This work studies experimentally the performance of an additively manufac- tured heat pipe with a triangular cross-section and grooved wick that uses acetone as the heat transfer fluid. The temperature time evolution at differ- ent axial positions of the heat pipe was measured for different heat transfer rates and fluid filling inventories. The experimental data analysis includes calculating heat losses and estimating the steady-state temperature, which has been shown to be critical for determining the thermal resistance and time constant accurately. We also propose a methodology to estimate the response time of the heat pipe to sudden changes in the thermal power de- mand. The presented prototype is able to evacuate up to 17 W in horizontal position with a thermal resistance lower than 1 K W−1. Keywords: Heat pipes, 3D-printing 1. Introduction 1 Heat pipes are devices that transport heat between two spatial locations 2 over a small temperature gradient. They find applications in very diverse 3 ∗Corresponding author Email address: b.cobo@madridspace.eu (Borja Cobo-Lopez) Wednesday 28thAugust, 2024 fields like nuclear engineering, geothermal heat harvesting or aerospace [1]. 4 The case of aerospace applications is particularly challenging, as electronic 5 components are increasing their performances very fast, which translates 6 into tighter heat dissipation demands that require technological leaps in 7 heat pipe technology [2]. One of the most promising technologies to enable 8 this leap is additive manufacturing. Additive manufacturing is able to pro- 9 vide lightweight structures with optimized geometries while exhibiting good 10 mechanical and thermal properties. In recent times, 3D-printed heat pipes 11 have been tested in different contexts [3, 4, 5, 6]. We summarize next some 12 works of special relevance for our study. 13 An aluminum 3D-printed heat pipe with microgrooves and working with 14 acetone was tested and applied to the thermal management of a LED [4]. 15 Other authors have also tested 3D-printed heat pipes in a CubeSat Thruster, 16 requiring a heat dissipation of 15 W [7]. Porous structures and acetone as 17 the working fluid were chosen in this study. The experiments showed good 18 performance in thermosiphon and horizontal orientation. Nevertheless, it 19 starts to deteriorate at inclinations of -2◦(with respect to the horizontal 20 plane), leading to the drying out of the wick at the evaporator. Esarte 21 and co-workers measured methanol imbibition in stainless-steel porous wicks 22 manufactured by selective laser melting, a 3D printing technology [3]. This 23 study showed higher permeability values, and thus faster imbibition, than in 24 a conventional copper wick manufactured by powder sintering. However, the 25 imbibition speed was lower than that of a stainless-steel mesh. Jafari et al. 26 [8] performed experiments to study the thermal performance of an additively 27 manufactured stainless steel heat pipe working with water, focusing also on 28 the optimal inventory (mass of working fluid) that a non-conventional, 3D- 29 printed wick design needs. They conclude that the optimum filling ratio 30 2 was 110% of the amount of fluid required to saturate the wick. Alterna- 31 tively, Chang et al. [4] defined the filling ratio as the proportion between 32 the volume of loaded working fluid and the inner space of the heat pipe, 33 finding that a filling ratio of 10% gave the best heat transfer performance 34 with the lowest thermal resistance. The enhanced performance compared 35 to conventional wick structures was attributed to an increase in the evap- 36 orating meniscus density at the liquid-vapor interface due to the presence 37 of sintered powder features. Park and collaborators [5] recently presented 38 a heat pipe with improved capillary transport and permeability, fabricated 39 using 3D printing technology, that includes a hybrid screen-groove wick in 40 the evaporator section and a homogeneous groove wick in the adiabatic and 41 condenser sections. They attribute the good wicking properties of their de- 42 sign to the additional roughness that the manufacturing technique endows 43 the wick surface. Finally, Yun and co-workers [6] tested an aluminum heat 44 pipe manufactured with selective laser melting that uses acetone as working 45 fluid. They obtain similar conclusions regarding the improved wicking capa- 46 bilities, as compared to other conventional manufacturing techniques. They 47 also present a mathematical model of the heat pipe performances which de- 48 scribe well their experimental measurements when the inventory is 100% of 49 the wick volume. Interestingly, for an inventory of 150%, the performances 50 seem to be better than expected. 51 In view of the works just described, laser powder bed fusion emerges 52 as the most popular technique for the additive manufacturing of metallic 53 heat pipe wicks. Given the novelty of the application of this technique 54 to the manufacturing of heat pipes, further research, including the design 55 of innovative geometries that can reduce the manufacturing cost, is needed. 56 Moreover, the issue of the optimal inventory seems to be quite open. Another 57 3 topic that is not sufficiently studied in these innovative designs is that of the 58 transient times the heat pipe takes to reach a steady state upon a sudden 59 change in the thermal boundary conditions. With these ideas in mind, 60 we present hear a new heat pipe design, manufactured with laser melting 61 technology. We put emphasis on understanding the effect of the inventory on 62 the heat pipe performances, characterized by the effective thermal resistance 63 and by the transient time taken to reach steady operation after a sudden 64 change in the evaporator temperature. To be able to carry out systematic 65 studies on the effect of the fluid inventory, we present the design of an 66 improved heat pipe test-bench that allows to try different inventories in a 67 same heat pipe instance without having to unmount it. The design of the 68 facility includes simple algorithms to estimate heat losses to the ambient 69 and to determine the final temperature reached after long transient times 70 without the need to wait until a steady state is fully reached. The proposed 71 methodology offers the possibility to speed up the testing of novel heat pipe 72 designs and their sensitivity to different operating conditions, including their 73 inclination or the fluid inventory. 74 2. Materials and Methods 75 2.1. Overall description of the facility and the filling procedure 76 A test bench was built (Fig. 2) to study the thermal performance of an 77 additively manufactured heat pipe at different inclinations, fluid inventories 78 and thermal demands. The tested prototype is 140 mm long with an exter- 79 nal quasi-triangular shape made of aluminum. The base of the triangle is 80 14.5 mm wide. The inner cross-section is 60 mm2and the wick is made of 81 rectangular grooves distributed along the three sides of the pipe (figure 1). 82 4 The pipe’s triangular design allows for additive production of the pipe in a 83 horizontal position without the need for support structures, simplifying pro- 84 cess planning and reducing waste material. In order to assess the heat pipe’s 85 performance, experiments were conducted to measure its thermal resistance 86 for different working conditions. 87 Figure 1: CAD view of the prototype internal cross-section 5 Figure 2: Experimental set-up The test bench shown in Fig. 2 was built for vacuuming the heat pipe, 88 filling it up and measuring its thermal resistance in an efficient way in a 89 variety of conditions. The vacuum line (shown as a yellow arrow in Fig. 2) 90 is connected from a stainless-steel valve (V3) to the vacuum pump, which 91 isolates the pump from the rest of the circuit. The vacuum pump is a dry 92 scroll pump (Scrollvac 10 plus) that provides a minimum pressure within 93 the prototype of 0 .10 mbar previously to filling it with the working fluid. 94 Downstream V3, the main line forks into two paths. On the one hand, 95 the right line that joins with V4 protects the pressure sensor from chemical 96 attack by the working fluid (Acetone). On the other hand, the bottom line 97 connects with the test prototype through valve V2. The pressure inside the 98 6 pipe is measured with a TTR 200 NS MEMS Pirani sensor with a range of 99 5·10−5mbar to 1500 mbar. This device is connected to a 24-V power supply 100 unit (PSU). 101 Before filling the heat pipe with the working fluid, we vacuum the in- 102 stallation. To do this, valves V2, V3 and V4 are opened (while V1 remains 103 closed) prior to starting the vacuum process. To verify that there are no 104 leaks in the circuit, a helium leak detector was used to ensure the tightness of 105 each connection. All connections showed a leak rate under 10−9mbar l s−1. 106 In addition to the vacuum pump, the same heater that supplies heat to the 107 heat pipe’s evaporator is activated to assist in the removal of condensable 108 gases. Once a minimum pressure of 0 .10 mbar is reached within the circuit, 109 V3 and the pump valve are closed. Subsequently, the heat pipe can be filled 110 through the designated pathway, marked by a blue arrow in Fig. 2. The 111 filling process is done using a 20 ml stainless-steel syringe with a 0 .5 ml res- 112 olution. This syringe is connected to the 3-way stainless steel valve (V1) 113 where one way connects to the heat pipe through a narrow conduit, and the 114 other is used to drain out the excess fluid used to feed and purge air from 115 the filling circuit. To charge the circuit and ensure that the syringe only 116 contains the required amount of fluid, valve V1 first connects the syringe 117 with the line intended for the removal of excess liquid. After that, valve 118 V1 is turned to the position that connects the heat pipe and the syringe. 119 The volume of the internal grooves, the volume of the tube connecting the 120 heat pipe to valve V1, and the dead volume of valve V1 are calculated from 121 prototype 3D models and added together to calculate the geometrical fluid 122 inventory ( Vgeom). Subtracting the volume of the tube connecting the heat 123 pipe to valve V1 and the dead volume of valve V1 to Vgeom yields the vol- 124 ume that will fill the heat pipe itself. This is referred to as the effective 125 7 fluid inventory ( Veff). The heat pipe must not be underfilled or overfilled, 126 as underfilling will result in performance degradation and overfilling will 127 result in condenser blockage [9]. In principle, the optimal fluid inventory 128 is the volume required to fill the wick with liquid and the vapor core with 129 gas. The volume required to fill the vapor core may be neglected because 130 it is far greater than the volume needed to fill the wick, owing to the large 131 density ratio between the liquid and its vapour. The initial filling of the 132 feeding circuit with working fluid is essential to minimize the amount of 133 non-condensable gases (air) introduced inside the heat pipe. Because it is 134 unavoidable to introduce some non-condensables during the filling, after the 135 pipe has been filled with the desired fluid inventory, the vacuum circuit is 136 opened (via valve V3) for a few seconds to eliminate its gas content. This 137 procedure is very efficient in eliminating non-condensables while having a 138 moderate impact on the amount of working fluid left inside the heat pipe 139 due to the large ratio between the vapor and liquid density. 140 2.2. Description of the testing procedure 141 In our experimental facility, once the filling is completed, the heat pipe 142 is not separated from the feeding circuit. This has the advantage of allowing 143 us to evaluate the performance of the prototype for different fluid invento- 144 ries in an easy and inexpensive way. However, it brings the disadvantage of 145 worse thermal insulation, as some heat will be lost to conduction through 146 the feeding circuit. Nonetheless, this is not a serious disadvantage, as we 147 can correct the measured heat pipe performances to account for the effect 148 of these losses (see Section 2.4 below). 149 150 In the heat pipe, heat is transferred to the evaporator by means of a 151 8 cartridge heater embedded in an aluminum block (Fig. 3). The surface area 152 where the heat is applied is equal to 30 mm ×14.5 mm. The condenser heat is 153 evacuated through a Peltier cell equipped with a fan-cooled heatsink. The 154 evaporator and condenser are both 30 mm long, and the adiabatic region 155 between them is 80 mm long. The temperature distribution is measured 156 by ten T-type thermocouples distributed along the longitudinal axis and at 157 both external and lateral sides of the evaporator and condenser regions. 158 The thermocouple placed at the condenser surface is used as input signal 159 of a Omega CN7500 PID controller to set the cold temperature during the 160 experiments. Every thermocouple and the pressure sensor are connected to a 161 NI-cDAQ system, which acquires data with a 10 Hz framerate. The assembly 162 is isolated from the ambient with Teflon, CPE (chlorinated polyethylene 163 elastomer) material, and neoprene foam. 164 Figure 3: Scheme of cartridge heater embedded in an aluminum block encapsulated with Teflon and CPE. To evaluate the performance of the heat pipe, the thermal resistance 165 (Fig. 4) was determined as 166 Rhp=Tp,e−Tp,c Qhp(1) 9 where Tp,eis the temperature of the outer surface of the evaporator at the 167 furthest axial position from the condenser, Tp,cis the temperature of the 168 outer surface of the condenser at the furthest axial position from the evapo- 169 rator and Qhpis the heat transfer rate that is effectively applied to the heat 170 pipe. 171 172 Figure 4: Scheme of the measured thermal resistance. The resistance was measured for different heat transfer rates in the range 173 of 0 to 20 W. The heat transfer rate is controlled by varying the input volt- 174 age to the heater by a power supply unit capable of delivering up to 60 VDC. 175 On the other hand, the PID controller described above, is connected with 176 a solid-state relay to the Peltier cell that refrigerates the condenser. The 177 Peltier is switched off when the temperature decreases below the set point 178 for the outer surface of the condenser, which is set to 20◦C in all experi- 179 ments reported here. 180 181 The heat transfer fluid selected for the heat pipe prototype was acetone. 182 10 Heat pipes commonly use acetone, ammonia, ethanol, methanol or methy- 183 lamine as working fluids. Water cannot be used as heat transfer fluid due 184 to its incompatibility with aluminum, since the hydrogen generated during 185 the experiments causes the degradation of the heat pipe performance [10]. 186 2.3. Steady-state temperature 187 During the experiments, it was observed that for the highest heat transfer 188 rates, it required a considerable amount of time ( >1 h) for the temperature 189 of the pipe envelope to reach a steady state. This may lead to very long 190 testing times if we are to be sure that the steady state has been reached. 191 To overcome this difficulty, the measured temperature time evolution were 192 fitted with the following equation to extrapolate the final steady-state tem- 193 perature: 194 Tfit(t) =T∞−(T∞−T0)e−t−t0 τ (2) where Tfitis the estimated temperature profile, T∞is the steady-state tem- 195 perature reached at each stage, tis the time vector at each stage, τis the 196 time exponential decay and t0andT0are the initial time and temperature at 197 the corresponding stage, respectively. Fig. 5 illustrates an example of how 198 Eq. (2) was applied to one of our experimental temperature time evolutions. 199 11 450 460 470 480 490 500 T ime [min]808284868890T emperature [°C]Figure 5: Comparison of the evaporator temperature time evolution (blue line) and the Eq. (2) (dashed orange line) measured in horizontal position and for a Qin= 21.00 W and a fluid inventory of 2 ml. The associated parameters of the temperature time evolution displayed 200 in Fig. 5 are T∞= 90.95◦C and τ= 1164 .90 s. 201 2.4. Heat loss to the environment 202 The tested prototype is thermally insulated from the environment, as 203 explained in Section 2; however, the specimen is connected to the vacuum 204 and filling lines by stainless-steel valves, and thus a non-negligible amount 205 of heat supplied by the cartridge heater is not only transferred to the heat 206 pipe but also lost through the connection lines. As a result, we propose the 207 following expression to account for the losses to the environment as well as 208 through the connection lines: 209 Qin=Qhp+Qloss (3) 12 where Qinis heat supplied by the heater, Qhpis the heat transfer rate 210 that actually goes to the prototype and Qlossare heat losses. Eq. (3) is 211 developed as a function of evaporator, condenser, and room temperature. A 212 batch of dry-tests with the pipe empty of fluid were performed at different 213 heat transfer rates ( Qin) to estimate the fitting parameters of our model 214 Qin=Tp,e−Tp,c Rdry+Kloss|Tp,e−Tamb|αloss (4) where the experimental data are the evaporator temperature Tp,e, condenser 215 temperature Tp,c, and the room temperature Tamb. The fitting parameters 216 are the heat pipe thermal resistance from dry-tests ( Rdry) and the losses to 217 the environment and the connection lines ( Klossandαloss). 218 The aforementioned fitting parameters are estimated according to the 219 following steps: 220 1. We define a cost function representing the sum of the squared error be- 221 tween the experimental values of Tp,e,Tp,c, and Tamband the numerical 222 ones computed using Eq. (4): 223 ε2(Rdry, Kloss, αloss) =NX n=1|Q2 num(Rdry, Kloss, αloss)−Q2 exp(Tp,e, Tp,c, Tamb)| (5) In this expression, Qnum(Rdry, Kloss, αloss) is the numerical solution 224 of the heat transfer rate of Eq. (4), whereas Qexp(Tp,e, Tp,c, Tamb) is 225 an experimental value for the heat transfer rate. The experimental 226 data from tests performed with the empty heat pipe can be found in 227 Supplemental Material. 228 13 2. We find the set of parameters ( Rdry, Kloss, αloss) that minimizes this 229 cost function for a given experimental curve Qexp(Tp,e, Tp,c, Tamb). The 230 minimization process is implemented using the function optimize. 231 minimize.fmin of the library SciPy . To obtain an initial guess for 232 the parameters, we use Rdry,0=Rgeom where Rgeom is the thermal 233 resistance of the given heat pipe based on its geometry, and Kloss= 234 Kloss,0andαloss=αloss,0being Kloss,0= 0.5 (in SI units) and αloss,0 235 = 0.2. 236 A comparison of the measured heat applied during the experiments and 237 the heat estimated using Eq. (4) is shown in Fig. 6. The fitting parameters 238 thus obtained are depicted in Table 1. Notice that, since αloss≈1, we 239 approximate the units of Klossto W K−1. 240 Table 1: Fitting parameters of Equation (4). Rdry[K W−1]Kloss[W K−1]αloss 7.48 0.0702 0.9752 The first ( Qhp) and second ( Qloss) terms of the right-hand side of Eq. (4) 241 are also represented in the same plot. As it can be seen, heat losses are not 242 negligible, and therefore they are calculated using the fitting parameters 243 obtained from dry tests data. Then, these parameters are used to deter- 244 mine the actual heat transfer rate ( Qhp) that is used in the calculation of 245 the thermal resistance of the heat pipe filled with acetone. Other authors 246 [11] have also remarked on the need to include heat losses in the transient 247 operation of heat pipes. 248 14 0 500 1000 1500 2000 2500 3000 T ime [min]024681012 P ower [W]Nominal P ower Q in Q hp Q lossFigure 6: Comparison of the measured heat transfer rate supplied by the heater (Nominal power) and the numerical solution for Qin. Estimate values for QhpandQloss are also included. 3. Results and discussion 249 As an example of our experimental methodology, we describe a series of 250 experiments in which we investigate the effect of the volume of loaded work- 251 ing fluid (the so-called fluid inventory, V) and working mode (thermosyphon 252 or pure heat pipe i.e.horizontal) on heat pipe performance. In particular, 253 we consider two performance parameters: the thermal resistance and the 254 response time to a sudden change in the input power. While the first one is 255 customarily used to characterize the performances of heat pipes, to the best 256 of our knowledge, there is no data in the literature of the response time of 257 heat pipes manufactured additively. 258 Table 2 summarizes the experimental runs performed on the heat pipe 259 prototype. In experiments 1-4 the heat pipe is kept vertical, thus working as 260 15 a thermosyphon, during the whole duration of the experiment. Conversely, 261 for experiments 5-7 the heat pipe is started-up vertically with the procedure 262 described in Section 2 and then aligned with the horizontal direction for 263 the test. The fluid inventories used in this work sweep a range around the 264 expected optimal fluid inventory, which is the volume required to fill the 265 wick ( Vw= 0.95 ml). 266 In this way, we can explore the sensitivity of the heat pipe performances 267 to moderate departures from the optimal inventory. For the thermosyphon 268 configuration, we used four different fluid inventories. After examining the 269 data, it was found that the fluid inventory V= 3 ml was significantly greater 270 than the optimal fluid inventory, resulting in high thermal resistance values. 271 As a result, it was not used in the horizontal configuration experiments. To 272 compare with the results obtained from other authors, we include in Table 2 273 the parameters they use. Chang et al. [4] expressed the filling ratio as V/V t, 274 ratio between the volume of loaded working fluid and the total inner space 275 of the heat pipe ( Vt), whereas Jafari et al. [8] expressed it as V/V w(ratio 276 between the volume of loaded working fluid and the volume of the wick). 277 Note that in the current work, some of the loaded fluid Vgoes to the tube 278 connecting the pipe and to the dead volume of the filling valve, and it is Veff 279 the part of the loaded volume that will fill the heat pipe itself. These ratios 280 were calculated for each experiment and are included in Table 2. 281 16 Table 2: Summary of the different experiments reported in this section. In the column “configuration”, V stands for vertical (thermosyphon) and H for horizontal (pure heat pipe). Exp.Number Configuration V[ml] Veff[ml] Veff/VtVeff/Vw 1 V 1 0.241 0.039 0.255 2 V 1.5 0.741 0.119 0.783 3 V 2 1.241 0.199 1.312 4 V 3 2.241 0.360 2.369 5 H 1 0.241 0.039 0.255 6 H 1.5 0.741 0.119 0.783 7 H 2 1.241 0.199 1.312 During the experiments, once the heat pipe is started up, the input heat 282 power Qinis varied in steps and the temperatures are measured at different 283 locations as a function of time. The sampling rate of these measurements 284 is high enough to achieve a good time resolution during the transient that 285 occurs after the input power is suddenly changed. The prescribed locations 286 at the outer surface of the heat pipe where the temperatures are measured 287 are: evaporator region bottom and lateral surface (Evp-Bot 1 and Evp-Side- 288 R, respectively); adiabatic section bottom surface (Adb-Bot) and condenser 289 region bottom and lateral surface (Cnd-Bot and Cnd-Side-R, respectively). 290 These measuring points are schematized in Fig. 7(a). 291 292 17 (a) 0 50 100 150 200 250 300 350102030405060T emperature [°C]Evp - Bot 1 Evp - Bot 2 Evp - Side - R Adb - Bot Cnd - Bot Cnd - Side - R 0 50 100 150 200 250 300 350 Time [min]051015Power [W]Q in Q hp (b) Figure 7: (a)Sketch showing the thermocouples’ locations. (b)Results of temperature time evolution (up) and input heat transfer rate (down) measured experimentally with V= 1.5 ml in horizontal configuration. The time evolution of the temperatures at the aforementioned positions, 293 for a test with a fluid inventory of V= 1.5 ml and the heat pipe placed 294 horizontally, is depicted in Fig. 7(b) (see Supplemental Material for the 295 18 remaining functional tests performed in this research). 296 The lower plot depicts the heat transfer rate supplied at the evapora- 297 tor,Qin, and the heat transfer rate actually transmitted to the pipe after 298 subtracting heat losses, Qhp. 299 In Fig. 7(b) we observe that under a heat transfer rate of 4 W, the 300 condenser temperature is maintained at approximately 20◦C. Then, the 301 condenser temperature increases to a maximum value of 50◦C, providing a 302 temperature difference between condenser and evaporator of approximately 303 7◦C. 304 3.1. Thermal Resistance 305 Fig. 8 displays the evolution of the thermal resistance as the effective 306 heat transfer rate increases for various fluid inventories for vertical and hor- 307 izontal positions. The thermal resistance decreases with increasing filling 308 ratio, as observed by [4] and [8]. Moreover, the thermal resistance decreases 309 as the heat transfer rate increases, since for low heat loads, a thick liq- 310 uid film remains in the evaporator at all times, reducing heat transfer [12]. 311 However, for the lowest filling ratio (1 ml) the thermal resistance increases 312 monotonically with heat transfer rate from 4 W onwards in both vertical 313 and horizontal orientations. The maximum heat flux that a heat pipe can 314 transport can be defined as the value at which the thermal resistance begins 315 to rise [12]. In this case, this increase is likely due to the wick drying out. 316 On the contrary, for the vertical thermosyphon configuration (Fig. 8(a)) and 317 the fluid inventories of 1 .5 ml, 2 ml and 3 ml, wick dry-out is not observed at 318 heat transfer rates lower than 10 W and the thermal resistance still presents 319 a decreasing tendency. Indeed, the fluid inventory of 1 .5 ml has the lowest 320 thermal resistance and maintains a constant value when increasing the ef- 321 19 fective heat transfer rate without drying out up to a value of 18 W. The 322 fluid inventory of 1.5 ml corresponds roughly to the calculated mass required 323 to fill the wick with liquid and the heat pipe core with vapor. The filling 324 ratio corresponding to 1.5 ml volume is 11.92% with respect to the internal 325 heat pipe volume and 71.2% concerning the total wick volume. This ratio 326 is similar to the one observed by [4] and [8]. 327 2 4 6 8 10 12 14 16 18 Q hp [W]01234R hp [K/W]V = 1 ml V = 1.5 ml V = 2 ml V = 3 ml (a) vertical 2 4 6 8 10 12 14 16 Q hp [W]01234R hp [K/W]V = 1 ml V = 1.5 ml V = 2 ml V = 2 ml (b) horizontal Figure 8: Thermal resistance for different fluid inventories ( V) as a function of the heat transfer rate in (a)vertical and (b)horizontal configuration. 20 Because the horizontal configuration is the most common in industrial 328 applications, the tests were also performed in this orientation (Fig. 8(b)). 329 The fluid inventory of 3 ml was discarded because it was clearly demon- 330 strated to be significantly higher than the optimal inventory. Additionally, 331 the 2 ml test was repeated, and the results of both tests are displayed in 332 Fig. 8(b), demonstrating good repeatability. The 1 .5 ml inventory exhibits 333 the lowest thermal resistance, with a value only 25% higher than the re- 334 sistance measured in the thermosyphon configuration. However, the ther- 335 mal resistance for this inventory increases for a heat transfer rate larger 336 than 12 W, whereas for an inventory of 2 ml, the thermal resistance remains 337 roughly constant until 17 W, when a slight increase is observed. The thermal 338 resistances shown in Fig. 8 were calculated using Eq. (1), which considers 339 only the heat that is transferred to the prototype Qhp, i.e. the heat supplied 340 by the heater minus heat losses. Thermal resistance values measured for the 341 presented prototype are of the same order of magnitude as those reported 342 by [6] for a comparable applied heat flux. 343 3.2. Transient Response 344 Fig. 9 represents the characteristic time of the temperature evolution 345 measured at the evaporator and fitted with the procedure explained in Sec- 346 tion 2.3, as a function of the effective heat transfer rate ( Qhp). For low 347 values of Qhp, the evaporator heats up almost instantaneously, and an ex- 348 ponential like behavior is not observed, as can be seen for heat fluxes lower 349 than 6 W in the experiment shown in Fig. 7(b). Thus, the characteristic 350 time is not represented in these cases. For larger values of Qhp, the charac- 351 teristic time is in the range of 500-1500 s as shown in Fig. 9. The results 352 show that the input heat has no significant effect on the characteristic time, 353 21 as also reported in the analytical works published by [13]. These analytical 354 models were then compared with the transient temperature profiles mea- 355 sured during the startup and shutdown of a copper flat-plate heat pipe [14]. 356 This research suggested that the convection heat transfer coefficient on the 357 outside water-cooled condenser surface strongly affects the time it takes to 358 reach a steady state, while input power has only a slight effect. 359 2.5 5.0 7.5 10.0 12.5 15.0 17.5 Q hp [W]050010001500200025003000τ [s]V = 1 ml V = 1.5 ml V = 2 ml V = 3 ml Dry- test (a) vertical 2 4 6 8 10 12 14 16 Q hp [W]050010001500200025003000τ [s]V = 1 ml V = 1.5 ml V = 2 ml V = 2 ml Dry- test (b) horizontal Figure 9: Characteristic time of the time evolution temperatures at the evaporator as a function of heat transfer rate for different fluid inventories ( V) in(a)vertical and (b) horizontal configurations. 22 4. Conclusions 360 The objective of the current investigation is to propose a novel experi- 361 mental facility dedicated to the quick and efficient evaluation of heat pipe 362 performances. The experimental procedure includes a methodology to de- 363 termine the heat losses to the ambient and the steady state temperature 364 from the unsteady measured profiles, which is required for an accurate anal- 365 ysis of the heat pipe characteristics. Moreover, the study seeks to validate 366 experimentally the suitability of the proposed design of an additively manu- 367 factured heat pipe to transport heat while upholding a minimal temperature 368 gradient along its entire length. 369 This research also placed emphasis on examining the influence of control- 370 ling the filling ratio, the so-called fluid inventory. Such investigation shows 371 values of the heat pipe thermal resistance, Rhp, as low as 0.53 K W−1for a 372 maximum heat transfer rate of 18 W in the vertical thermosyphon configu- 373 ration. The filling ratio that provides this result is 11.9% with respect to the 374 internal heat pipe volume and 78.3% concerning the total wick volume. The 375 same inventory exhibits the lowest thermal resistance in the horizontal con- 376 figuration, with a value that is only 25% higher than in the thermosyphon 377 configuration. However, a higher fluid inventory is needed in this orientation 378 to operate the heat pipe up to a heat transfer rate of 17 W without degrad- 379 ing thermal performance. Finally, values of the characteristic time of the 380 time evolution temperature at the evaporator region are presented. These 381 values are not substantially affected, within the experimental uncertainty, 382 by the thermal power that the heat pipe transports, nor by the amount of 383 fluid inventory. 384 23 Acknowledgments 385 The authors acknowledge the financial support of the Regional Government 386 of Madrid through the Industrial Doctorate program, Grant No. IND2019- 387 TIC-17109. 388 24