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1 1 Applied Thermal Engineering xxx (7) xxx xxx wwwelseviercom/locate/apthermeng 2 Air heat exchangers with long heat pipes: Experiments and predictions 3 H Hagens a, FLA Ganzevles b, CWM van der Geld b, *, MHM Grooten b 4 a VDL Klima bv Meerenakkerweg 3, 5652 AV Eindhoven, Netherlands 5 b Department of Mechanical Engineering, Technische Universiteit Eindhoven, Postbus 513, 5 MB Eindhoven, Netherlands 6 Received 16 October 6; accepted 1 March Abstract 9 This paper presents measurements and predictions of a heat pipe-equipped heat exchanger with two filling ratios of R134a, 19% and 1 59% The length of the heat pipe, or rather thermosyphon, is long (15 m) as compared to its diameter (16 mm) The airflow rate varied 11 from 4 to kg/s The temperatures at the evaporator side of the heat pipe varied from to 7 C and at the condenser part from 12 to C The measured performance of the heat pipe has been compared with predictions of two pool boiling models and two filmwise 13 condensation models A good agreement is found This study demonstrates that a heat pipe equipped heat exchanger is a good alterna- 14 tive for air air exchangers in process conditions when air water cooling is impossible, typically in warmer countries 15 Ó 7 Published by Elsevier Ltd 16 Keywords: Finned tube; Heat exchanger; Heat pipe; R-134a; Thermosyphon Introduction 19 Stand-alone electricity power generators are usually cooled with ambient air Standard practice is air-to-air heat 21 transfer or using a tube-in-plate heat exchanger with water 22 as an intermediate medium In some situations water is not 23 available or ambient temperatures are too high to use 24 ambient air In those cases heat pipes may provide an alter- 25 native for cooling powers in excess of 1 kw Multiple 26 heat pipes then connect two plate heat exchangers 27 The heat transfer in the system is based on the continu- 28 ous cycle of the vaporization and condensation process 29 The thermosyphon, or heat pipe if equipped with a wick 3 inside, is heated at the evaporator, which causes evapora- 31 tion of a part of the fluid The vapour flows to the con- 32 denser, where the fluid condenses while giving off its 33 latent heat, caused by cooling from the outside The con- 34 densate flows back to the heated section along the wall 35 by gravitation or capillarity, which closes the cycle Thermosyphons can be used to foster heat transfer between two gas streams [1,2] Vasiliev [3,4] gives an overview of applications of heat pipes and thermosyphons, including heat pipes for application in space Advantages are high heat recovery effectiveness, compactness, no moving parts, light weight, relative economy, no external power requirements, pressure tightness, no cross-contamination between streams and reliability [5,6] The heat transfer being based on evaporation and condensation, the latent heat of the fluid is an important parameter The higher the latent heat of a fluid, the higher the transfer of heat is at a lower pressure The working principles of the thermosyphon imply that the fluid should evaporate and condense within the temperature range Taking the possible application of cooling an electricity generator with ambient air into consideration, the working fluid R- 134a is an option The hot air will be in a range of 8 C, the ambient air will be in a range of to C The refrigerant R-134a sublimates at C and 51 kpa, so phase change from liquid to gas only occurs above this temperature [7] The critical temperature of R-134a is 116 C [8], which defines the extremes of the temperature range of R-134a, at a critical pressure of 6 MPa * Corresponding author Tel: ; fax: address: cwmvdgeld@tuenl (CWM van der Geld) /$ - see front matter Ó 7 Published by Elsevier Ltd doi:1116/japplthermaleng734

2 2 H Hagens et al / Applied Thermal Engineering xxx (7) xxx xxx Nomenclature A surface area, m 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Bo Bond number, Bo ¼ q f gd 2 =r, c p heat capacity at constant pressure, J/kg K d diameter, m d i inner pipe diameter, m D h hydraulic diameter, m F e filling degree, g acceleration due to gravity, m/s 2 h fin distance, m L length, m _m mass flow rate, kg/s M molecular weight, kg/kmol Nu Nusselt number, p pressure, Pa p r reduced pressure, Pr Prandtl number, q heat flux, W/m 2 Q heat flow rate, W r radius, m R heat resistance, K/W Re Reynolds number, S fin distance, m T temperature, C V volume, m 3 W distance between pipes, m Greek symbols a heat transfer coefficient, W/m 2 K k thermal conductivity, W/mK 59 Other possible working fluids are ammonia, pentane or water [5] All these fluids have the advantage over R-134a 61 that they have a higher latent heat, which enhances heat 62 transfer Unfortunately, the maximum practical tempera- 63 ture limit of ammonia is C [9], which is too low for 64 the situation at hand Water has the risk of freezing at 65 lower temperatures Pentane could be a useful alternative 66 for R-134a, considering its temperature range from 67 to 1 C, the higher latent heat and the higher surface ten- 68 sion coefficient [5,1,11] A higher surface tension coeffi- 69 cient has the benefit of lowering the risk of entrainment, 7 which is the most likely occurring limit in the application 71 of the thermosyphon [12] Other hydrocarbon refrigerants 72 mentioned by Lee et al [13] are possible working fluids 73 as well The type of filling fluid and the operational limits 74 will be subject of later research by the present authors 75 This paper presents experimental data of air heat pipe 76 air heat exchangers with long pipes (15 m) at two filling 77 ratios Nearly all data found in the literature are for much 78 shorter thermosyphons The results are compared with 79 those of a model that is based on existing correlations of 8 the literature The results will further be analyzed with 81 the aid of trends measured with a single pipe thermosy- d thickness, m Dh fg enthalpy of evaporation, J/kg g fin fin efficiency, l dynamic viscosity, Pa s q mass density, kg/m 3 r Surface tension coefficient, N/m v geometric correction factor Subscripts and superscripts b boiling c condensation cond condenser evap evaporator f fluid ff fluid film i inner lm logarithmic mean max maximum min minimum o outer tot total v vapour w wall x, y Cartesian coordinates phon, as for example those of Noie [14] Results of this study show which conditions foster application of this novel type of heat exchanger 2 Experimental A laboratory scale test rig was designed and built to 86 compare the performances of conventional plate-type 87 exchangers (with water as intermediate medium) and heat 88 pipe equipped plate heat exchangers A range of mass flow 89 rates of ambient air of 2 25 kg/s is possible The temper- 9 ature difference between hot and cold sides of the heat pipe 91 may vary up to C Let the volume of the evaporator, 92 V evap, be defined as the inner volume of that part of the 93 heat pipe that is in contact with hot air, see Fig 1 It will 94 be quantified, below, as the volume p 2 i L evap with r i = mm and L evap = 6 mm Two filling degrees, F e,as 96 defined in Eq (1), of the heat pipe with R-134a have been 97 examined 19 ± 1% and 59 ± 1% (for sake of conve- 98 nience these cases are indicated with F e = 19% and F e = 99 59% in the following): 1 11 F e ¼ðvolume of fluid in the tubeþ=v evap : ð1þ

3 H Hagens et al / Applied Thermal Engineering xxx (7) xxx xxx 3 orifice m in m out 4 temperature sensors each manometers heat pipe heat exchanger Fig 1 Schematic of the test rig air heater 14 Note that the volume of fluid is the volume of liquid plus 15 the volume that would be obtained if the vapour would be 16 condensed to liquid In this study, the overall heat transfer 17 and temperature distribution are assessed under mass flow 18 rates of ambient air varying from 4 kg/s to kg/s The 19 ambient air temperature varies from to C, whereas 11 the hot air flow has temperatures in the range from to C A schematic overview of the setup is shown in 112 Fig 1 The upper side is the cold side, where ambient air 113 enters Up- and downstream of the heat exchanger temper- 114 atures are measured with 16 Pt1 s (IC Istec ME 19), 115 with an accuracy of 1 C The temperatures of four sen- 116 sors are averaged and the results are denoted as T 1, T 2, 117 T 3 and T 4, see the LHS of Fig 2 At each axial location, 118 four sensors are mounted at 1/4 and 3/4 of the length of 119 the two diagonals of the mm 2 rectangular duct 1 The air stream velocity profile was measured and found 121 to be homogeneous Downstream of the hot section, ten 122 Pt-1 temperature sensors are mounted to investigate 123 the temperature variation over the height of the pipe at 124 the evaporator section They are mounted vertically at 125 mm distance from each other and at 117 mm of the side- 126 wall The Pt-1 sensors are all calibrated with accuracy 127 better than 1 C for the temperature range of 1 C 128 The measurement section is thermally insulated to mini- 129 mize errors in the heat fluxes deduced 13 At the entry, dynamic pressure measurement with an 131 orifice gives the air mass flow rate, with an accuracy of 132 2% The uncertainties of all measured and calculated 133 parameters are estimated according to [15] The air heater is a water air heat exchanger, with 3 mm 134 spaced vertical fins, which allows a uniform velocity profile 135 upstream of the evaporator This neutralizes the induced 136 swirl in the airflow caused by the radial fan 137 The heat exchanger consists of four rows of alternating and 13 vertical copper pipes, see the RHS of Fig 2 These 139 pipes have an outer diameter of 16 mm and a wall thickness 1 of 8 mm The total length of each pipe is 15 m, with m in the condenser section and the evaporator section 142 each The adiabatic length is 22 m This is the distance 143 between the two sections of the airflow in the wind tunnel 144 The inner surface of each pipe has small spiral grooves, to 145 enhance the heat transfer in evaporation and condensation 146 The grooves are 2 mm wide and 2 mm deep each, sepa- 147 rated 1 mm, under an angle of 25 with the vertical The dis- 148 tance between the pipes in a row is 365 mm The rows are mm apart and the total length in airflow direction of 1 the aluminium fins including the four rows is 1145 mm, 151 see Fig 2 At the top of each row, the pressure is measured 152 with a WIKA type RB manometer, at a frequency of Hz, with an accuracy of 1% after calibration The range 154 of the manometers is 1 MPa The saturation tempera- 155 ture of R134a is given by the Antoine relation (2) obtained 156 from data from NIST [8] with temperatures in degrees Cel- 157 sius and pressure in kpa T ¼ B=fA lnðp v =1Þg C ð2þ 161 with A = 152, B = 2484, C = To analyze the performance of the heat pipe equipped 163 heat exchanger, the heat flow rate as given by Eq (3) is 164 determined: Q ¼ _mc p DT ð3þ 168 Here DT is the temperature difference in the airflow up- and 169 downstream the heat exchanger The heat loss to the 17 environment was in separate measurements with a dedi- 171 cated heat flux sensor measured to be less than W/m This is negligible as compared to the measured heat flow 173 rates In addition, differences between incoming and outgo- 174 ing heat fluxes will be assessed below 175 The effectiveness of the heat transfer at both the hot and 176 cold side of the heat pipe heat exchanger is expressed in the 177 overall heat transfer coefficient a tot as defined by Eq (4) 178 [16]: a tot ¼ Q=ðAvDT lm Þ ð4þ 182 ambient air m in T 1 T 2 heat pipe heat exchanger m out T 4 T 3 hot air 275 mm 365 mm Fig 2 Definition of temperatures in air streams and tube arrangement

4 4 H Hagens et al / Applied Thermal Engineering xxx (7) xxx xxx 183 with A the total heat transferring area to be specified be- 184 low, va geometrical correction factor, here valued 1 [16], 185 and with 187 DT lm ¼ðDT max DT min Þ= lnðdt max =DT min Þ 188 Here DT max and DT min denote the maximum and minimum 189 temperature differences between the airflow and heat pipes 19 of the first and last row The area A is either the area 191 A fin,con on the condenser side (243 m 2 )ora fin,evap on the 192 evaporator side (386 m 2 ) Both Q and a tot will be used to 193 assess the heat transfer performance of the heat exchanger Prediction methods from the literature 195 A Nusselt number for heat transfer from the air to the 196 fins is given by Nu = a fin D h /k with the hydraulic diameter 197 taken to be 2S, which is twice the distance between two 198 neighbouring fin-plates (here 16 mm on the hot side and mm on the cold side) Also the Reynolds number, Re, is based on the hydraulic diameter Hewitt [17] provides 1 the following correlation 2 Nu ¼ :19 a :2 :18 :14 S h Re :65 Pr :33 ¼ :1124Re :65 b d d 4 5 with a the tube distance in a row (here 365 mm), b the dis- 6 tance between the tube in two successive rows (here 7 33 mm from heart-to-heart, see Fig 2, and 275 mm in 8 flow direction), d the tube diameter (here 16 mm) and h 9 the fin length in gas flow direction (here 137 mm) The Pra- 21 ndtl number is nearly constant (69 71), allowing for the 211 last equality in (6) 212 The heat resistance of the wall of the heat pipe is given by 216 R w ¼ lnðr o=r i Þ 2pk w L cond ¼ 1 a w A w 217 with r o and r i the outer and inner radii of the pipe (here mm and 72 mm, respectively), k w the thermal conductiv- 219 ity of the copper pipe and L cond the length of the evapora- 2 tor or the condenser section (here 6 mm) Area A w is 221 taken to be given by 2pr i L cond = 29 m 2 The right hand 222 side of Eq (7) is obviously a (simple) implicit expression 223 for the heat transfer coefficient a w The form of Eq (7) is 224 preferred since thermal resistances will be summed, in Eq 225 (12) 226 The heat transfer from the air to the tube is usually 227 described with the fin efficiency [18] with g fin ¼ tanhðml fin Þ=ðml fin Þ ð5þ ð6þ ð7þ ð8þ fer coefficient from the air to the fin, given by Eq (6), d Every tube in the tube bank is supposed to have its own 233 segment of fins This leads to a fin length, l fin, of half the 234 distance between two tubes (183 mm); this l fin is the length 235 from fin tip to tube wall Furthermore, a fin is the heat trans fin the fin thickness, here 2 mm, k fin the thermal conductivity 238 of the fin material, here aluminium, 236 W/mK The total 239 heat transferring area, A in Eq (4), is taken to be the heat 2 transferring area of the fins; it is 243 m 2 on the condenser 241 side, where A = A fin,cond, and 386 m 2 on the evaporator 242 side, where A = A fin,evap This yields the following heat 243 resistance between air and outer wall of the heat pipes [18]: R fin ¼ ð1þ g fin a fin A fin 247 The total heat transfer coefficient, is found from the 248 summation of the partial heat resistances, which are given 249 by Eqs (7) and (1) and one in the thermosyphon, 2 1/(a ff A w), see Fig 3, that can be evaluated in a way 251 described below This yields, by definition of a tot : 252 a tot ¼ 1 ; R tot A fin ð11þ 254 with the total resistance given by R tot ¼ 1 þ 1 1 þ ð12þ a ff A w a w A w g fin a fin A fin 258 Last but not least, a ff now needs to be evaluated 259 The heat resistance of the condensate in the thermosy- 2 phon can be obtained from: 261 R ff;c ¼ 1=ða ff;c A ff;c Þ ð13þ 263 with a ff,c a heat transfer coefficient, given below, and with A ff,c the wetted area inside the heat pipe at the condenser side, which will be taken to be equal to the full inside area air A fin wall filling fluid A w m ¼ 2a :5 finð1 þ d fin =l fin Þ ð9þ k f d fin ηfin αfin αw αff Fig 3 Schematic of heat transfer areas and resistances

5 H Hagens et al / Applied Thermal Engineering xxx (7) xxx xxx at this side, A w The analysis is therefore mainly applicable 268 to fully wetting fluids; consistent with this assumption is 269 the taking of L cond to be the full height of the condenser 27 side, below 271 The mean heat transfer coefficient at the condenser side, 272 a ff,c, has been estimated using two correlations from the 273 literature The first one is the famous result of Nusselt s 274 analysis of filmwise condensation on vertical plates [18, p ]: a ff;c;1 ¼ 1:47Re 1=3 f 1=3 q f ðq f q v Þg k f ; ð14þ l 2 f 279 with q v the mass density of the vapour and the film Rey- 28 nolds number, Re f, defined as: 282 Re f ¼ 4 _m cond =l f ð15þ 283 The way the local mass flow rate per unit of periphery 284 per tube, _m cond, is evaluated will be described shortly All 285 fluid properties are evaluated at the saturation temperature 286 corresponding to the prevailing pressure in the thermosy- 287 phon The heat transfer coefficient given by Eq (14) was 288 proven to be in agreement with experiments in a wide range 289 of flow and fluid conditions [18] Typical film thicknesses, 29 d x, have been computed and have been found to be two 291 orders of magnitude less than the tube diameter, d The 292 correlation (14) for vertical flat plates is therefore applica- 293 ble to our thermosyphons as well The mass flow rate of 294 liquid per unit of periphery per tube, _m cond, needs to be that 295 at the condenser end Conservation of mass implies that the 296 mass condensed at the total length of the condenser equals 297 the film mass flow rate at the condenser end in steady oper- 298 ation If Q is the total heat flow rate to a total of N tubes in 299 the heat exchanger and Dh fg the latent heat of the conden- 3 sate, the mass flow rate _m cond is therefore given by 32 _m cond ¼ Q=ðNpdDh fg Þ: ð16þ 33 The present analysis aims at exploring the possibilities of 34 existing, well-known correlations for predicting heat trans- 35 fer in heat-pipe equipped exchangers The Nusselt expres- 36 sion for the heat transfer coefficient was originally 37 derived for laminar flow, but is here merely considered as 38 a correlation It could be extended with correction param- 39 eters to account for turbulence and/or waves on the 31 vapour liquid interface, see [22 24] for example, but such 311 extensions are only deemed necessary if agreement between 312 measurement and prediction would turn out to be poor 313 For further comparison, a second correlation is examined 314 Another way to compute the heat transfer coefficient for 315 filmwise condensation is given by Rohsenow et al [18,19]: 317 a ff;c;2 ¼ 1=3 Re f qf ðq f q v Þg k 1:8Re 1:22 f 5:2 l 2 f ; ð17þ f 318 with Re f in the range 3 1 Estimates for Re f in our 319 thermosyphons are in the range 3 1 In the evaporator pool boiling occurs The Bond num- 3 ber, defined as 321 Bo ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q f gd 2 =r; ð18þ 323 is typically in the range 16 34, which makes it unnecessary to account for the special effects that occur in confined boiling (Bo would need to be less than or around 1 for this to be the case) Even if the length scale in Bo would have been taken to be the width of small grooves (2 mm), the Bond number would still be exceeding 1 The models of Cooper, see Eq (19), and Gorenflo, see Eq (), predict the pool boiling heat transfer coefficient, a ff,b [] :12 :4343 lnðrpþ a ff;b;1 ¼ 55pr ð :4343 lnðp r ÞÞ :55 M :5 q : ð19þ 334 with p r the reduced pressure, p/p c (p c is 6 MPa for the 335 fluid R-134a used here), R p surface roughness in lm (typi- 336 cally 1), M molecular weight of the condensate in kg/kmol 337 (typically 12 for R-134a) and q the heat flux a ff;b;2 ¼ F PF ðq=þ :9 :3p:3 r ðr p =:4Þ :133 ðþ 341 with 342 and a is given by a at the evaporator side and by a F PF ¼ 1:2p :27 r þ 2:5p r þ p r =ð1 p r Þ 344 Of course, either a ff,b,1 or a ff,b,2 is to be taken for a ff,b, ff ff,b ff,c at the condenser side Results The measurements are performed at steady state, and it typically took 9 min to reach steady state condition Measurements were done at each condition during 5 min to check steady state condition and to guarantee proper averaging Fig 4 shows a typical example of the airflow temper- Air temperature [ C] = 4 kg/s, F e = 19% T 4-59 C Time [s] T 1-2 C T 3-7 C T 2-39 C Fig 4 Typical histories of air temperatures, see also Fig 2, up- and downstream of the heat exchanger Mean values are T 3 = 7821 ± 3 C, T 4 = 84 ± 2 C, T 1 = 2476 ± 3 C and T 2 = 13 ± 2 C

6 6 H Hagens et al / Applied Thermal Engineering xxx (7) xxx xxx Q evap [kw] Q cond [kw] Fig 5 Comparison of measured heat flow rates at evaporator and condenser side of the heat pipe 354 ature histories during a measurement This figure shows 355 that the variation is less than 1 C 356 The heat flow rate is measured from the temperature dif- 357 ference over the heat exchanger both at the evaporator and 358 condenser part of the heat pipe At steady state these heat 359 flow rates should be equal Fig 5, with error bars to indi- 3 cate the measurement error [15], shows the comparison of 361 the heat flow rates at the evaporator side and condenser 362 part of the experiments This figure shows that the heat 363 flow rate of evaporator is about 4% larger than the heat 364 flow rate of the condenser, for which we have no 365 explanation 366 In some cases the heat flow rate is that high that the heat 367 pipe can dry out Ten Pt1 s were mounted downstream 368 the evaporator to measure the temperature distribution 369 along the evaporator Fig 6 shows four distributions at 37 two process conditions for two filling degrees of the heat 371 pipe A local, nongradual increase in temperature along T 4 [ C] = 4 kg/s, F e = 19% = 12 kg/s, F e = 19% = 4 kg/s, F e = 59% = 12 kg/s, F e = 59% the evaporator indicates a dry-out At dry-out, the inner wall of the thermosyphon is not fully covered with liquid This occurs at low filling degree and high heat flow rate (Fig 6) If dry-out occurs, the measurement is skipped from the analysis Figs 7 and 8 show the performance of the heat pipe at the evaporator side for various Reynolds numbers and filling degrees The measurement error of the heat transfer coefficient [15] is about 7% In Fig 7 the total heat transfer coefficient at F e of 19% is shown, whereas Fig 8 shows results at the higher filling degree The figures show that the performance increases with increasing heat flow rate An increase of the Reynolds number of the airflow leads also to a better performance Some process conditions have been repeated with a higher filling degree The results are given in Fig 8 A higher filling degree gives a higher overall heat transfer coefficient at otherwise identical process conditions Figs 9 and 1 show the performance of the heat pipe at the condenser side for various Reynolds numbers and filling degrees Fig 9 presents the total heat transfer coefficient at T 3 = 77 C, T 1 = 413 C 1 3 Location from top evaporator [mm] α tot [W/m 2 K] 3 1 Re = 2 Re = Re = 1 Re = 2 Re = 1 Re = Q [kw] Fig 7 Measured heat transfer coefficient evaporator side for various Reynolds numbers at F e = 19% α tot [W/m 2 K] 3 1 Re = 2 Re = Re = 1 Re = 2 Re = Re = Q [kw] Fig 6 The effect of filling degree and of mass flow rate on temperature distribution downstream of the evaporator Fig 8 Measured heat transfer coefficient evaporator side for various Reynolds numbers at F e = 59%

7 H Hagens et al / Applied Thermal Engineering xxx (7) xxx xxx 7 α tot [W/m 2 K] F e of 19% and that of the filling degree of 59% is shown in 394 Fig 1 The figures show that the performance improves 395 with increasing heat flow rate As on the evaporator side, 396 an increase of the Reynolds number of the airflow leads 397 also to a better performance Some process conditions have 398 been repeated with a higher filling degree The results are 399 given in Fig 1 A higher filling degree gives a higher over- all heat transfer coefficient at some process conditions 1 Figs 7 1 show that the performance of the condenser is 2 better than that of the evaporator at the same heat flow 3 rate, if performance is measured in terms of net heat trans- 4 fer coefficient 5 5 Analysis Re = Re = Q [kw] Fig 9 Measured heat transfer coefficient condenser side for various Reynolds numbers at F e = 19% α tot [W/m 2 K] 3 1 Re = Re = Q [kw] Fig 1 Measured heat transfer coefficient condenser side for various Reynolds numbers at F e = 59% 6 The trend of the heat transfer coefficient to level off and 7 even to decrease with increasing heat flow rate, most clearly 8 seen at F e = 59% in Fig 8, was by Hahne and Gross [21] 9 only found for angles of inclination (from the vertical) 41 exceeding The more horizontal, the more pronounced 411 this effect was, and their explanation was vapour blanket- Fig 11 Comparison of measured and predicted total heat transfer coefficient of the evaporator at F e = 19% and at airflow Reynolds number of 2 Fig 12 Comparison of measured and predicted total heat transfer coefficient of the evaporator at F e = 19% and at airflow Reynolds number of 8 ing at one side of the thermosyphon 1 The present measurements are in a vertical thermosyphon, and the observed trend is found to be more pronounced at the higher filling ratio Probably vapour blocking again plays a role, and this phenomenon is expected to manifest itself only if sufficient fluid is present Park et al [22, Fig 4] found for heat flow rates to a smooth tube (and PFC, C 6 F 14, as working fluid) a similar dependence on evaporating heat flux, and a similar dependence on filling ratio Figs 11 and 12 show a comparison of the measured total heat transfer coefficient and predictions based on models of pool boiling of Gorenflo and Cooper [], see Section 3 Fig 11 shows the comparison at airflow Reynolds number (based on 2S) of 2 (±2) whereas Fig 12 1 The force interpretation given by Hahne and Gross is incomplete: inertia forces are not merely in the main flow direction since bubbles growing at a wall experience inertia forces in other directions as well

8 8 H Hagens et al / Applied Thermal Engineering xxx (7) xxx xxx 426 presents the comparison at (±8) In both cases 427 the Gorenflo correlation predicts a higher heat transfer 428 coefficient than Cooper Both correlations yield the same 429 trend with respect to dependency on heat flux as the corre- 43 sponding measurements, and the agreement with measure- 431 ments is quite good for each Reynolds number The small 432 differences between the two models and the measurements 433 could be caused by a slight overestimation of the Nusselt 434 number for the airflow to the fins If the temperature is 435 not homogenously distributed the Nusselt number should 436 be lower than the estimated one The heat transfer estimate 437 from the air to the fins has a large influence on the total 438 heat transfer, so any inaccuracy in it is directly reflected 439 in comparisons like those of Figs 11,12 4 The best predictions are obtained with correlations for 441 boiling in the heat pipe (Gorenflo or even better Coo- 442 per) The use of well-established correlations as those of 443 Cooper has usually led to good agreement between mea- 444 surement and prediction of heat transfer in a thermosy- 445 phon, see for example [21,22,25] 446 Figs 13 and 14 show a comparison of the measured 447 total heat transfer coefficient and predictions based on 448 models of filmwise condensation of Butterworth and Nus- 449 selt [15], see Section 3 Fig 13 shows the comparison at air- 4 flow Reynolds number whereas Fig 14 presents the 451 comparison at Fig 13 shows a good agreement 452 between the predictions and the measurements At higher 453 airflow Reynolds numbers the difference between predic- 454 tion and measured heat transfer coefficient increases a bit 455 (Fig 14) and in this case the models underpredict the actual 456 heat transfer Similar to the evaporation side the difference 457 might be due to the estimation of the Nusselt number for 458 the airflow to the fins However, at both Reynolds numbers 459 the predicted heat flux decreases with increasing heat flow 4 rate, which is a different trend than the one measured This 461 measured trend is in agreement with measurements 462 reported by Hahne and Gross [21] for the heat transfer coefficients a ff of R115 The more vertical the thermosyphon, the bigger the increase of a ff with increasing heat flow rate This indicates that distribution phenomena along the circumference play a role, something that is not captured by the correlations of Butterworth and Nusselt, of course 6 Conclusions The performance of a heat pipe equipped heat exchanger for air has been measured and analyzed The heat pipe has no wick, so it is a thermosyphon, and is long compared to its diameter: 1 cm vs 16 cm No measurements with thermosyphons that long have been found in literature except those of Noie [1] with a multi-row heat pipe heat exchanger with a thermosyphon length of 13 cm and except those with a single tube of 8 m in Ref [26] The overall heat transfer of the heat exchanger has been assessed At the evaporator side 1 W/m 2 K has been measured and at the condenser side of the heat pipe W/m 2 K The temperature distribution over the evaporator has been found to be indicative of proper filling degree A model to predict the heat transfer and to calculate the performance of the heat pipe equipped heat exchanger based on correlations from literature has been presented This model yields good agreement between experiments and predictions Trends have been interpreted with the aid of various findings reported with single-tube thermosyphons The result of this study is that a heat pipe equipped heat exchanger can replace a water-cooled heat exchanger without loss of performance The tested process conditions are typical for warmer countries like Bahrain This study therefore demonstrates that it is possible to apply heat-pipebased cooling equipment in practical conditions of warmer countries More research has to be carried out to find, for example, the most suitable working fluid, the optimal heat pipe geometry, operating limits Fig 13 Comparison of measured and predicted total heat transfer coefficient of the condenser at F e = 19% and at airflow Reynolds number of Fig 14 Comparison of measured and predicted total heat transfer coefficient of the condenser at F e = 19% and at airflow Reynolds number of

9 H Hagens et al / Applied Thermal Engineering xxx (7) xxx xxx Acknowledgements We are obliged to VDL Klima bv, the Netherlands, for 1 financial support and to one of the reviewers for useful 2 suggestions 3 References 4 [1] SH Noie, Investigation of thermal performance of an air-to-air 5 thermosyphon heat exchanger using e-ntu method, Appl Therm 6 Eng 26 (5 6) (6) [2] SH Noie-Baghban, GR Majideian, Waste heat recovery using heat 8 pipe heat exchanger (HPHE) for surgery rooms in hospitals, Appl 9 Therm Eng (14) () [3] LL Vasiliev, Heat pipes in modern heat exchangers, Appl Therm 511 Eng 25 (1) (5) [4] LL Vasiliev, State-of-the-art on heat pipe technology in former 513 Soviet Union, Appl Therm Eng 18 (7) (1998) [5] PD Dunn, DA Reay, Heat Pipes, fourth ed, Pergamon Press, [6] T Wadowski, A Akbarzadeh, P Johnson, Characteristics of a 516 gravity assisted heat pipe based heat exchanger, Heat Recov Syst 517 CHP 11 (1) (1991) [7] MJ Morgan, HN Shapiro, Fundamentals of Engineering Thermo- 519 dynamics, second ed, John Wiley & Sons Inc, [8] NIST Standard Reference Database 69, June 5 Release, NIST 521 Chemistry WebBook 522 [9] J Unk, Ein Beitrag zur Theorie des geschlossenen Zweiphasen- 523 Thermosiphons, Dissertation Technische Universität Berlin, [1] AP Fröba, L Penedo Pellegrino, A Leipertz, Viscosity and surface 525 tension of saturated n-pentane, Int J Thermophys 25 (4) [11] AP Fröba, S Will, A Leipertz, Saturated liquid viscosity and 528 surface tension of alternative refrigerants, in: 14th Symposium on 529 Thermophysical Properties, Boulder, CO, USA, [12] DA Reay, Heat Exchanger Selection Part 4: Heat Pipe Heat 53 Exchangers, International Research & Development Co Ltd, [13] HS Lee, JL Yoon, JD Kim, Pradeep Bansal, Evaporating heat 532 transfer and pressure drop of hydrocarbon refrigerants in 952 and mm smooth tube, Int J Heat Mass Transf 48 (12) (5) [14] SH Noie, Heat transfer characteristics of a two-phase closed thermosyphon, Appl Therm Eng 25 (4) (5) [15] SJ Kline, FA McKlintock, Describing uncertainties in single- 538 sample experiments, Mech Eng 75 (1953) [16] VDI-Wärmeatlas, Berechnungsblaetter fuer den Waermeuebergang, 5 6 erw Auflage, VDI Verlag GmbH, [17] GF Hewitt, Heat Exchanger Design Handbook, Begell House, [18] WM Rohsenow, JP Hartnett, YI Cho, Handbook of Heat 543 Transfer, third ed, McGraw-Hill, [19] HD Baehr, K Stephan, Heat and Mass Transfer, Springer, [] JG Collier, JR Thome, Convective Boiling and Condensation, 546 Clarendon Press, [21] E Hahne, U Gross, The influence of the inclination angle on the 548 performance of a closed two-phase thermosyphon, Heat Recov Syst (1981) [22] YJ Park, HK Kang, CJ Kim, Heat transfer characteristics of a 551 two-phase closed thermosyphon to the fill charge ratio, Int J Heat 552 Mass Transf 45 (2) [23] S Thumm, Ch Phillipp, U Gross, Film condensation of water in a 554 vertical tube with countercurrent vapour flow, Int J Heat Mass 555 Transf 44 (1) [24] SG Kandlikar, Handbook of phase change, Boiling and Condensa- 557 tion, Taylor and Francis, [25] E Azad, F Geoola, A design procedure for gravity-assisted heat pipe 559 heat exchanger, Heat Recov Syst 4 (2) (1984) [26] KS Ong, Md Haider-E-Alahi, Performance of a R-134a-filled 561 thermosyphon, Appl Therm Eng 23 (18) (3)