EFFECT OF VARIATION IN LENGTH OF THE CONVENTIONAL HEAT PIPE ON THE THERMAL PERFORMANCE

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1 EFFECT OF VAIATION IN LENGTH OF THE CONVENTIONAL HEAT PIPE ON THE THEMAL PEFOMANCE Yung Min Se, Yng Gap Pak and Man Yeng Ha* *Auth f cespndence Schl f Mechanical Engineeing, Pusan Natinal Uniesity, Suth Kea, myha@pusan.ac.k ABSTACT One-dimensinal numeical simulatins wee cnducted f the pefmance f the cnentinal heat pipe(chp). In the cuent inestigatin, the peating limitatins f an CHP wee theetically studied in de t detemine its maximum heat tanspt capability. The themal netwk appach was used t calculate the pefmance f the CHP, based n the methdlgy t pduce esults f easnable accuacy. In the pesent study, the effect f aiatin in length f the CHP n the pefmance was analyzed using the cespnding themal netwks. INTODUCTION Heat pipes ae passie deices with a minimal diing tempeatue diffeence thugh a small css sectinal aea. These deices ae peated by utilizing the latent heat f an intenal wking fluid t tansfe lage amunts f heat. Heat pipe applicatins ange fm the cling cnsume electnics such as laptps t themal management f spacecaft [-3]. F seeal decades a numbe f eseaches hae inestigated the effects f aius paametes n the pefmance f many heat pipe cnfiguatins as the numeical methdlgy was deelped. Nemec et al. [4] studied the heat tanspt limitatin standad-used cnstuctin wick heat pipes with aius wking fluids peating at wide tempeatue anges. They epted that the limitatin alues depend n heat pipe paametes, wick stuctue paametes and the themphysical ppeties f the wking fluid. D.Yin et al. [5] theetically studied the peating limitatin f the scillating heat pipe based n the mass-sping system. They fund that the peating limitatin f an OHP depends n the wking fluid, tun numbe, peating tempeatue, and filling ati. Theefe, thee ae aius paametes that put limitatins and cnstaints n the steady and tansient peatin f heat pipes and cnsequently the ate f heat tanspt thugh a heat pipe is subject t a numbe f peating limits. The cnsequents f biling in a heat pipe depend n numeus design and pefmance facts, and ae difficult t pedict, and hence the cmplicated mathematical expessins and numeical schemes in peius studies hae been deelped. Hwee, it is usually nt desiable necessay t get int detail effects f mst pactical applicatins. Theefe, a simple way, which can calculate the pefmance f heat pipe, is essential. NOMENCLATUE Symbls A [m ] Suface aea C [-] Celatin cefficient d [m] Diamete f [-] Celatin cefficient f fictin g [m/s ] Gaity acceleatin h [W/m K] heat tansfe cefficient h fg [kj/kg] k eff [W/mK] Effectie themal cnductiity f the wick k [W/mK] themal cnductiity L [m] length L eff [m] Effectie length f the pipe P [Pa] Vap pessue P c.m [Pa] Maximum capillay pessue diffeenc [W] Heat tansfe ate b [W] Biling limit c [W] Capillay limit e [W] Entainment limit s [W] Snic limit [W] Viscus limit ce [m] Effectie capillay adius f the wick hw [m] Hydaulic adius f the wick [m] HP adius n [m] Citical nucleatin site adius [K/W] Themal esistance g [J/kgK] Specific gas cnstant e [-] eynlds numbe f ap t [m] thickness T [K] Vap tempeatue Geek symbls α [-] Accmmdatin cefficient σ [N/m] Suface tensin f the fluid μ l [Pa-s] Viscsity f the liquid μ [Pa-s] Viscsity f the apu ρ l [kg/m 3 ] Density f the liquid ρ [kg/m 3 ] Density f the ap γ [-] ati f specific heat Ψ Tilt angle Sub/supescipts a c c.i c.in e e.i e.in hp i Adiabatic secin Cndense sectin Cndense liquid-ap inteface Inne suface f the liquid film in the cndense Eapat sectin length Eapat liquid-ap inteface Inne suface f the liquid film in the eapat Heat pipe Inne 43

2 inte tt w wk Intefacial Oute Ttal Vap wall Wick ZUO and Faghi [6] suggested a unique iew int the physics behind the heat pipe peatin, which was cnsideed a themal netwk f aius cmpnents. They descibed tansient heat pipe behaiu using fist de, linea, dinay diffeential equatin. Tady and Sami [7] deelped a mathematical mdel t pedict the themal behaiu f heat pipes with themal stage duing a cling cycle. They epted that the deelped numeical mdel is in excellent ageement with the expeimental data. Shaifi et al. [8] studied extenally-finned heat pipes with themal cntact esistances. They used a detailed HP mdel t quantify the influence f the cntact esistances n the heat tansfe and fluid flw within the HP, as well as n the eall heat tansfe ate. In the pesent study, theefe, auths cnside the cnentinal heat pipe cnfiguatin haing aius heat tansfe limitatins, and ealuate the pefmance f a heat pipe mdel using the themal esistance netwking. Detailed heat tansfe limitatins wee calculated using the analytical expessin f pedicting biling, capillay, entainment, snic, and iscus heat tanspt limits in the cnectinal heat pipe. In additin, the pefmance f the heat pipe was analysed using the epesentatie celatins and expessins abut the themal esistance f a single mdel suggested by Shabgad et al. [], and cnsequently the effect f aiatin in length f cnectinal heat pipe was addessed. NUMEICAL METHODS In the design f heat pipes, it is imptant t establish that heat tanspt will take place at the equied ate withut encunteing limits n heat tanspt capability. Theefe, the heat pipes ae subject t a numbe f heat tansfe limitatin. These limitatins detemine the maximum heat tansfe ate a paticula heat pipe can achiee unde cetain wking cnditins. Mathematical methds f the pedictin f heat tanspt limits ae pesented as fllws: Biling limit b b Le Keff T ( )( P c. m) () h ln( / ) fg i n Capillay limit c l g( d cs Leff sin ) ce c Cf e l ( ) Leff A h KA h hw fg w fg l () Entainment limit e / e A hfg ( ) (3) hw Snic limit s s A h fg Viscus limit T ( ) ( ) / (4) 4 hfg P (5) Leff The heat tansfe limitatin can be any f the abe limitatins depending n the size and shape f the pipe, wking fluid, wick stuctue, and peating tempeatue. The lwest limit amng the cnstaints defines the maximum heat tanspt limitatin f a heat pipe at a gien tempeatue. Futhe details n the peating limitatin f the cnentinal heat pipe ae descibed in Tai [9]. The themal netwk appach is a bust engineeing tl that is easy t implement and pgam, is use fiendly, staightfwad, cmputatinally efficient, and sees as a baseline methdlgy t pduce esults f easnable accuacy. Theefe, in the pesent study, the themal esistance netwk was applied t calculate the heat tansfe pefmance f heat pipe, by adpting the simila methd used by Shabgad et al. []. Figue Themal esistances f a heat pipe used t calculate hp and ttal themal esistance t calculate tt used by Shabgad et al. []. Figue shws the maj themal esistances f a cylindical heat pipe at steady state. Hee, e.w, c.w,, e.wk, c.wk, e.inte, c.inte, a.w, a.wk, e.ex and c.ex dente the esistance assciated with the eapat wall, the cndense wall, the apu pessue dp alng the HP length, the eapat wick, the cndense wick, the intefacial eapatin, the intefacial cndensatin, the adiabatic sectin wall, the adiabatic sectin wick, the extenal themal esistance at eapat and cndense, espectiely. The indiidual esistances ae as fllws: adial cnductin thugh the eapat sectin wall, e.w ln( ) i ew. (6) kwle adial cnductin thugh the cndense sectin wall, c.w ln( ) i c. w (7) kwlc Themal esistance due t apu pessue dp, 44

3 g e c a 4 fg i 8 T ( L L ) / L h P (8) adial cnductin thugh the eapat wick, e.wk ln( i ) e. wk (9) k L eff e adial cnductin thugh the cndense wick, c.wk ln( i ) e. wk (0) k L eff c Eapatin at the eapat liquid-ap inteface, e.inte e. inte he. inte A () e. i Cndensatin at the cndense liquid-ap inteface, c.inte c. inte hc. inte A () c. i whee h e.inte and h c.inte ae the intefacial eapatin and cndensatin heat tansfe cefficient, and ae detemined as fllws. hfg P he. inte ( )( ) ( ) (3) T gt hfg Hea, α is the accmmdatin cefficient ( 0 ) and depends n the natue f the suface, as well as n gas cnditins such as cmpsitin, pessue, and the facts. Futhe details n the accmmdatin cefficient ae descibed in Hall and Dste [0] and Gdman and Wachman []. Axial cnductin thugh the adiabatic sectin wall, a.w La aw. ( i ) kw (4) Axial heat cnductin thugh the adiabatic sectin f the HP wick, a.wk La a. wk (5) ( i ) keff Cnectin esistance between the extenal flw and the eapat sectin, e.ex e. ex (6) ha e e. Cnectin esistance between the extenal flw and the cndense sectin, c.ex c. ex (7) ha c c. The intenal themal esistance f a single heat pipe can be calculated using the fllwing equatin, due t the paallel cnnectin amng the cmpnents f themal esistance. (.... )(. ) [ e wk e inte c inte c wk a wk e. w c. w ]( a. w) ( e. wk e. inte c. inte c. wk ) ( a. wk ) hp (.... )(. ) [ e wk e inte c inte c wk a wk e. w c. w ] ( aw. ) ( e. wk e. inte c. inte c. wk ) ( a. wk ) (8) Once the themal esistances f a single heat pipe ae detemined, the ttal themal esistance may be calculated fm the fllwing equatin: tt e. ex hp c. ex (9) The ttal themal esistance, tt, is as the ati f the diing ptential (tempeatue) t the cespnding heat tansfe as fllws: tt T, T tt (0) COMPUTATIONAL CONDITIONS Figue shws the cmputatinal dmain f the cnectinal heat pipe cnfiguatin f the system cnsideed in the pesent study. The intei suface f the clsed cntaine is lined with a thin laye f pus mateial, usually efeed t as a wick. The pes f the wick ae filled with a liquid apppiate t the applicatin, and the apu f the liquid ccupies the emaining intenal lume inside the cntaine haing a cylindical shape. Figue Schematic f cnentinal heat pipe Heat applied t the eapat sectin by an extenal suce is cnducted thugh the pipe wall and wick stuctue, whee it apizes the wking fluid. The esulting apu pessue dies the apu fm the eapat t the cndense thugh the adiabatic sectin, and cnsequently the apu cndenses, eleasing its latent heat f apizatin t the pided heat sink. In additin, the cndensed fluid mes fm the cndense t the eapat thugh the wick stuctue due t capillay pessue. This pcess will cntinue as lng as thee is a sufficient capillay pessue t die the cndensate back t the eapat. Table Heat pipe cnfiguatin Heat pipe cnfiguatin Wking fluid Wate d [m] 0.0 Cntaine mateial Cppe L [m] 0.75 Oientatin Hizntal L e [m] 0.5 (0.05~0.45) Wick stuctue Wie sceen L c [m] 0.5 (0.05~0.45) N 00 L a [m] 0.5 (0.05~0.45) Wie diamete [m].43x0-4 t [m] Numbe f layes 3 45

4 In the pesent study, the heat pipe is cnsideed using the cnfiguatin f heat pipe suggested by Tai [9]. The diamete, the ttal length and the thickness f heat pipe ae 0.0[m], 0.75[m], and 0.005[m] espectiely. The wking fluid and the cntaine mateial ae wate and cppe. The angle f heat pipe is fixed t 0 O, meaning the hizntal f ientatin. The wick stuctue is cnsideed t wie sceen shape haing the mesh numbe f 00, the wie diamete f.43x0-4, and the laye numbe f 3. The length f the heat pipe is diided int thee pats haing a length f 0.5[m], espectiely: eapat, adiabatic sectin, and cndense. Thus, auths fcus n the aiatin in pefmance f cnectinal heat pipe at aius length f thee pats n the ange f 0.05<L<0.45. VALIDATION TEST The peliminay numeical simulatins n the cnentinal heat pipe cnsideed by Shaifi et al. [8] wee cnducted t alidate the pesent numeical simulatin cde. The esults abut the themal esistance in each cmpnent f a heat pipe btained by the pesent cde wee cmpaed t thse btained by Shaifi et al. [8]. Table shws the themal esistances in each cmpnent f a heat pipe with channel flw cling. Sdium-Stainless steel ae used as wking fluid and cntaine mateial, espectiely. Heat tansfe cefficient and tempeatue at eapat and cndense wee gien in Shaifi et al. [8]. As a esult, the themal esistances in each cmpnent f a heat pipe is in excellent ageement with the empiical/analytical esults epted in the peius studies, except f haing the de f 0-4 due t an e induced by the diffeence in themal ppeties. Hwee, as shwn in Table, the themal esistance f hp and tt in the pesent study match well with thse f peius study. Theefe, accding t the alidatin test, the analysis f the themal esistance netwking abut a single heat pipe can be cnducted with easnable accuacy. Table Cmpaisn f themal esistance btained fm the pesent study with thse f peius empiical/analytical and numeical esults. Themal Shaifi et al. [8] Pesent esistance Empiical/ Numeical study [K/W] Analytical E [%] e.w 5.69e e e e.wk 3.4e e e e.inte 4.33e-04.69e e e e e c.w.63e-03.6e-03.63e c.wk 8.96e e e c.inte.4e-04.9e-04.5e e.ex.87e-0.88e-0.87e c.ex hp.7e-0.0e-0.4e-0.5 tt ESULTS AND DISCUSSION Figue 3 shws the esults f peating limitatins in heat pipe cnfiguatin. The tempeatue ange is cnsideed fm 73.6[K] t 373.6[K], because the useful peating ange is geneally smalle than the whle tempeatue ange between melting pint and the biling pint. Figue 3 Opeating limitatins f heat pipe cnfiguatin. As shwn in Figue 3, in the pesent study, the capillay limit is always lwe that the alues f the the heat tansfe limits. Theefe, the dminant limit f the heat pipe, which detemines its maximum heat tanspt capability, is the capillay limit. In additin, accding t the fundamental equatins f heat tansfe limits, the capillay, the entainment, the snic, and the iscus limit inceases with inceasing useful peating ange f tempeatue, while the biling limit deceases with inceasing tempeatue. Theefe, the heat tansfe pefmance f heat pipe shuld be smalle than the capillay limit haing the smallest alue amng the peating limitatins. Table The pefmance f heat pipe fm the themal esistance netwking analysis Themal esistance f heat pipe [K/W] e.ex a.w.9903 c.ex e.w a.wk c.w e.wk e-08 c.wk e.inte 8.87e-06 c.inte 8.38e-06 hp tt.6335 [W] Table shws the pefmance f heat pipe fm the themal esistance netwking analysis. The ap tempeatue was calculated by the heat balance between the eapat and the cndense. The maximum alue f the themal esistance in the cmpnent f heat pipe is f a.wk. The alues f, e.inte, and c.inte ae ey smalle than a.wk, and hence these alues ae almst insignificant n hp and tt. The alue f hp is calculated t by the paallel cnnectin. The pefmance f heat pipe is btained t 37.97[W] by the alue f tt. Theefe, this alue is smalle than the capillay limit f ap tempeatue, and cnsequently the peating limitatins f heat pipe ae satisfied. Figue 4 Cmpaisn in the pefmance abut length aiatin f heat pipe 46

5 Figue 4 shws the cmpaisn in the pefmance abut the length aiatin f heat pipe thee pats (eapat, adiabatic sectin, cndense) calculated by the themal esistance netwking. As shwn in Figue 4, the pefmance f heat pipe inceases with inceasing length f eapat and cndense, because the esistances in cmpnents assciated with eapat and cndense deceases. Hwee, it deceases with inceasing length f adiabatic sectin due t the incease f, and cnsequently the pefmance f heat pipe shws the biggest change. The paametes in de f the stength f thei effects ae the cndense length, the eapat length, and the adiabatic length, and hence these paametes must be cnsideed as design aiables f heat pipe cnfiguatin ptimizatin. CONCLUSION [7] Tady F., and Sami S.M., Themal analysis f heat pipes duing themal stage, Applied Themal Engineeing, Vl. 9, 009, pp [8] Shaifi N., Stak J.., Begman T.L., Faghi A., The influence f themal cntact esistance n the elatie pefmance f heat pipe-fin aay systems, Applied Themal Engineeing, Vl. 05, 06, pp [9] Tai, A cmpaatie inestigatin f heat tansfe capacity limits f heat pipes, Dctal dissetatin, Middle East Technical Uniesity, 007. [0] Hall M.L., Dste J.M., A sensitiity study f the effects f eapatin/cndensatin accmmdatin cefficients n tansient heat pipe mdeling, Intenatinal Junal f Heat and Mass Tansfe, Vl. 33, 990, pp [] Gdman F.O., Wachman H.Y., Fmula f themal accmmdatin cefficients, The Junal f Chemical Physics, Vl. 46, 967, pp One-dimensinal numeical simulatin wee cnducted f the pefmance f the cnentinal heat pipe(chp) in this study. The peating limitatins f an CHP wee calculated in de t detemine its maximum heat tanspt capability. In additin, the effect f aiatin in length f the CHP n the pefmance was analyzed using the cespnding themal netwks. In the pesent study, the dminant limit f the heat pipe, which detemines its maximum heat tanspt capability, was the capillay limit. Theefe, as a esult f themal esistance netwking analysis, the pefmance f heat pipe btained fm tt is smalle than the capillay limit f ap tempeatue, and cnsequently the peating limitatins f heat pipe ae satisfied. In additin, the pefmance f heat pipe becmes inceased with inceasing length f eapat and cndense, because the esistances in cmpnents assciated with eapat and cndense deceases. Hwee, it becmes deceased with inceasing length f adiabatic sectin due t the incease f, and cnsequently the pefmance f heat pipe shwed the biggest change. ACKNOLEDGMENTS This subject is suppted by Kea Ministy f Eninment(MOE) as "the Chemical Accident Peentin Technlgy Deelpment Pject(N )." EFEENCES [] Shabgad H., Allen M.J., Shaifi N., Benn S.P., Faghi A., Begman T., Heat pipe heat exchanges and heat sinks: pptunities, challenges, applicatins, analysis, and state f the at, Intenatinal Junal f Heat Mass Tansfe, Vl. 89, 05, pp [] Faghi A., eiew and adances in heat pipe science and technlgy, Junal f Heat Tansfe Vl. 34, 0, pp [3] Andesn W.G., Taau C., Vaiable cnductance heat pipes f adiistpe stiling systems, AIP Cnfeence Pceedings, Vl. 969, 008, pp [4] Nemec P., Caja A., Malch M., Mathematical mdel f heat tansfe limitatins f heat pipe, Mathematical and Cmpute Mdelling, Vl , pp [5] Yin D., Wang H., Ma H.B., Ji Y.L., Opeatin limitatin f an scillating heat pipe, Intenatinal Junal f Heat and Mass Tansfe, Vl. 94, 06, pp [6] Zu Z.J., Faghi A., A netwk themdynamic analysis f the heat pipe, Intenatinal Junal f Heat and Mass Tansfe, Vl. 4, 998, pp