Effects of mass transfer time relaxation parameters on condensation in a thermosyphon

Transcription

1 Journa of Mechanica Science and Technoogy 29 (12) (2015) 5497~ DOI /s Effects of mass transfer time reaxation parameters on condenion in a thermosyphon Youngchu Kim 1, Jongwook Choi 2,*, Sungcho Kim 2 and Yuwen Zhang 3 1 Department of Aerospace Engineering, Graduate Schoo, Sunchon Nationa Uniersity, Jeonnam, 57922, Korea 2 Schoo of Mechanica and Aerospace Engineering, Sunchon Nationa Uniersity, Jeonnam, 57922, Korea 3 Department of Mechanica and Aerospace Engineering, Uniersity of Missouri, Coumbia, MO 65211, USA (Manuscript Receied Apri 22, 2015; Reised Juy 29, 2015; Accepted August 4, 2015) Abstract Mass transfer time reaxation parameters for condenion affect the amount of the mass transfer in the phase change. In the present study, a numerica inestigation has been impemented with four different parameters for the condenion process in a thermosyphon, with the parameter of 0.1 for the eaporation process. The numerica resuts were compared with the experimenta resuts to aidate the numerica methods. When the mass transfer time reaxation parameter for the condenion was set to the aue considering the density ratio out of the four parameters, the numerica resut was in good agreement with the experimenta resut. This numerica process is expected to be used to predict the temperature distribution in the thermosyphon more accuratey. Keywords: Condenion; Eaporation; Heat pipe; Mass transfer time reaxation parameter; Phase change; Thermosyphon Introduction A heat pipe is a passie deice that keeps the heat transfer steady ony by a sma temperature difference between the eaporator and the condenser without any externa driing power. In outer space with no conection phenomena by air, the heat pipe has been used to coo the eectronic components in a eite. For ground appications, the heat pipe has been appied to heat exchangers, dehumidification, air conditioning systems, soar water heating systems, injection mods, and diecasting dies to increase the therma or cooing efficiency [1]. The conentiona heat pipe has a wick, that is, a porous structure, on the wa [2]. The eaporated working fuid is condensed on the condenser wa and then the condensed working fuid is circuated into the eaporator aong the wick by the capiary force. In other words, the eaporation pressure in the heat pipe pays a roe in pushing the working fuid to the direction of the condenser, whie the capiary pressure by the wick performs a roe in transporting the working fuid from the condenser back to the eaporator. Athough the performance of the heat pipe with the wick may be affected by graity, a heat pipe with the proper design can operate against graity. Meanwhie, a heat pipe without a wick has been deeoped, where the condenser is arranged at the top and the eaporator at the bottom in order to use graity to return the condene * Corresponding author. Te.: , Fax.: E-mai address: choijw99@scnu.ac.kr Recommended by Associate Editor Ji Hwan Jeong KSME & Springer 2015 to the eaporator section. The eaporated working fuid goes up through the center of the heat pipe due to free conection and the condene goes down aong the wa due to graity. The circuation of the working fuid is maintained by a phase change. This heat pipe operated by graity is caed a thermosyphon, for which a numerica anaysis has been carried out in the present study. Many eary researches for the heat pipe were mainy conducted through experiments. These studies focused on the heat transfer characteristics of the heat pipe with the fiing ratio of the working fuid, the aspect ratio of the heat pipe, the heat input in the eaporator, the cooant mass fow rate in the condenser, and so on [3, 4]. The therma performance of the incined heat pipe was aso studied experimentay using a nanofuid as the working fuid [5]. In the eary numerica studies, the anayses of the fuid fow and the heat transfer were impemented without using the phase change modes of the working fuid in the heat pipe [6, 7]. In recent years, the phase change has been numericay considered in the eaporation and the condenion processes [8-13]. The VOF (Voume of fuid) mode [14-16] has been used in the simuation of a phase change with a free surface. The amount of the mass transfer in the phase change is affected by the mass transfer time reaxation parameters whose aues hae not been ceary suggested. These parameters for the eaporation and the condenion were used with the same aue of 0.1 by some researchers [8, 10, 11]. Aso, these parameters hae been used as the defaut aues in the Fuent

2 5498 Y. Kim et a. / Journa of Mechanica Science and Technoogy 29 (12) (2015) 5497~5505 program [17]. In another study, the mass transfer time reaxation parameters were set equa to the aue of 100 for the eaporation and the condenion [18, 19]. Howeer, these parameters shoud be set differenty for eaporation and condenion because the iquid density is much arger than the apor density. In recent researches, these parameters were decided with consideration for the baance of the condenion mass and the eaporation mass [12, 13]. As mentioned aboe, arious aues of the mass transfer time reaxation parameters hae been proposed in the numerica anaysis with a phase change in the heat pipe. In the present study, numerica anayses hae been impemented with four parameters for condenion whie the parameter for eaporation has been fixed at 0.1. The numerica resuts hae been compared with the experimenta resuts to erify the numerica method. The condenion process of the apor has been isuaized using the numerica data, and the mass transfer time reaxation parameter for the condenion has been chosen reasonaby among the four parameters. 2. Physica mode 2.1 Goerning equations The phase change process between the iquid phase and the apor phase shoud be incuded in the numerica anaysis of the thermosyphon. In the present study, the VOF mode has been empoyed to simuate the phase change and the free surface [20]. In the puing heat pipe, the oume change of the apor is ery significant because the pressure difference of the apor makes the driing force. In the thermosyphon, howeer, the oume change of the apor is itte significant because free conection and graity force make the driing forces. Thus, the working fuids are assumed to be incompressibe in this study. The continuity equations for the iquid phase and the apor phase in the VOF mode are: 1 é ( ) ( ) ( J J) r t a r a r ù ê + Ñ = - ú ë û, (1) 1 é ( ) ( ) ( J J) r t a r a r ù ê + Ñ = - ú ë û. (2) The oume fractions for the iquid and apor phases must isfy: a + a = 1. (3) Void regions are not aowed in the VOF mode because each ce shoud be occupied by either a singe phase or a combination of phases. The oume fraction for the iquid phase is used to get the oume-fraction-aeraged density when the iquid phase and the apor phase are combined in a ce: r = a r + (1 - a ) r. (4) Aso, the oume-fraction-aeraged density is required in the momentum and the energy equations. In the VOF mode, the momentum equation is expressed in Eq. (5) and a singe set of the momentum equation is used without making a distinction between the iquid phase and the apor phase. The externa forces consist of the pressure, the iscous, the graity, and the surface tension ike the terms of the right hand side in Eq. (5). The CFS (Continuum surface force) mode [21] is empoyed for the surface tension aong the interface between the two phases: ( r) + Ñ ( r) = -Ñ p + Ñ ém( Ñ + Ñ T ) ù + rg + F t ë û, (5) where the dynamic iscosity and the surface tension force are obtained from: m = a m + (1 - a ) m, (6) F = s æ Ña ö rñ Ña ç a è Ñ ø, (7) 1 ( r + r ) 2 and the contact ange on the wa is set to 40 degrees for wa adhesion [22, 23]. The energy equation is represented in Eq. (8), incuding the source term caused by the phase change: ( re) + Ñ é( re + p) ù = Ñ ( kñ T ) + Q t ë û, (8) where E, k, Q are defined as: a (1 ), (1 ), ( ) re + -a re éa r C p + -a rc ù p T - T E = = ë û, a r + (1 - a ) r a r + (1 -a ) r k = ak + (1 - a ) k, (10) Q = L( J - J ). (11) 2.2 Mass transfer time reaxation parameters In most researches, the mass transfer time reaxation parameter was proposed on the basis of the Hertz-Knudsen equation and the net mass fux of the apor-iquid interphase in the eaporation process is [24, 25]: M æ p p ( T ) ö J ' = a -, (12) 2p R ç T T è ø where a is the accommodation coefficient obtained from the (9)

3 Y. Kim et a. / Journa of Mechanica Science and Technoogy 29 (12) (2015) 5497~ ratio of the experimentay obsered eaporation eocity to the theoreticay maximum eaporation eocity in the eaporation process. Aso, it can be used in the condenion process. Under the condition that the temperature and the pressure are cose to the uration state in the Causius-Capeyron equation [26], the foowing reation can be obtained: DH p - p = - T - T T r r ( 1 / 1/ ) ( ) - Substituting Eq. (13) in Eq. (12), one obtains:. (13) J ' = a M DH T - T 2p RT (1/ r -1/ r ) T. (14) The source term in the goerning equation of the fuid fow and the heat transfer can be obtained by mutipying the oumetric interfacia surface area by Eq. (14), which reates to the mean Sauter diameter. The equations of the mass fux in the eaporation and the condenion processes are [25]: Fig. 1. Geometry and grid generation of thermosyphon. not conerge in the numerica cacuation if b e and b c are too arge, whie the mass transfer wi hardy occur in the phase change if b e and b c is too sma. J J T - T = bea r, (15) T T - T = bca r, (16) T where b e and b c are the mass transfer time reaxation parameters for the eaporation and the condenion: 6 M be = D 2p RT 6 M bc = D 2p RT rdh, (17) ( r - r ) rdh. (18) ( r - r ) 3. Numerica anaysis A numerica anaysis of the fuid fow and the heat transfer incuding the phase change in the thermosyphon has been carried out by the Fuent program. The numerica resut has been compared with the experimenta resut [11] to aidate the numerica method. On the other hand, the puing mode in the heat pipe occurs when the inner diameter is smaer than the critica diameter [28]. The equation of the critica diameter is reated to the surface tension and the buoyancy as foows: σ d cri = 2 (ρ ρ )g -. (20) Generay, b e and b c hae been set equa to 0.1 in the numerica anaysis. Howeer, b e and b c shoud be set with being proportiona to r and r, respectiey. If they hae the same aue, the amount of the mass transfer in the phase change wi not keep the baance because of the difference between the iquid density and the apor density. In the present study, the mass transfer time reaxation parameter for the condenion ( b c ) has been offered to soe this probem: b r c = be, (19) r where b e is 0.1 on the basis of the Ref. [27]. Eq. (19) takes the ratio of the iquid density to the apor density into account. The parameter considering the density ratio wi maintain a baance between the eaporating mass transfer and the condensing mass transfer in the phase change. The soution wi Generay, the critica diameter is found in the range of 3-5 mm for the puing mode. Therefore, the puing mode has not been considered because the inner diameter of 22 mm is used in this study. 3.1 Geometry and grid generation of thermosyphon The two-dimensiona geometry of the thermosyphon using the rectanguar coordinate system, which has been used in a number of numerica inestigations [8, 10, 11], is shown in Fig. 1. Both the eaporator and the condenser sections hae 0.2 m ength, whie the adiabatic section has 0.1 m ength. The thermosyphon is 0.5 m in the entire ength and the inner and the outer diameters are m and m, respectiey. The grids in the upper section of the thermosyphon, which hae been generated in the soid domain as we as in the fuid domain, are represented in Fig. 1. Aso, the fine meshes hae been buit in the icinity of the wa so as to get a thin fim.

4 5500 Y. Kim et a. / Journa of Mechanica Science and Technoogy 29 (12) (2015) 5497~5505 Tabe 1. Properties in fuid and soid domains. Property(unit) The tota meshes are composed of about 80,000 ces since the ces of oer 69,092 are required in the grid-independence test for the same configuration [11]. 3.2 Cacuation conditions Vaue r (kg/m 3 ) T T 2 r (kg/m 3 ) m (kg/m s) m (kg/m s) s T T 2 k (W/m K) 0.6 k (W/m K) C p, (J/kg K) 4,182 C p, (J/kg K) 1, T T T T 4 k s (W/m K) L (J/kg) 2,455,000 The main properties in the fuid and the soid domains are shown in Tabe 1. The iquid density, the surface tension coefficient, and the specific heat of the apor are gien as a function of the temperature and the others as a constant. The iquid temperature can be aried from K to 373 K, whie the apor temperature can be aried from 373 K to ess than 400 K. Thus, the iquid density has a arge difference of 30.4 kg/m 3, whie the apor density has a sma difference of kg/m 3. Accordingy, the apor density is assumed to be constant, whereas the iquid density is gien as the function of the temperature. The boundary and the initia conditions used in the numerica anaysis are represented in Tabe 2. In the boundary condition, a constant heat fux is imposed on the eaporator section and conectie heat transfer is appied to the condenser section cooed by the water jacket. Here, the conectie heat transfer coefficient is obtained from the experiment [11]. Adiabatic conditions are proided at the top and the bottom sections as we as in the midde section of the thermosyphon. The wa boundary to soe the momentum equation has a nosip condition. In the initia condition, the fiing ratio, which means the ratio of the initia iquid oume to the tota oume of the eaporation section, is set to 50% as depicted in Fig. 1. The iquid oume fraction is defined as 1.0 in the iquid region whie 0.0 in the apor region. Aso, the initia temperatures of the iquid region and the apor region are set to 372 K and 374 K, respectiey. These temperatures wi ead to a steady state Tabe 2. Boundary and initia conditions. Condition Section Vaue Boundary condition Initia condition Eaporator Adiabatic Condenser Top and bottom Wa Liquid (Incuding soid contacted with iquid) Vapor (Incuding soid contacted with apor) Constant heat fux : q w = (W) Zero heat fux : q w = 0(W) Conectie heat transfer : q w = h(t - T w), h = 707.6(W/m 2 K), T = (K) Zero heat fux : q w = 0(W) No sip : = 0(m/s) Voume fraction : α = 1 Temperature : T = 372(K) Voume fraction : α = 0 Temperature : T = 374(K) Tabe 3. Soution methods and cacuation conditions. Parameter Pressure-eocity couping Determination of momentum and energy Voume fraction Pressure interpoation Residua conergence criterion Mass Veocity Energy Scheme / aue SIMPLE First-order upwind Geo-Reconstruct PRESTO Time step (sec) Maximum aowed Courant No. 3 quicky because the uration temperature is 373 K at one atmosphere pressure. The initia temperatures of the soid region are made to correspond to those of the iquid region and the apor region, respectiey. The initia eocity is defined equa to 0.0, and the operating pressure and the operating density are set to Pa and kg/m 3, respectiey. The soution methods and the cacuation conditions are shown in Tabe 3 to anayze the heat and fuid fow in the thermosyphon using the Fuent program which is made on the basis of the FVM (Finite oume method). The schemes of SIMPLE, First-order upwind, Geo-Reconstruct, and PRESTO are used for the pressure-eocity couping, the determination of momentum and energy, the oume fraction, and the pressure interpoation, respectiey. Aso, the residua conergence criterions for the mass, the eocity, the energy are set 4 to 10-4, 10-6, and 10 -, respectiey. The initia time step is sec, and this time step wi be automaticay decreased

5 Y. Kim et a. / Journa of Mechanica Science and Technoogy 29 (12) (2015) 5497~ Tabe 4. Source terms in continuity and energy equations. J - J Continuity equation æ T - T ö æ T - T ö = bc a r ç - be a r T ç T è ø è ø L( J - J ) Energy equation é æ T - T ö æ T - T öù = L êbc a r ç - be a r ú T ç T êë è ø è øúû Source term Temperature condition Phase change process T > T Eaporation T < T Condenion T > T Eaporation T < T Condenion Tabe 5. Four cacuation conditions with arious mass transfer time reaxation parameters. Mass transfer time reaxation parameter for eaporation( b e ) Mass transfer time reaxation parameter for condenion( b c ) Case Case β c,od ìï mc - m ü e ï - βc,od í ý ïî max ( mc, me ) ïþ Case Case r be r under the condition that Courant number is ess than Four cases with mass transfer time reaxation parameter To simuate the mass transfer in the phase change, the source terms of the continuity and the energy equations shoud be cacuated according to the temperature condition in Tabe 4. In the continuity equation, the iquid mass is transferred to the apor mass if the iquid temperature is greater than the uration temperature, whie the apor mass is transferred to the iquid mass if the apor temperature is ess than the uration temperature. In the energy equation, the atent heat caused by the phase change shoud be considered as the source term. To cacuate the source terms for the phase change process, the UDF (user-defined function) shoud be added to the Fuent program [29]. For reference, the eaporation-condenion mode offered by the Fuent program can be aaiabe ony with the mixture and Euerian mutiphase modes except the VOF mode [17]. The mass transfer time reaxation parameters ( b e, b c ) in the source terms shoud be defined as the appropriate aues in order to determine the amount of mass transfer in the eaporation and the condenion. In the present study, we did a numerica anaysis for the four cases as shown in Tabe 5. Here, the mass transfer time reaxation parameter for the eaporation ( b e ) has been fixed on 0.1, which is based on the preious Fig. 2. Temperature profies aong outer wa of thermosyphon with time in case 4. studies, whie the mass transfer time parameter for the condenion ( b c ) has been set to the four different aues. In case 1, the aue of 0.1 has been used for the condenion, which was obtained from the Refs. [8, 10, 11]. In case 2, the equation for the mass baance between the eaporation and the condenion has been utiized for the parameter, which was described in the Refs. [12, 13]. In case 3, the aue of 100 has been used for the parameter, which was suggested in the Refs. [18, 19]. In case 4, the parameter has been presented with consideration for the ratio of the iquid density to the apor density. 4. Resuts and discussion 4.1 Vaidation of numerica anaysis Due to the characteristics of the VOF mode, a transient simuation was done for the heat and fuid fow in the thermosyphon. At the steady state, the resuts from the numerica soution hae been compared with the resuts measured in the experiment. To check out the steady state, the temperature profies are represented at an intera of 10 sec at the eight points aong the outer wa of the thermosyphon as shown in Fig. 2. Here, the measurement positions from the y-axis are 0.05 m and 0.15 m for the eaporator section, 0.25 m for the adiabatic section, and 0.32 m, 0.36 m, 0.40 m, 0.44 m, and 0.48 m for the condenser section, respectiey. The resuts of case 4 are used for the comparison. In the resut, the temperature aues are considered to hae reached steady state at around 50 sec. On the other hand, it took the temperature more

6 5502 Y. Kim et a. / Journa of Mechanica Science and Technoogy 29 (12) (2015) 5497~5505 Fig. 3. Comparison between experimenta and numerica temperature profies in condenser section. Fig. 5. Variations of parameter for condenion with time in case 2. than about 17 days per each case to reach a steady state using the computer with Inte Core i7-3930k CPU, 32 GB RAM, and 64 bit operating system. The comparison between the experimenta and numerica temperature profies in the condenser section is represented in Fig. 3 in order to aidate the numerica resuts. The numerica aues are ower than the experimenta aues in the condenser section. On the other hand, ony the aues in the condenser section are used to compare with the resuts because the origina experimenta data in the eaporator section had a probem as Fadh et a. mentioned in their paper [11]. The probem was that the thermocoupes were not ocated on the wires of the heater wrapped around the eaporator section, but ocated between the wires in the experiment. Unike the experimenta data in the eaporator section with the heat wire, the experimenta data in the condenser section with the water jacket can sti be aaiabe because there was not any probem for measuring the temperature. Aso, this study focuses on the effects of the parameters in the condenser section ony. Thus, the comparisons between the experimenta and numerica resuts are confined to the condenser section. The reatie errors of the numerica cacuation for the experimenta data in the condenser section are shown in Fig. 4. In case 4 with the smaest error, the reatie errors are 1.18% on aerage for the condenser section. Consequenty, the cacuated resuts can be accepted as the reasonabe resuts. 4.2 Resuts with mass transfer time reaxation parameter Fig. 4. Comparison of reatie error distribution for four cases in condenser section. The main objectie of the present study is to identify the appropriate aue of the mass transfer time reaxation parameter for the condenser ( b c ). The numerica anayses for the four cases hae been conducted to find the parameter. When the aue of b c increases, the numerica resuts approach the experimenta ones as shown in Fig. 3. The aue of b c reates to the thickness of the condensed iquid fim, which means the amount of the mass transfer in the phase change by Eq. (16), and affects the temperature distribution. If the aue of b c is on the increase, the amount of the mass transfer is aso on the rise when the apor phase is changed to the iquid phase. Accordingy, the amount of the iquid dropets formed on the wa in the condenser section affects the iquid fim thickness, that is, the more the iquid dropets are, the thicker the iquid fim gets. In case 2, the aue of b c expressed by the equation increases with increasing time as represented in Fig. 5 and reaches steady state after about 25 sec. Here, the aues of b c are between around 50 and 55 at the steady state. In case 4, the aue of b c considering the density ratio is about 173 at the uration temperature of 373 K. Thus, according to aues of b c, the four cases can be arranged as case 4 > case 3 > case 2 > case 1. As a resut, the appropriate aue of b c is determined to be the aue in case 4, which is the ratio of the iquid density to the apor density, out of the four parameters. 4.3 Discussion on heat and fuid fow in thermosyphon The distribution of the iquid oume fraction for the thermosyphon in case 4 is shown in Fig. 6. A thin iquid fim is formed aong the cod wa of the condenser as represented in Fig. 6(a). The iquid dropet, not the iquid fim, is obsered in the adiabatic section as shown in Fig. 6(b) since the iquid fim descending from the condenser is somewhat eaporated. The eaporated bubbes appear in the eaporator section as shown in Fig. 6(c). Fig. 7 indicates that the iquid dropet is coming

7 Y. Kim et a. / Journa of Mechanica Science and Technoogy 29 (12) (2015) 5497~ numerica anaysis of the heat and fuid fow and the phase change using the VOF mode with the parameter considering the density ratio for the thermosyphon. Fig. 6. Liquid oume fraction at steady state in case Concusions The effects of the mass transfer time reaxation parameters on the eaporation and the condenion in a thermosyphon hae been inestigated. The foowing concusions hae been obtained: The mass transfer time reaxation parameters affect the amount of the mass transfer in the phase change, and shoud be decided with consideration for the same ratio in the condenion mass and the eaporation mass. The mass transfer time reaxation parameter for the condenion is recommended to be the aue considering the density ratio, that is, 0.1 ( r / r ), whie the parameter for the eaporation is set to 0.1. Reasonabe resuts can be obtained from a numerica anaysis of the heat transfer and the fuid fow incuding the phase change in the thermosyphon using the VOF mode with the appropriate mass transfer time reaxation parameter. For future study, a numerica inestigation on the PHP (puing heat pipe) wi be conducted considering the puing mode and the compressibe effects in the phase change. Fig. 7. Descending iquid dropet due to graity with time in case 4. Acknowedgment This paper was supported by Sunchon Nationa Uniersity Research Fund in Nomencature Fig. 8. Temperature distribution and eocity ector at steady state in case 4. down with time owing to graity at the eary stage of the condenser in case 4. The thin iquid fim is deeoped, as shown in Fig. 6(a), from the assembage of the iquid dropet in the course of time. Fig. 8 depicts the temperature distribution and the eocity ector in the thermosyphon incuding the soid domain in case 4. The adiabatic section in the soid domain has a inear temperature distribution between the high temperature of the eaporator section and the ow temperature of the condenser as shown in Fig. 8(b). Ascending fow is obsered in the center of the thermosyphon by free conection, and descending fow is seen on the cod wa of the condenser section. Finay, reasonabe resuts can be obtained from a a : Accommodation coefficient C p : Specific heat (J/kg K) D : Mean Sauter diameter (m) d : Thermosyphon diameter (m) E : Interna energy (J/kg) F : Vector of surface tension force (N/m 3 ) g : Vector of graity acceeration (m/s 2 ) D H : Vaporization enthapy (J/kg) h : Conectie heat transfer coefficient (W/m 2 K) J : Net mass fux oer apor-iquid interface (kg/m 2 s) J : Mass transfer (kg/m 3 s) k : Therma conductiity (W/m K) L : Latent heat (J/kg) M : Moecuar weight (kg/kmoe) m : Tota mass (kg) max : Maximum aue p : Pressure (Pa) Q : Heat source due to phase change (W/m 3 ) q : Heat fux (W) R : Uniersa gas constant (J/mo K) T : Temperature (K) t : Time (s)

8 5504 Y. Kim et a. / Journa of Mechanica Science and Technoogy 29 (12) (2015) 5497~5505 Greek symbos a b m p : Veocity ector (m/s) : Voume fraction : Mass transfer time reaxation parameter (1/s) : Dynamic iscosity (kg/m s) : Mathematica constant equa to circe s circumference diided by its diameter r : Density (kg/m 3 ) s : Surface tension coefficient Subscripts c : Condenion cri : Critica e : Eaporation : Liquid phase : From iquid phase to apor phase od : Preious step : Saturation : Vapor phase : From apor phase to iquid phase w : Wa : Ambient References [1] F. Iorizzo, Couping of umped and distributed parameter modes for numerica simuation of a sintered heat pipe, Thesis, in Poitecnico di Miano, Itay (2012). [2] N. Pooyoo, S. Kumar, J. Charoensuk and A. Suksangpanomrung, Numerica simuation of cyindrica heat pipe considering non-darcian transport for iquid fow inside wick and mass fow rate at iquid-apor interface, Internationa Journa of Heat and Mass Transfer, 70 (2014) [3] S. H. Noie, Heat transfer characteristics of a two-phase cosed thermosyphon, Appied Therma Engineering, 25 (2005) [4] I. Khazaee, R. Hosseini and S. H. Noie, Experimenta inestigation of effectie parameters and correation of geyser boiing in a two-phase cosed thermosyphon, Appied Therma Engineering, 30 (2010) [5] Z.-H. Liu, Y.-Y. Li and R. Bao, Therma performance of incined grooed heat pipes using nanofuids, Internationa J. of Therma Science, 49 (2010) [6] M. Zhang, Z. Liu, G. Ma and S. Cheng, Numerica simuation and experimenta erification of a fat two-phase thermosyphon, Energy Conersion and Management, 50 (2009) [7] A. S. Annamaai and V. Ramaingam, Experimenta inestigation and computationa fuid dynamics anaysis of a air cooed condenser heat pipe, Therma Science, 15 (3) (2011) [8] A. Aizadehdakhe, M. Rahimi and A. A. Asairafi, CFD modeing of fow and heat transfer in a thermosyphon, Internationa Communications in Heat and Mass Transfer, 37 (2010) [9] D.-L. Sun, J.-L. Xu and L. Wang, Deeopment of a aporiquid phase change mode for oume-of-fuid method in FLUENT, Internationa Communications in Heat and Mass Transfer, 39 (2012) [10] L. Asmaie, M. Haghshenasfard, A. Mehrabani-Zeinabad and M. N. Esfahany, Therma performance anaysis of nanofuids in a thermosyphon heat pipe using CFD modeing, Heat and Mass Transfer, 49 (2013) [11] B. Fadh, L. C. Wrobe and H. Jouhara, Numerica modeing of the temperature distribution in a two-phase cosed thermosyphon, Appied Therma Engineering, 60 (2013) [12] K. Kafee and A. Turan, Axi-symmetric simuation of a two phase ertica thermosyphon using euerian two-fuid methodoogy, Heat and Mass Transfer, 49 (2013) [13] K. Kafee and A. Turan, Simuation of the response of a thermosyphon under pused heat input conditions, Internationa J. of Therma Sciences, 80 (2014) [14] Y. Zhang, A. Faghri and M. B. Shafii, Capiary bocking in forced conectie condenion in horizonta miniature channes, J. of Heat Transfer, 123 (3) (2001) [15] Y. Zhang and A. Faghri, Numerica simuation of condenion on a capiary grooed structure, Numerica Heat Transfer (Part A), 39 (3) (2001) [16] S. C. K. D. Schepper, G. J. Heynderickx and G. B. Marin, CFD modeing of a gas-iquid and apor-iquid fow regimes predicted by the baker chart, Chemica Engineering J., 138 (2008) [17] ANSYS, ANSYS FLUENT User s Guide, Reease 14.0, ANSYS Inc., PA, USA (2011). [18] Z. Yang, X. F. Peng and P. Ye, Numerica and experimenta inestigation of two phase fow during boiing in a coied tube, Internationa J. of Heat and Mass Transfer, 51 (2008) [19] C. Fang, M. Daid, A. Rogacs and K. Goodson, Voume of fuid simuation of boiing two-phase fow in a apor-enting microchanne, Frontiers in Heat and Mass Transfer, 1 (013002) (2010) [20] ANSYS, ANSYS FLUENT Theory Guide, Reease 14.0, ANSYS Inc., PA, USA (2011). [21] J. U. Brackbi, D. B. Kothe and C. Zemach, A continuum method for modeing surface tension, J. of computationa physics, 100 (1992) [22] W. A. Zisman, Reation of the equiibrium contact ange to iquid and soid constitution, Adances in Chemistry, 43 (1964) [23] S. G. Kandikar and M. E. Steinke, Contact anges of dropets during spread and recoi after impinging on a heated surface, Chemica Engineering Research and Design, 79 (4) (2001) [24] M. Knudsen, The kinetic theory of gases: Some modern aspects, Methuen and Co. Ltd., London, UK (1934). [25] S. C. K. D. Schepper, G. J. Heynderickx and G. B. Marin, Modeing the eaporation of a hydrocarbon feedstock in the conection section of a steam cracker, Computers and Chemica Engineering, 33 (2009) [26] D. R. Lide, CRC handbook of chemistry and physics, CRC Press, Boston, USA (1998). [27] H. L. Wu, X. F. Peng, P. Ye and Y. E. Gong, Simuation of refrigerant fow boiing in serpentine tubes, Internationa J. of

9 Y. Kim et a. / Journa of Mechanica Science and Technoogy 29 (12) (2015) 5497~ Heat and Mass Transfer, 50 (2007) [28] P. R. Pachghare and A. M. Mahae, Thermo-hydrodynamics of cosed oop puing heat pipe: an experimenta study, JMST, 28 (8) (2014) [29] ANSYS, ANSYS FLUENT UDF Manua, Reease 14.0, ANSYS Inc., PA, USA (2011). Youngchu Kim receied his B.S. and M.S. in Aerospace Engineering from Sunchon Nationa Uniersity, Korea, in 2013 and 2015, respectiey. He is currenty a Researcher at Keyyang Precision Co., Ltd. in Gyeongbuk, Korea. Mr. Kim s research interests incude heat pipes, turbo charger, and dust coection system. Jongwook Choi receied his B.S., M.S., and Ph.D. in Mechanica Engineering from Chonnam Nationa Uniersity, Korea, in 1993, 1995, and 1999, respectiey. He is currenty a Professor at the Schoo of Mechanica and Aerospace Engineering at Sunchon Nationa Uniersiy in Jeonnam, Korea. Dr. Choi s research interests incude heat pipes, nano-fuids, and aerodynamics. Sungcho Kim receied his B.S. in Mechanica Engineering from Hanyang Uniersity, Korea, in He then receied his M.S. and Ph.D. in Aeronautica Engineering from KAIST in 1985 and 1989, respectiey. Dr. Kim is currenty a Professor at the Schoo of Mechanica and Aerospace Engineering at Sunchon Nationa Uniersity in Jeonnam, Korea. Dr. Kim s research interests incude aerodynamics using experimenta and computationa fuid engineering. Yuwen Zhang receied his B.S. and M.S. in Energy and Power Engineering from Xi an Jiaotong Uniersity, China, in 1985 and 1988, respectiey. He then receied his Ph.D. in Mechanica Engineering from the Uniersity of Connecticut, USA, in Dr. Zhang is currenty the James C. Dowe Professor and Chairman of the Department of Mechanica and Aerospace Engineering at the Uniersity of Missouri-Coumbia, USA. His research interests incude aser materias processing, seectie aser sintering, heat pipes, microscae heat transfer, and inerse heat transfer.