block’s top surface, T_s1, and the evaporator bottom’s temperature, T_s2, can be determined by Equations (28) and (29).

$$T_{s1}=\frac{1}{3}\left[\left(T_1-\frac{3\left(q{\delta }_1\right)}{k}\right)+\left(T_2-\frac{2\left(q{\delta }_1\right)}{k}\right)+\left(T_3-\frac{\left(q{\delta }_1\right)}{k}\right)\right]$$

(28)

$$T_{s2}=T_4+\frac{q{\delta }_2}{k}$$

(29)

$$R_e=\frac{T_{s2}-T_{eo}}{Q}$$

(30)

$$R_c=\frac{T_{ci}-T_{wa-i}}{Q_c}$$

(31)

$$Q_c=m_{wa}{C}_p\left(T_{wa-o}-T_{wa-i}\right)$$

(32)

$$R_{ct}=\frac{T_{s1}-T_{s2}}{Q}$$

(33)

$$h_e=\frac{q}{T_{bf}-T_{eo}}$$

(34)

$$h_{esat}=\frac{q}{T_{bf}-T_{esat}}$$

(35)

$$T_{bf}=T_4-\frac{q{\delta }_2}{k}$$

(36)

3. Results and Discussion

Figure 9 displays the values of temperature at various locations in the experiment. The results show that the stainless-steel wick exhibits higher heat flux when compared to the ceramic wick. During the heat load range of 50 to 520 W in Figure 9a and 53 to 155 W in Figure 9b, the values of T_eo and T_ci are almost similar, and T_co and T_cci are nearly equal. We affirm that the working fluid circulates stably inside the loop heat pipe. However, in the LHP with a ceramic wick, some fluctuations were found in the range of heat power, from 53 to 80 W, where the values of T_cci were higher than T_co. This phenomenon happened because there was the intermittent appearance of a vapor–liquid interface near the position of thermocouple T_cci in the liquid line. In the experiment of the LHP with a stainless steel wick, the supplying liquid for the compensation chamber was more stable than the LHP with the ceramic wick. Moreover, in this experimental research, temperature T_s1 on the heating block’s top surface can be viewed as the electronics temperature, which is normally recommended to be lower than 85 °C for reliable and effective operation [23]. Therefore, this present LHP, with stainless steel and ceramic wicks, can satisfy the recommendation until the heat load reaches 350 and 54 W, respectively. The measured values and frequency of pore distribution by the mercury injection method [24] are given in

Table 7. Test results of pore distribution measurement by the mercury injection method.

Wick Materials	Ceramic	Stainless Steel
Pore volume in total (cm3·g−1)	0.20	0.07
Central pore diameter (μm)	1.29	16.40
Total pore specific surface area (m2·g−1)	0.66	0.02
Average pore size (μm)	1.18	11.85
Bulk density (g.cm−3)	2.01	4.34
Porosity (%)	39.3	31.5

and Figure 10.

3.1. Performance Evaluation

The thermal performance can be evaluated in terms of heat flux q, heat transfer coefficient h_e, and thermal resistances, which are evaporator R_e, condenser R_c, and contact surface R_ct, as shown in Figure 11 and Figure 12. In this study, the evaporator heat transfer coefficient was calculated from vapor temperature T_eo at the outlet of the evaporator and saturation temperature T_esat, accessed from the vapor pressure measured at the outlet of the evaporator.

In both experiments of stainless steel and ceramic LHPs, the evaporator heat transfer coefficient obtained from T_eo was higher than the values calculated from saturation temperature T_esat. Observing the difference in the results, the vapor might be superheated before leaving the evaporator. This superheating process could happen when vapor flows in the crossing grooves, and the heat of this process comes from the surrounding area of the fins and the grooves’ surface. The possible operating heat flux for the stainless-steel wick was higher than the ceramic wick. Comparing the evaporator heat transfer coefficient of the LHPs, the evaporator operating with the ceramic wick had the higher evaporator heat transfer coefficient when the heat transfer coefficient, h_e, linearly increased with the heat flux in the LHP with the stainless steel wick. However, the ceramic LHP did not operate better than the stainless steel one. The significant mass flow rate of vapor requires large pore sizes in the ceramic wick to reduce resistance. Otherwise, the performance of the condenser decreases. The numerical values obtained from the experimental uncertainty analysis of the computed heat transfer coefficients are presented in

Table 8. Uncertainty values of the computed heat transfer coefficients for LHPs with stainless steel wicks.

Q	q	δ(q)	he	δ(he)	hesat	δ(hesat)
W	W/m2	%	W/(m2‧K)	%	W/(m2‧K)	%
50.22	18,598.44	30.42	4592.67	30.46	1345.93	62.64
100.29	37,299.05	15.17	5588.10	15.25	2150.30	37.71
147.91	54,451.96	10.39	8458.43	10.39	3984.10	32.14
188.17	69,832.60	8.10	8323.83	8.12	4804.16	25.30
237.16	87,723.91	6.45	8368.00	6.43	5676.28	17.73
290.03	107,645.92	5.26	8427.34	5.14	6428.54	12.52
350.72	129,896.27	4.35	9388.90	4.31	7633.87	9.80
401.67	148,767.07	3.80	10,023.39	3.77	8228.43	7.74
445.87	165,137.27	3.43	10,651.51	3.46	9177.51	6.74
503.47	186,469.50	3.03	11,785.25	3.08	10,499.12	5.67
520.70	192,826.71	2.93	11,900.59	2.99	10,742.33	5.26

and

Table 9. Uncertainty values of the computed heat transfer coefficients for LHPs with ceramic wicks.

Q	q	δ(q)	he	δ(he)	hesat	δ(hesat)
W	W/m2	%	W/(m2‧K)	%	W/(m2‧K)	%
53.41	19,782.71	28.59	13,195.93	26.67	13,932.62	48.68
79.59	29,477.46	19.19	11,352.25	16.61	9709.18	21.12
105.72	39,154.18	14.45	10,783.11	14.27	8046.37	16.92
132.38	49,028.99	11.54	11,805.62	11.73	8359.43	14.03
155.45	57,574.38	9.83	10,737.34	9.87	7810.08	11.71

.

Performance of Evaporator and Condenser

Figure 12a,b displays the evaporator and condenser thermal resistances, R_e and R_c, of the stainless steel and ceramics LHPs. In the LHP with the stainless steel wick, the values of R_e became smaller with the increase in heating power. However, thermal resistance R_e for the ceramic one gradually increased in the same operating conditions, although the performance of the evaporator with the ceramic wick was more effective than the one with the stainless steel wick. For the thermal resistances of the condenser at the stainless steel LHP, it was reduced to the minimum value of 0.09 K.W⁻¹, then raised up slightly, as shown in Figure 12a. The higher the heat power supplied to the evaporator, the less liquid exists inside the compensation chamber. As a result, with more liquid present in the condenser with the increasing heat load, the performance of the condenser was slightly reduced.

For the LHP with the ceramic wick, Rc’s values were significantly high, i.e., 1.8 K.W⁻¹ at 53 W, due to the lower performance of the condenser. Additionally, particle differences between the stainless steel wick and ceramic wick are apparent in Figure 11a,b; the interfaces between the particles in Figure 11b are not as straightforward as those in Figure 11a. In the loop heat pipe with the stainless-steel wick, the working fluid was smoothly circulating inside the LHP because the flow resistance through the stainless-steel wick was lower than that of the ceramic wick. Therefore, the heat supplied made the working fluid evaporate, and the heat leak through the stainless-steel wick became small. In the ceramic wick’s case, the working fluid was not able to circulate correctly inside the LHP due to the high hydraulic resistance in the ceramic wick. As a result, heat flow, called a heat leak, became dominant in the evaporator with the ceramic wick.

4. Conclusions

The influence of two different wicks was tested in this study and used to describe the LHPs’ performance with a flat rectangular evaporator. The experimental results demonstrate that the LHP with the stainless-steel wick has better cooling performance than the LHP with the ceramic wick. The heater surface temperature of the LHP with the stainless steel wick increased from 40 to 105 °C in the range of a heat load from 50 to 520 W. In the ceramic wick LHP, this surface temperature reached 106 °C at a heat load of 155 W. Under gravity-assisted conditions, the LHP with the stainless steel wick could keep the temperature on the heater surface at 85 °C for a heat load of 350 W. However, the LHP with the ceramic wick could operate only at lower than 118 W for the same LHP, and the heater’s surface temperature approached 85 °C when the LHP was conducted at 54 W (20 kW·m⁻²). The ceramic wick cannot handle a high heat flux because of the conflict between vapor release and liquid suction. Large pore sizes are required to reduce resistance for the significant mass flow rate of vapor. It has been explained by Meléndez and Reyes [26].

$$m_v=\frac{\pi }{128}\left(\frac{{\rho }_v\sigma }{{\mu }_v}\right)\left(\frac{\epsilon d_e^3}{d}\right)$$

(37)

where

m_v is the vapor mass flow rate; ρ_v, σ, μ_v, and ε are vapor density, surface tension, viscosity, and porosity, respectively; δ is the wick thickness, and d_e is the effective pore diameter.

On the other hand, large capillary pressure is achieved by tiny pores for liquid suction, according to the Laplace-Young equation.

$$\mathsf{∆}P=\frac{4\sigma cos\propto }{d_e}, \propto is the contact angle$$

(38)

As a result, the vapor release and liquid suction of the ceramic wick require different pore sizes for better heat performance in LHPs.