A Review of Concentric Annular Heat Pipes

Transcription

1 Heat Tansfe Engineeing, 266):45 58, 2005 Copyight C Taylo and Fancis Inc. ISSN: pint / online DOI: / A Review of Concentic Annula Heat Pipes A. NOURI-BORUJERDI and M. LAYEGHI School of Mechanical Engineeing, Shaif Univesity of Technology, Tehan, Ian Downloaded By: [Canadian Reseach Knowledge Netwok] At: 07:56 5 Septembe 2010 A detailed desciption of a concentic annula heat pipe CAHP) opeation is pesented in low to modeate tempeatue anges C). The steady-state esponse of a CAHP to vaious heat fluxes in the evapoato and condense sections ae discussed. Two-dimensional mathematical modeling of the fluid flow and heat tansfe in the annula vapo space and the wicks ae descibed. The fundamental aspects and limitations of the opeation of a CAHP ae also discussed. Peviously used numeical and expeimental appoaches fo the analysis of the CAHPs and some elated concepts ae eviewed. The Navie-Stokes and simila equations ae ecommended fo the simulation of fluid flow and heat tansfe in the annula vapo space and the wicks. A numbe of impotant concepts, such as two-phase flow, heat tansfe in the heat pipe wicks, the vapo liquid inteface conditions, design consideations, testing, and manufactue of a CAHP, ae also biefly discussed. The esults of this eseach have shown that the available numeical and expeimental data in the liteatue ae sufficiently accuate in many applications. Howeve, new mathematical models and expeimental woks ae needed fo the bette design and manufactue of vaious types of CAHPs. INTRODUCTION The concept of using heat pipe was oiginally initiated by King and Pekins in thei patents egisteed in the mid-1800s [1, 2]. These patents descibe a device efeed to as the Pekins tube, which utilizes eithe single o two-phase pocesses to tansfe heat fom a funace to a boile. Gay [3] obtained a patent on a device simila to the Pekins tube in which a numbe of vetical tubes wee aanged with the evapoato located below the condense. These devices, which ae actually classified as themosyphons, laid the goundwok fo the late development of what is now commonly efeed to as a heat pipe. The heat pipe concept eceived elatively little attention, howeve, until Gove et al. [4] published the esults of an independent investigation and applied the tem heat pipe fo the fist time. Since that time, heat pipes have been employed in vaious applications. A conventional heat pipe, which opeates on a closed twophase cycle, consists of a sealed containe lined with a wicking mateial. The containe of the heat pipe can be constucted fom metals, ceamics, composite mateials, o glass. In all applications, caeful consideation must be given to the mateial type, Addess coespondence to D. A. Noui-Boujedi, School of Mechanical Engineeing, Shaif Univesity of Technology, P.O. Box , Azadi Ave., Tehan, Ian. anoui@shaif.edu themophysical popeties, and compatibility. Fo example, the containe mateial must be compatible with both the woking fluid and the wicking mateial, stong enough to withstand pessues associated with the satuation tempeatues encounteed duing heat addition and nomal opeation, and have a high themal conductivity. In addition to these chaacteistics, which ae pimaily concened with the intenal effects, the containe mateial must often be esistant to coosion esulting fom inteaction with the envionment and malleable enough to be fomed into the appopiate size and shape. To opeate the heat pipe, the containe is evacuated and backfilled with just enough liquid to fully satuate the wicks. Because only pue liquid and vapo ae pesent within the containe, the woking fluid will emain at satuation conditions as long as the opeating tempeatue is between the tiple point and the citical state. The selection of a suitable fluid with appopiate themophysical popeties has an impotant ole in the design and manufactue of heat pipes. The opeating tempeatue ange must be adequate fo each specific application. In addition, consideation must be given to the ability of the woking fluid wettability and to the wick and wall mateials. The woking fluid can vay fom nitogen o helium fo vey low-tempeatue cyogenic) heat pipes to lithium, potassium, o sodium fo vey high-tempeatue liquid metal) heat pipes. Futhe citeia fo the selection of the woking fluids have been pesented by Faghi [5], Dunn and Reay [6], and Heine and Goll [7], in which a numbe of othe 45

2 46 A. NOURI-BORUJERDI AND M. LAYEGHI Downloaded By: [Canadian Reseach Knowledge Netwok] At: 07:56 5 Septembe 2010 factos including the liquid and vapo pessue, flow limits, and compatibility of the mateials ae consideed. The wicking mateial can be made up of sceens, wie meshes, sinteed metal powdes, woven fibeglass, o gooves. The wicking mateial usually has two functions in heat pipe opeation: it etuns the woking fluid fom the condense to the evapoato and ensues that the woking fluid is evenly distibuted ove the evapoato suface. Gaugle [8] utilized a wicking mateial as pat of a passive two-phase heat tansfe device capable of tansfeing lage quantities of heat with a minimal tempeatue dop. Tefethen [9] eexamined this concept in connection with the space pogam and in the fom of a patent application [10]. A heat pipe consists of thee distinct sections: an evapoato o heat addition section, a condense o heat ejection section, and an adiabatic o isothemal section. These thee pats have equal impotance and can significantly affect the pefomance of a heat pipe. When heat is added to the evapoato section of the containe, the woking fluid pesent in the wicking stuctue is heated until it vapoizes. The high tempeatue and coesponding high pessue in the evapoato section cause the vapo to flow to the coole condense section, whee the vapo condenses and eleases its latent heat of vapoization. The capillay foces existing in the wicking stuctue then pump the liquid back to the evapoato. The evapoato and condense sections of a heat pipe function independently, needing only common liquid and vapo steams. Fo this eason, the aea ove which heat is intoduced can diffe in size and shape fom the aea ove which it is ejected, povided that the ate at which the liquid is vapoized does not exceed the ate at which it can be condensed. Hence, high heat fluxes geneated ove elatively small aeas can be dissipated ove lage aeas with educed heat fluxes. This is paticulaly useful in the themal contol of electonic components and systems, because it allows the high heat fluxes geneated at the component level to be educed and fee o foced convection to be used to dissipate the heat. Because heat pipes opeate on a closed two-phase cycle, the heat tansfe capacity may be seveal odes of magnitude geate than even the best solid conductos. This esults in a elatively small themal esistance and allows the physical sepaation of the evapoato and condense without a high penalty in oveall tempeatue dop. Also, any incease in the heat flux in the evapoato may esult in an incease in the ate at which the woking fluid is vapoized without a significant incease in the opeating tempeatue. Thus, the heat pipe can function as a nealy isothemal device, adjusting the evapoation ate to accommodate a wide ange of powe inputs while maintaining a elatively constant tempeatue. Anothe advantage of a heat pipe is its small themal esponse time. Because heat pipes utilize a closed two-phase cycle, the themal esponse time is consideably less than fo othe types of heat tansfe devices, paticulaly solid conductos. This esponse time is not a function of length. The heat pipe application includes tempeatue and humidity contol, cooling lage diesel pistons [11], the emoval of heat fom lase diodes and othe small localized heat-geneating devices, the emoval of heat dissipation fom the leading edge of Figue 1 heat tansfe engineeing vol. 26 no Schematic of a CAHP and coodinate system. hypesonic aicaft, and numeous othe industial applications in a wide ange of tempeatues. Finally, the high heat tansfe chaacteistic, the ability to maintain constant evapoato tempeatues unde diffeent heat flux levels, and the divesity and vaiability of evapoato and condense sizes make heat pipes effective devices fo use in many divese situations. A concentic annula heat pipe CAHP) is simila to the conventional heat pipe except that the coss-section of the vapo space is annula instead of cicula see Figue 1). This enables the designe to place the wick mateials on the inside of the oute pipe and the outside of the inne pipe. In this manne, the suface aea fo heat addition and ejection can be inceased significantly without inceasing the oute diamete of the heat pipe. The sizes and shapes of CAHPs ae almost as vaied as the applications. Vapo- and liquid-flow coss-sectional aeas also vay significantly, fom those encounteed in ectangula cosssection annula heat pipes, which have vey lage flow aeas, to vey small mico annula heat pipes. The dy-out phenomenon, which is a seious limitation in a conventional heat pipe, can be effectively contolled by using a CAHP at a specific heat flux. The popely designed CAHP can have a vey long life and its use in space applications and online themal contols is actual, eliable, and highly ecommended. Finally, the use of the CAHPs can be twice as effective as conventional heat pipes in compact heat exchange applications. The CAHP applications ae also simila to the conventional heat pipes; howeve, the use of the CAHPs in some applications is pefeed. These applications include the cooling of annula spaces such as tansfomes o capacitos) in electical components and the annula cooling of heat sinks coes. In addition, the annula heat pipe has been used as an isothemal funace with excellent esults due to its tempeatue flattening capabilities and fast esponse time to a cold chage [5]. It is also well suited fo use in educed gavity envionments. CAHP can be fixed o vaiable in length and eithe igid o flexible fo situations whee elative motion o vibation poses a poblem. Taditionally, the analysis of the pefomance of a heat pipe consists of the analysis of vapo flow, the liquid flow though the wick, and the vapo liquid inteface. The last two pats of this analysis ae basically simila fo diffeent heat pipe stuctues. Fo non-conventional heat pipes, howeve, the dynamics of

3 A. NOURI-BORUJERDI AND M. LAYEGHI 47 Downloaded By: [Canadian Reseach Knowledge Netwok] At: 07:56 5 Septembe 2010 vapo flow is moe complex due to the geomety and bounday specifications. Mathematical modeling of a heat pipe involves a vaiety of subjects, such as heat and fluid flow in poous media, two-phase flow, heat and mass tansfe, and fluid dynamics. Fotunately, a numbe of simple models have shown good ageement with the expeimental esults and been used extensively in the liteatue. In many cases, the available two-dimensional models have shown to be accuate and eliable. Many investigatos have analyzed the conventional heat pipes using a vaiety of numeical and expeimental techniques. Faghi [5], Dunn and Reay [6], Chi [12], Tepsta and Van Veen [13], and Peteson [14] have published seveal of these techniques, theoies, and applications of diffeent heat pipe stuctues. Thee ae, howeve, only a limited numbe of woks concening the CAHP in the liteatue. Recently, Noui-Boujedi and Layeghi [15] simulated the vapo flow and pessue dop along a CAHP fo vaious symmetic and asymmetic heat addition and ejection cicumstances. They showed that unde asymmetic heat addition and ejection cicumstances, a numbe of eciculation zones may be ceated at both the evapoato and condense sections. They discussed qualitatively that these eciculation zones can be vey effective zones fo inceasing heat tansfe between objects of diffeent diametes even at high adial Reynolds numbes. In this pape, an oveview of theoetical and expeimental esults fo the analysis of low-tempeatue conventional and concentic annula heat pipes is pesented. The main objective is to eview the pevious expeiences and models that have been used o can be used fo the analysis of low-tempeatue CAHPs. Fo vapo flow analysis, the elliptic, paabolic, and incompessible models ae descibed, and some impotant conclusions ae dawn. The govening equations of vapo flow and liquid flow in the wicks and vapo liquid intefaces and appopiate bounday conditions fo vapo flow analysis ae discussed. The CAHP limitations and advantages ae also discussed, and useful methods fo bette design and manufactue of a CAHP ae ecommended. LIQUID FLOW THROUGH WICK AND CAPILLARY PRESSURE A capillay pessue exists at the vapo liquid inteface due to the suface tension of the woking fluid and the cuved stuctue of the inteface see Figue 1). The diffeence in the cuvatue of the menisci along the vapo liquid inteface causes the capillay pessue to change along the pipe. This capillay pessue gadient ciculates the fluid against the liquid and vapo pessue losses and advese body foces such as gavity. The capillay pessue ceated by the menisci in the wick pumps the condensed fluid back to the evapoato section. Theefoe, the heat pipe can continuously tanspot the latent heat of vapoization fom the evapoato to the condense section. This pocess will continue as long as thee is a sufficient capillay pessue to dive the condensate back to the evapoato. The menisci at the vapo liquid inteface ae highly cuved in the evapoato section due to the fact that the liquid ecedes into the poes of the wick. Duing the condensation pocess, the menisci in the condense section ae nealy flat. In thei expeimental study of a CAHP, Faghi and Thomas [16] found that not all of the woking fluid that condenses onto the inne pipe wall in the condense section eaches the inne evapoato section. A meniscus was fomed in the condense section whee the inne pipe and the end cap wee joined, which allowed pat of the woking fluid that condensed onto the inne pipe to be dained down to the oute pipe. They descibed that this phenomenon is the esult of communication of the woking fluid between the inne and oute pipes. This phenomenon should be pevented by pope wick and end cap design, which would incease the amount of heat that can be tansfeed by the inne pipe. VAPOR FLOW IN THE ANNULAR SPACE The vapo pessue changes along the concentic heat pipe ae due to fiction, inetia, and evapoation and condensation effects, while the liquid pessue in the wick changes mainly as a esult of fiction. Figue 2 shows a typical axial vaiation of the liquid and vapo pessues fo loapo flow ates. The pessue distibution along the inne and oute wicks is also nealy simila. Thus, only one pessue distibution is shown. The maximum local capillay pessue should be equal to the sum of the pessue dops in the vapo and the liquid acoss each of the heat pipe wicks in the absence of body foces. When body foces such as advese gavitational foces ae pesent, the liquid pessue dop is geate, indicating that the capillay pessue must be highe in ode to etun the liquid to the evapoato fo agiven heat input. At modeate vapo flow ates, dynamic effects cause vapo pessue dop and ecovey along the condense section. The local vapo liquid pessue diffeence is small, but this pessue gadient appoaches zeo at the condense end cap simila to the loapo flow ate case. Again, the capillay pessue diffeence at the evapoato end cap should be balanced by the sum of the total pessue dop in the vapo and liquid acoss the heat pipe. The geneal tend at high vapo flow ates with low liquid pessue dops is diffeent fom the above two cases. The vapo pessue dop can exceed the liquid pessue dop in the Figue 2 heat tansfe engineeing vol. 26 no Vapo and liquid pessue distibutions in a CAHP.

4 48 A. NOURI-BORUJERDI AND M. LAYEGHI Downloaded By: [Canadian Reseach Knowledge Netwok] At: 07:56 5 Septembe 2010 condense section. In such a case, the liquid pessue would be highe than the vapo pessue in the condense section if the pessue in the liquid and vapo phases ae equal at the condense end cap. In eality, the wet point is not situated at the condense end cap, and the menisci at the vapo liquid inteface in the condense ae cuved. It is also impotant to note that the above desciption fo the physics of the opeation of a CAHP is esticted to a nealy symmetic heat addition and ejection condition. The symmetic heat addition and ejection conditions ae conditions such that all adial Reynolds numbes in the evapoato and condense sections ae the same. In some special situations, called asymmetic conditions, this assumption may not be valid. Unde the asymmetic heat addition and ejection conditions, the vapo liquid inteface behavio and heat tansfe though heat pipe, walls, wicks, and vapo can be moe complex, and vaious asymmetic phenomena may be obseved and need to be moe studied. LIMITATIONS ON THE HEAT TRANSPORT CAPACITY Thee ae a numbe of paametes that put limitations on the steady-state opeation of a CAHP. Each paamete usually coesponds to a physical phenomenon that can have a substantial effect on the heat tanspot capacity of a CAHP. Although the heat pipe pefomance and opeation ae stongly dependent on the shape, the woking fluid, and the wick stuctue, the fundamental phenomenon that govens the opeation aises fom the diffeence in the capillay pessue acoss the vapo liquid intefaces in the evapoato and condense sections. When this capillay pessue is not sufficient to pomote the flow of liquid fom the condense to the evapoato, the heat pipe is said to have eached its capillay limit, and dy-out of the evapoato wick occus. Fo a CAHP, the dy-out phenomenon can occu fo both the inne and the oute pipe wicks in the evapoato section. Thus, the capillay limit can be defined as a condition in which the dy-out phenomenon occus at least in one of the CAHP wicks, and the maximum capillay limit is the maximum amount of heat addition in which dy-out phenomenon occus in both wicks. The capillay limit is appoximately detemined using a simple one-dimensional analysis of the vapo and liquid flows in a CAHP with symmetic heat addition and ejection as follows: q e ) max = [ whee [ ) ] Cosθi 2π σ c,i + Cosθ o c,o ρ l ρ v )gl Sin α µ v f v Re v,z ρ v R 2 vo R2 vi)r vo R vi ) 2 + q µ l K i ρ l R 2 vi R2 li) + h fg 1 q )µ l K o ρ l R 2 lo R2 vo) ] L eff q = q i,e / q e = q i,c / q c heat tansfe engineeing vol. 26 no ) and q e = q c = q i,e + q o,e. It has been shown that Eq. 1) has good accuacy in the ange of low to modeate adial Reynolds numbes. In deivation of Eq. 1), it has been assumed that the wet and dy points ae located at both ends of the heat pipe. Howeve, this assumption may not be valid in a numbe of situations. The dy point is a point at the vapo liquid inteface whee the meniscus has a minimum adius of cuvatue and usually occus in the evapoato at the point futhest fom the condense egion. The wet point is a point whee the vapo pessue and liquid pessue ae appoximately equal o whee the adius of cuvatue appoaches infinity, and it is usually located at the condense section. Faghi and Thomas [16] showed expeimentally that the maximum stable opeating limit of a CAHP can be 82 pecent moe than a conventional heat pipe with the same oute diamete. Duing steady-state opeation, seveal othe impotant mechanisms can limit the maximum amount of heat that a CAHP can tansfe. Among these ae the viscous limit, sonic limit, entainment limit, and boiling limit. The capillay wicking limit and viscous limit deal with the pessue dops occuing in the liquid and vapo phases, espectively. The sonic limit esults fom the occuence of choked flow in the annula vapo space, while the entainment limit is due to the high vapo liquid shea foces developed as the vapo passes in a counte-flow diection ove the liquid-satuated wicks. Faghi [5] has also analyzed the sonic limit of a CAHP. Pediction of the entainment limit in a CAHP can be moe complex especially when the heat pipe opeation is unde the asymmetic heat addition and ejection condition. All of the above limits ae axial heat flux limits; that is, they ae a function of the axial heat tanspot capacity of the heat pipe. The boiling limit, howeve, is a adial heat flux limit and is eached when the heat flux applied in the evapoation potion is so high that nucleate boiling occus in each of the evapoato wicks. This ceates vapo bubbles that patially block the etun of fluid and may ultimately lead to pematue dy-out of the evapoato. Fo low- to modeate-tempeatue annula heat pipes, the most significant of these limits is the capillay wicking limit. Howeve, the significance of this limit deceases somewhat fo educed gavity applications. In vey low-tempeatue applications, such as those using cyogenic woking fluids, eithe the viscous limit o capillay limit occus fist, while in hightempeatue heat pipes, such as those that use liquid metal woking fluids, the sonic and entainment limits ae of inceased impotance. The theoy and fundamental phenomenon that cause each of those limitations have been the subject of a consideable numbe of investigations fo conventional heat pipes. The most famous woks have been pesented and discussed by Dunn and Reay [6], Bennan and Koliczek [10], Chi [12], Cotte [17], Chisholm [18], Tien [19], Feldman [20]. Howeve, thee ae numeous published papes duing the past foty yeas but only

5 A. NOURI-BORUJERDI AND M. LAYEGHI 49 a limited numbe of publications about the opeation limitations in a CAHP [21]. The appopiate bounday conditions ae 0, ) = v v 0, ) = 0, 6a) Downloaded By: [Canadian Reseach Knowledge Netwok] At: 07:56 5 Septembe 2010 MATHEMATICAL MODELLING Mathematical modeling of a CAHP can be categoized in thee sections: vapo flow model, liquid flow though wicks, and vapo liquid inteface analysis. Thee ae a numbe of models that can be used in each categoy, but hee the most impotant and applicable models ae discussed. The basis of the models is on thei validity and extensive use fo the analysis of conventional heat pipes and CAHPs. Howeve, the validity and eliability of some of these models must be checked numeically o expeimentally fo each special application. VAPOR FLOW MODELS Elliptic Model The evapoation and condensation ae modeled as a unifom injection and suction, but no phase change is actually involved in the calculations [22]. The enegy equation is usually solved numeically only fo the vapo egion. The elliptic Navie-Stokes and enegy equations associated with this axisymmetic poblem ae consideed, and both evapoation and condensation ae consideed to occu at the suface of the heat pipe walls and assumed to be unifom. This model has been used by Faghi [21] fo the vapo flow analysis of a CAHP. The consevation of mass, momentum, and enegy equations fo the incompessible vapo flow analysis ae as follows see Figue 1): ρ v [ ρ v [ ρ v C pv [ z + 1 z + v v v v z + v v T v z + v v vv ) = 0 2) ] = P [ v 1 z + µ v + 2 ] z 2 ] v v = P [ v 1 + µ v v v 2 + ] [ T v 1 = k v 2 ] v v z 2 ) T v + ) ) v v 2 ] T v z 2 3) 4) 5) L, ) = v v L, ) = 0, z, R i ) = z, R o ) = 0 ±V j,e 0 < z < L e v v z, R j ) = 0 L e < z < L e + L a L e + L a < z < L P v 0, R i < < R o ) = 0 V j,c 6b) 6c) 6d) 6e) The unifom adial blowing and suction velocities at the inne and oute walls in the evapoato and condense ae computed as see Figue 1). whee q j,e V j,e = 2πR j L e ρ v h fg q j,c V j,c = 2πR j L c ρ v h fg j = i, o, 7a) 7b) indicating the location at the inne o oute wall. The ± signs efe to the diection of the adial velocity, e and c efe to the evapoato and condense, and q j,e and q j,c ae the heat tansfe to the evapoato and fom the condense sections, espectively. The tempeatue at the vapo liquid inteface of the evapoato and condense is calculated appoximately using Clausius- Clapeyon equation 1 T int = 1 T sat R h fg ln P 8) v P sat whee P sat and T sat ae satuated pessue and tempeatue as a efeence state and R is the vapo gas constant. Paabolic Model heat tansfe engineeing vol. 26 no In this model, the paabolized vesion of the Navie-Stokes equations can be deived fom Eqs. 3, 4) by neglecting the tems 2 φ/ z 2 fo φ =,v v and T v.faghi [23] used this model fo analyzing the two-dimensional, steady, and incompessible flow of vapo in a CAHP. The esults have shown good ageement with elliptic model too, but in the condense section, the elliptic model seems to be moe accuate. This is because the physics of the vapo motion in the condense section is clealy of the elliptic type. The esults have shown that the flow eveses in long condense segments o at vey high condensation ates, and the paabolic pesentation povides a sufficiently accuate pictue of the vapo pessue vaiation at both low and high evapoation and condensation ates.

6 50 A. NOURI-BORUJERDI AND M. LAYEGHI Fully Developed Model Downloaded By: [Canadian Reseach Knowledge Netwok] At: 07:56 5 Septembe 2010 Fom the study by Faghi and Pavani [22], one can genealize that the vapo flow in an annula heat pipe becomes fully developed in a vey shot distance fom the evapoato end cap. This pofile epeats itself in the adiabatic and condense sections fo low as well as modeate adial Reynolds numbes. The enty distance is not of significance in many pactical applications. The citeion fo a fully developed flow is that the nomalized axial vapo velocity is invaiant along the pipe. A vey inteesting featue of the numeical esults given by Faghi and Pavani [22] was that the vapo axial velocity was simila fo vaious adial Reynolds numbes, including the case with zeo inne and oute adial Reynolds numbes. The fully developed nomalized velocity pofile fo annula flow fo zeo blowing velocity can be easily obtained analytically as: whee 2 [ R 2 i ln Ri = 2 w a 1 R 4 i 1 R 2 i = /R o R i = R i /R o + 1 R 2 i ln Ri ln ] 9) and w a is the mean axial vapo velocity in the adiabatic section: q i,e + q o,e w a = ρ v π Ro 2 ) R2 i h fg 10) Faghi and Pavani [22] used Eqs. 2 4) with appopiate bounday conditions fo the analysis of the evapoato, condense and adiabatic sections of a CAHP. They deived a numbe of analytical expessions fo detemining the pessue dop along vaious pats of a CAHP. It has been found that the fully developed esults pedict the pessue vaiation when the flow eveses as Figue 3 Pessue distibution of the vapo fo thee vapo flow models fo well. diffeent Reynolds numbes, a) Low, b) Modeate, and c) Lage, Faghi [5]. In Figue 3, the esults of the vaious vapo flow models ae compaed. The ageement between the fully developed solution and complete solution of the two-dimensional elliptic vesion gids [24]. A unifom mesh has been used in this of the consevation equations indicates that the axial velocity numeical analysis. pofile becomes fully developed in a shot distance and stays paabolic all along the length of the heat pipe fo both cases. Figues 3a and 3b show that flow evesal in the condense did LIQUID FLOW THROUGH A WICK not occu fo the low and modeate adial Reynolds numbe cases because the condense zone is shot. Thee is a egion whee the flow eveses in the condense fo high adial Reynolds numbes, which is shown by the lage pessue ecovey in the condense in Figue 3c. Typical velocity vectos and steamlines in a CAHP when flow evesal occus in the condense section ae shown in Figue 4. These esults have been obtained by solving Eqs. 2 5) numeically using a finite volume method based on staggeed In the analysis of the liquid flow in the wick stuctues, it is geneally assumed that the liquid flow is a steady, twodimensional, incompessible lamina flow with negligible body foces. The fluid and the wick stuctue ae assumed to be in local themal equilibium, and the velocities in the adial and axial diections ae the local volume-aveaged velocities ove a coss-section of the wick egion instead of the absolute velocities. Also, the inne and oute wall wicks ae assumed to heat tansfe engineeing vol. 26 no

7 A. NOURI-BORUJERDI AND M. LAYEGHI 51 whee ± ρ v ρ V j,e 0 < z < L e v j z, R vj ) = 0 L e < z < L e + L a, j = i, o ρ v ρ V j,c L e + L a z < L t 17) Downloaded By: [Canadian Reseach Knowledge Netwok] At: 07:56 5 Septembe 2010 Figue 4 Velocity vectos in a CAHP fo Re = 100. be isotopic, homogeneous, and the same type. The steady-state consevation equations fo mass and momentum in the wick egions can be witten as: w z + 1 v) = 0 11) ρ v w 2 + w w ) = p z z µw K + µ[ 1 ) w + ρ v v 2 + ) = p z µv K + µ [ 1 v 2 + ρc p v T + w T ) = 1 k eff z The bounday conditions ae + z [ k eff 2 v z 2 ] ) T 2 T z 2 ] 2 w z 2 w0, ) = v0, ) = wl, ) = vl, ) = 0, { Rli < < R vi, if j = i R vo < < R lo if j = o ] ) v 12) 13) 14) 15) wz, R lj ) = vz, R lj ) = wz, R vj ) = 0, j = i, o 16) Indexes j = i, o indicate the inne and oute wall wicks, espectively. The ± signs indicate the diection of the injection o suction mean vapo velocity at the vapo liquid inteface, is the poosity of the liquid, and µ is the viscosity. Also, w and v ae the axial and adial volume-aveaged velocities at the wall wicks, espectively; K is the pemeability of the poous mateial, that chaacteizes its ability to tansmit liquid unde the action of an applied pessue gadient; and V j,e and V j,c ae calculated using Eqs. 7a, b). The effective themal conductivity of the wick is dependent on both the wick mateial and the woking fluid. The effective themal conductivity fo vaious types of wick stuctues have been pesented by Faghi [5]. VAPOR LIQUID INTERFACE ANALYSIS Pope analysis of vapo liquid intefaces in an opeational heat pipe has an impotant ole in pedicting the eal heat pipe limitations. The wok of Beaves and Josef [25] was one of the fist attempts to study the fluid flow bounday conditions at the inteface egion. They pefomed expeiments and detected a slip in the velocity at the inteface. Neale and Nade [26] pesented one of the ealie attempts egading this type of bounday condition. In this study, the authos poposed continuity in both the velocity and the velocity gadient at the inteface by intoducing the Binkman tem in the momentum equation fo the poous side. Vafai and Thiyagaaja [27] analytically studied the fluid flow and heat tansfe fo thee types of intefaces namely, the inteface between two diffeent poous media, the inteface sepaating a poous medium fom a fluid egion, and the inteface between a poous medium and an impemeable medium. Continuity of shea stess and heat flux wee taken into account in thei study while employing the Fochheime-Extended Dacy equation in thei analysis. Vafai and Kim [28] pesented an exact solution fo the fluid flow at the inteface between a poous medium and a fluid laye, including the inetia and bounday effects. In this study, the shea stess in the fluid and the poous medium wee taken to be equal at the inteface egion. Othe studies conside the same set of bounday conditions fo the fluid flow and heat tansfe used in the woks pesented by Vafai and Thiyagaaja [27], Poulikakos and Kazmieczak [29], Vafai and Kim [30], Kim and Choi [31], and Ochoa-Tapia and Whitake [32]. Sahaoui and Kaviany [33] have poposed a hybid inteface condition fo the heat tansfe pat. They used the continuity of heat tansfe engineeing vol. 26 no

8 52 A. NOURI-BORUJERDI AND M. LAYEGHI Downloaded By: [Canadian Reseach Knowledge Netwok] At: 07:56 5 Septembe 2010 the heat flux at the inteface along with a slip in the tempeatue at the inteface. Ochoa-Tapia and Whitake [34, 35] have poposed ahybid inteface condition in which a jump in the shea stess at the inteface egion is assumed. In thei study, the shea stess jump is invesely popotional to the pemeability of the poous medium. This poposed set of inteface conditions was used in the woks pesented by Kuznetsov [36 40]. Ochoa-Tapia and Whitake [41] have pesented anothe shea stess jump bounday condition whee the inetia effects become impotant. Futhe same investigation by Ochoa-Tapia and Whitake [42] has pesented anothe hybid inteface condition fo the heat tansfe pat in which they intoduce a jump condition to account fo a possible excess in the heat flux at the inteface. Alazmi and Vafai [43] pesented a compehensive analysis of vaiants within the tanspot models in poous media. In thei study, fou majo categoies namely, constant poosity, vaiable poosity, themal dispesion, and local themal non-equilibium wee consideed in geat detail. Moe ecently, Alazmi and Vafai [44] citically examined the diffeences in the fluid flow and heat tansfe chaacteistics due to diffeent inteface conditions, including all of the afoementioned models. They pefomed a systematic analysis of the vaiances among diffeent bounday conditions, showing that in geneal, the vaiances have a moe ponounced effect on the velocity field, a substantially smalle effect on the tempeatue field, and an even smalle effect on the Nusselt numbe distibutions. The most impotant limitation that is diectly elated to the vapo liquid inteface is the entainment limitation. The phenomenon of entainment occus when high velocity vapo flow pass ove the vapo liquid inteface and entain the small liquid dops fom that inteface. Many eseaches have studied the entainment limit in conventional heat pipes e.g., [45, 46]), but the phenomenon of entainment seems to be moe complex, and the pevious theoetical and expeimental esults ae limited to a numbe of configuations, wick stuctues, and mateials. The esults of the pevious woks include a numbe of coelations, citeia, and simulations. The most accuate expeimental esult coesponds to an attactive appoach followed by Kim and Peteson [46]. They eview the twelve impotant models and completed extensive expeiments with a coppe wate, ectangula coss-section, 2.16 metes-long heat pipe. They also pefomed paametic studies and used compute modeling to compae thei esults. They classified the entainment in thei heat pipe expeiment into thee majo modes: wave-induced, pulsating, and intemediate modes, accoding to not only the floisualization expeiment but also the tempeatue fluctuation pattens at the onset of the individual entainment modes. Finally, they poposed a coelation fo pedicting the citical Webe numbe fo the stability of the liquid inteface. The othe impotant esult of the expeiments done by Kim and Peteson [46] was that the capillay limit occued befoe boiling o entainment limit. It can be found fom the pevious eseach that fo the analysis of the vapo liquid inteface in a CAHP, both expeimental and numeical analysis ae equied. On the othe hand, some of the esults of the pevious studies elated to conventional heat pipe can be used o genealized fo the concentic annula case. It seems to be useful to evaluate the vapo liquid inteface behavio in a long CAHP by ceating a visible egion at the adiabatic section and utilizing advanced measuement systems. The expeimental esults can then be used to validate the numeical esults. TEST PROCEDURES Once the heat pipe is fully instumented, setup in the ig see Figue 5), the condense jacket flow may be stated and heat can be applied to the evapoato section. Heat input should pefeably be applied at fist in steps, building up to design capability and allowing the tempeatues along the heat pipe to achieve a steady-state befoe adding moe powe. When the steady-state condition is eached, powe input, powe output, and the tempeatue pofile along the heat pipe should be noted [47]. If tempeatue pofiles change unifomly with adding moe powe, the heat pipe is opeating satisfactoily. Howeve, seveal modes of failue can occu, all being ecognizable by tempeatue changes at the evapoato o condense section. The most common failue is dy-out ceated by excessive powe input at the evapoato section. It is chaacteized by a apid ise in evapoato tempeatue compaed to othe egions of the heat pipe. Once dy-out has occued, the wick has to be epimed, and this is best achieved by cutting off the powe input completely. When the tempeatue diffeence along the heat pipe dops to 1 2 C, the powe may be eapplied. The second failue mechanism ecognizable by an inceased evapoato tempeatue and known as oveheating occus at elevated tempeatues. In geneal, the evapoato tempeatue does not incease as quickly as in a bun-out condition, but these two phenomena ae difficult to distinguish. Tempeatue changes at the condense section can also point to failue mechanisms o a decease in pefomance. A sudden dop in tempeatue at the end of the heat pipe downsteam of the cooling jacket occuing at high powes can be attibuted to the collection of woking fluid in that egion, insulating the wall and ceating a cold spot. This has been called cool-out. Complete failue need not necessaily occu when this happens, but the oveall tempeatue diffeence will be substantially inceased, and the effective heat pipe length is educed. A simila dop in Figue 5 heat tansfe engineeing vol. 26 no Schematic of a CAHP with heating and cooling systems.

9 A. NOURI-BORUJERDI AND M. LAYEGHI 53 Downloaded By: [Canadian Reseach Knowledge Netwok] At: 07:56 5 Septembe 2010 tempeatue can occu when the fluid inventoy is geate than that needed to completely satuate the wick. The vapo tends to push the excess fluid to the coole end of the heat pipe, whee because of the small vapo space volume, a small excess of fluid will ceate a long cold egion. Containe Mateials Of the many mateials available fo the containe, thee ae by fa the most common in use name coppe, aluminum, and stainless steel. Coppe is eminently satisfactoy fo heat pipes opeating between Cinapplications such as electonics cooling. While commecially pue coppe tube is suitable, the oxygen-fee high conductivity type is pefeable. Like aluminum and stainless steel, the mateial is eadily available and can be obtained in a wide vaiety of diametes and wall thicknesses in its tubula fom. Wick Stuctue Avey lage numbe of wick stuctues can be used in vaious types of CAHPs. The most common fom of wick is a woven wie mesh o twill, which can be made in many metals. In this case, the spot welding is a convenient technique fo peseving o attaching the wick to the wall in cases whee the heat pipe diamete is sufficiently lage to pemit insetion of an electode. Failing this, a coil sping can be used. It is vey impotant to make a close contact between the wicks and heat pipe walls. Diffusion bonding is a useful pocess that can be used to ensue such a close contact. A simila stuctue having intimate contact with the heat pipe wall is a sinteed wick. This pocess involves bonding togethe a lage numbe of paticles in the fom of a packed metal powde. The poe size of the wick thus fomed can be aanged to suit by selecting powdes having a paticula size. This kind of wick stuctue is descibed in Dunn and Reay [6]. The sinteed wicks ae extensively used nowadays because they can be manufactued with high conductivity popety and can etun the woking fluid effectively even when the heat pipe is tilted. Othe wick stuctues, such as vapo deposition manufactued wicks, gooved wicks, felts, and foams, can also be used as a wick stuctue in a CAHP. the wick, good wetting has occued, and satisfactoy cleanliness has been achieved. If the woking fluid is a solvent, such as acetone, no exteme pecautions ae necessay to ensue good wetting, and an acid pickle followed by a inse in the woking fluid appeas to be satisfactoy. Pickling of coppe demands a 50/50 phosphoic acid and nitic acid solution. An ultasonic cleaning bath is a useful addition fo speeding up the cleaning pocess but is by no means essential fo low-tempeatue heat pipes. Mateial Outgassing When the wick o wall mateial is unde a vacuum, gases will be dawn out, paticulaly if the components ae metallic. If not emoved pio to sealing of the heat pipe, these gases could collect in the heat pipe vapo space. The pocess is known as out gassing. Out gassing does not appea to be a poblem in low-tempeatue heat pipes. Geneally, the out gassing ate is stongly dependent on tempeatue, inceasing apidly as the component tempeatue is aised. Fitting of Wicks and End Caps The fitting of wicks depends on the type of the wicks and the geomety of the heat pipe. Fo conventional heat pipes, the fitting pocess of mesh wicks is eadily done by coiling a sping tightly aound a mandel, giving a good intenal cleaance in the heat pipe. Howeve, fo CAHPs, an annula mandel can be used to fit the mesh wicks. An annula mandel can also be used fo the installation of sinteed wicks. The fitting of end caps is nomally caied out by agon ac welding. This need not be done in a glove box and is applicable to coppe, stainless steel, and aluminum heat pipes. The advantage of welding ove bazing o soldeing is that no flux is equied; theefoe, the inside of cleaned pipes do not suffe fom possible contamination. The use of a themal absobent paste to suound the aea of heat pipe local to the weld can consideably educe the amount of oxide fomed. Electon beam welding may also be used fo heat pipe assembly, but this added expense cannot be justified in most applications. Leak Detection Cleaning of Containe and Wick All of the mateials used in a heat pipe must be clean. Cleanliness achieves two objectives: it ensues that the woking fluid will wet the mateials and that no foeign matte is pesent that could hinde capillay action o ceate incompatibilities. Cleanliness is difficult to quantify, and the best test is to add a dop of deminealized wate to the cleaned suface. If the dop immediately speads acoss the suface o is completely absobed into heat tansfe engineeing vol. 26 no All welds on heat pipes should be checked fo leaks. If quality contol is to be maintained, a igoous leak check pocedue is necessay. The best way to test the heat pipe fo leaks is to use a mass spectomete, which can be used to evaluate the heat pipe to a vey high vacuum, bette than 10 5 To, using a diffusion pump. The weld aea is then tested by diecting a small jet of helium gas onto it. If a leak is pesent, the gauge head on the mass spectomete will sense the pesence of helium once it entes the heat pipe. Afte an investigation of the weld aeas and

10 54 A. NOURI-BORUJERDI AND M. LAYEGHI Downloaded By: [Canadian Reseach Knowledge Netwok] At: 07:56 5 Septembe 2010 Figue 6 location of the geneal leak aeas), if pesent, a hypodemic needle can be attached to the helium line and caeful tavesing of the suspected egion can lead to vey accuate identification of the leak position, possibly necessitating only a vey local ewelding pocedue to seal it. Pepaation of the Woking Fluid The woking fluid should be the most highly pue fluid available, and futhe puification may be necessay following puchase. This may be caied out by distillation. Low-tempeatue woking fluids, such as acetone, methanol, and ammonia, in the pesence of wate can lead to incompatibilities, and the minimum possible wate content should be achieved. A pocedue ecommended fo all heat pipe woking fluids used up to 200 Cis feeze-degassing. This pocess emoves all dissolved gases fom the woking fluid if the gases ae not emoved, they could be eleased duing heat pipe opeation and collected in the condense section. Feeze-degassing may be caied out on the heat Schematic of two diffeent typical filling igs fo low-tempeatue CAHP. pipe filling ig descibed in Figue 6 and is a simple pocess. The fluid is placed in a containe in the ig diectly connected to the vacuum system and is fozen by suounding the containe with a flask containing liquid nitogen. When the woking fluid is completely fozen, the containe is evacuated and eleased and the liquid nitogen flask emoved. The woking fluid is then allowed to thaw, and dissolved gases will be seen to bubble out of the liquid. The woking fluid is then efozen and the pocess epeated. All gases will be emoved afte thee o fou feezing cycles. The liquid will now be in a sufficiently pue state fo insetion into the heat pipe. Filling Rig heat tansfe engineeing vol. 26 no The usual method fo filling a heat pipe with a woking fluid is constucting an appopiate filling ig, as shown in Figue 6a [14]. The ig may also be used to cay out the pocesses such as woking fluid degassing, woking fluid meteing, heat pipe degassing, and heat pipe filling with inet gas Figue 6b) [48].

11 A. NOURI-BORUJERDI AND M. LAYEGHI 55 Downloaded By: [Canadian Reseach Knowledge Netwok] At: 07:56 5 Septembe 2010 The mateial of constuction fo pipe-wok is geneally eithe glass o stainless steel. Glass has advantages when handling liquids in that the pesence of liquid doplets in the duct-wok can be obseved and thei vapoization unde vacuum noted. Stainless steel has obvious stength benefits and must be used fo all high-tempeatue wok, togethe with high-tempeatue packless valves such as Hoke-Bellows valves. The ig that is shown in Figue 6 is fo low-tempeatue heat pipe manufactue. Valves used in vacuum igs should pefeably have O ing seals, and it is impotant to ensue that the ductwok is not too long o has a small diamete, as this can geatly incease evacuation times. The vacuum pump may be the diffusion type o absoption pump containing a molecula sieve, which poduces vacuums as low as 10 4 To. It is, of couse, advisable to efe to expets in the field of high vacuum technology when consideing designing a filling ig. Sealing Unless the heat pipe is to be used as a demonstation unit o fo life testing, in which case a valve may be etained on one end, the filling tube must be pemanently sealed. With coppe, this is conveniently caied out using a tool that will cimp and cold weld the filling tube. If stainless steel o aluminum is used as the heat pipe filling tube mateial, cimping followed by agon ac welding is a moe satisfactoy technique. Afte sealing, the filling tube may be potected by a cap having an oute diamete the same as that of the heat pipe wall. The cap may be filled with solde, a metal-loaded esin, o any othe suitable mateial. Netwok Model Zuo and Faghi [49] pefomed a netwok themodynamic analysis of the conventional heat pipe. They povided a unique view into the physics behind the heat pipe opeation, which was consideed a themal netwok of vaious components. Themal heat pipe behavio was descibed by fist ode, linea, odinay diffeential equations. They assumed that the woking fluid undegoes a themodynamic cycle and analyzed the cycle by T-s diagams. They analyzed both tansient and steady-state opeation of the conventional heat pipe. They found that successful establishment of the themodynamic cycle equies compatibility between the themophysical popeties of the woking fluid envelop mateial combination and geometic dimensions of the heat pipe. If this equiement is not satisfied, the heat pipe cannot function popely. Thei analysis povided a easonably accuate and paticulaly simple way to tansient heat pipe analysis and design. A simila pocedue can be followed fo tansient analysis of a CAHP. themodynamics. They pefomed a detailed paametic analysis in which the effects of vaious heat pipe paametes on entopy geneation wee examined. They concluded that thee exists a themodynamic equiement that the vapo tempeatue must be geate than a cetain value in ode fo the heat pipe to opeate. Thee is also an optimum condense ambient tempeatue that coesponds to a minimum entopy geneation. It is also found that both the condense ambient tempeatue and the convection heat tansfe coefficient in the tanspot section must be coespondingly adjusted to obtain a minimum entopy geneation. To educe the entopy geneation in fluid flow, the evapoato length should be as small as possible and the wick coss-sectional hydaulic diamete as lage as possible. Tempeatue dop in the vapo flow inceases the entopy geneation and coespondingly deceases the second law efficiency. Thus, an optimum heat pipe should be based on the minimization of the entopy geneation, which ensues a minimum loss in availability in the system. A simila pocedue can be followed fo the analysis of entopy geneation in a CAHP system. Vapo-Liquid Coupling and Non-Dacian Tanspot Zhu and Vafai [51] pesented a two-dimensional analytical model fo low-tempeatue cylindical heat pipes. They obtained a closed fom solution that incopoated vapo liquid intefacial hydodynamic coupling and non-dacian tanspot though the poous wick fo the fist time fo pedicting the vapo and liquid velocity and pessue distibutions. The effects of the vapo liquid intefacial hydo-dynamic coupling and non- Dacian tanspot though the poous wick on the vapo and liquid velocity and pessue distibutions as well as the heat pipe capillay limit have been discussed and assessed. The pesented closed-fom analytical solutions povided a quick, accuate pediction method fo low-tempeatue heat pipe opeation and wee found to be in vey good ageement with both expeimental and numeical esults. The esults also show that the intefacial effects ae small and can be neglected. Howeve substantial eos can occu when using Dacy s law in calculating the liquid pessue distibutions as well as the maximum heat emoval capability of the heat pipe. Khustalev and Faghi [52] have done an impotant analysis of the coupling between the liquid and vapo flow in miniatue passages. Zhang and Wang [53] have done the most ecent themodynamic analysis of the vapo liquid inteface. Fo a CAHP, a two-dimensional analysis simila to that used by Zhu and Vafai [51] can be developed. This is the subject of the authos cuent eseach. Making Impovement in Pefomance of a Heat Pipe Entopy Geneation in a Heat Pipe System Khalkhali et al. [50] developed a themodynamic model of a conventional cylindical heat pipe based on the second law of heat tansfe engineeing vol. 26 no Joudi and Wiwit [54] expeimentally investigated the pefomance of gavity-assisted wickless heat pipes and modified heat pipes with a sepaato in the adiabatic section. They found that the pesence of the adiabatic sepaato caused a maked

12 56 A. NOURI-BORUJERDI AND M. LAYEGHI Downloaded By: [Canadian Reseach Knowledge Netwok] At: 07:56 5 Septembe 2010 impovement maximum 35%) in all heat pipes tested fo all lengths and inclination angles. A numbe of simila techniques can be used to impove the CAHP pefomance, effectively. CONCLUSIONS Concentic annula heat pipe CAHP) is an effective device in vaious heat tansfe, heat ecovey, and heat exchange applications. It can be designed and manufactued in a wide ange of sizes and shapes and can have a wide tempeatue ange of opeation. It can be utilized in spacecaft applications, lage industial applications, o as a heat sink to cool electonic components and packages. CAHP can also be used to connect two conventional heat pipes side-by-side to tansfe the heat to a place fa fom the heat souce o device. The use of mico CAHPs is paticulaly pomising, as inceases in powe density will equie the use of phase change heat tansfe fo tempeatue contol. Many types of CAHPs can be used as a low weight, long-life solution to vaious types of themal poblems. Although investigations continue to detemine and evaluate new wick mateials, woking fluids, and efficient sizes and configuations, little additional eseach is needed on the moe simple devices povided that mateials with poven compatibility ae chosen and that pope cleaning, filling, and sealing pocedues ae followed. The fluid flow and heat tansfe in a CAHP can be accuately simulated using the pesented elliptic models. Vapo flow analysis in a CAHP can be done using an elliptic o paabolic vesion of Navie-Stokes equations and fully developed solutions. The esults ae vey close to each othe, and the diffeence between the vaious vapo flow models is negligible at least fo low to modeate adial Reynolds numbes. It also has been found that the models wok well fo the pediction of vapo flow evesal. Howeve, tansition to tubulence phenomenon was not consideed in the pevious eseach, and futhe studies and moe complete models ae needed to pedict the flow evesal and tansition to tubulence phenomena fo a eal condition in a CAHP. The model can be used to analyze the steady-state vapo flow and heat tansfe in a CAHP. A two-dimensional model fo analyzing the liquid flow though wicks has also been pesented. It is found that the vapo liquid inteface models in the pevious eseach have many simplifications. But the eos coesponding to these simplifications have been negligible, at least fo the cases studied by Faghi [5] and Alazmi and Vafai [44]. But, by implementing futhe details such as the effects of the vapo shea stess on the vapo liquid inteface in the mathematical models, it is possible to get a bette physical insight into the vaious phenomena that affect the pefomance of the CAHP. The effects of the vaious paametes such as liquid fill atio, noncondensable gases, and popety vaiations can be consideed in the futue studies. The phenomenon of tansition to tubulence in a CAHP is also an attactive concept fo both numeical and expeimental studies. Limitations on the heat tanspot capacity of a low-tempeatue CAHP ae vey simila to those fo a conventional heat pipe. The most impotant one is the capillay limit. Duing steady-state opeation, seveal othe impotant mechanisms can limit the maximum amount of heat that a CAHP can tansfe. Among these ae the viscous limit, sonic limit, entainment limit, and boiling limit. Howeve, exact mathematical modeling and pediction of these limitations needs to be moe studied fo a paticula CAHP. A netwok model of the cylindical heat pipe, consisting of a netwok of themal esistance and a woking fluid cycle, can be fist developed to analyze the heat pipe tansients. Then the steady-state woking fluid ciculation and the elated themodynamic constaints can be analyzed by themodynamic T-s diagams. Entopy geneation and the effects of vapo liquid coupling and non-dacian tanspot of liquid in the wicks in a conventional heat pipe o CAHP ae inteesting and impotant concepts that can be studied in the futue. Making impovements in pefomance of a CAHP is possible at least by adding a sepaato in the adiabatic section. Howeve, some othe innovations seem to be applicable, especially using new numeical techniques and expeimental tools. NOMENCLATURE A C p f g h fg k K L P Ṗ q R Re T v V w z ampee heat capacity at constant pessue fiction facto acceleation of gavity latent heat of vapoization themal conductivity pemeability length pessue powe heat tansfe ate adial coodinate gas constant, adius adial Reynolds numbe, ρrv/µ tempeatue adial velocity adial blowing and suction velocity o volt axial velocity axial coodinate Geek Symbols α tilt angle poosity θ contact angle µ viscosity ρ density σ suface tension φ geneal vaiable heat tansfe engineeing vol. 26 no

13 A. NOURI-BORUJERDI AND M. LAYEGHI 57 Downloaded By: [Canadian Reseach Knowledge Netwok] At: 07:56 5 Septembe 2010 Subscipts a adiabatic c condense, capillay e evapoato eff effective i inne, inlet int inteface l liquid max maximum o oute, outlet sat satuation v vapo Supescipts aveage dimensionless, ) = )/R o REFERENCES [1] King, C. R., Pekins Hemetic Tube Boiles, The Enginee, vol. 152, pp , [2] Pekins, L. P., and Buck, W. E., Impovements in Devices fo the Diffusion o Tansfeence of Heat, UK Patent 22,272, London, England, [3] Gay, F. W., Heat Tansfe Means, U.S. Patent 1,725,906, [4] Gove, G. M., Cotte, T. P., and Eikson, G. F., Stuctues of Vey High Themal Conductivity, Jounal of Applied Physics, vol. 35, pp , [5] Faghi, A., Heat Pipe Science and Technology,Taylo & Fancis, Washington, DC, [6] Dunn, P. D., and Reay, D. A., Heat Pipes, Pegamon, Oxfod, [7] Heine, D., and Goll, M., Compatibility of Oganic Fluids with Commecial Stuctue Mateials fo Use in Heat Pipes, Poc. 5th Intenational Heat Pipe Confeence, Tsukuba, Japan, pp , [8] Gaugle, R. S., Heat Tansfe Devices, U.S. Patent 2,350,348, [9] Tefethen, L., On the Suface Tension Pumping of Liquids o a Possible Role of the Candlewick in Space Exploation, G. E. Tech. Info., seial no. 615 D114, Detoit, MI, [10] Bennan, P. J., and Koliczek, E. J., Heat Pipe Design Handbook, B&K Engineeing, Towson, MD, [11] Wang, Q., Cao, Y., Wang, R., Mignano, F., and Chen, G., Studies of a Heat Pipe Cooled Piston Cown, ASME Jounal of Engineeing fo Tubines and Powe, vol. 122, pp , [12] Chi, S. W., Heat Pipe Theoy and Pactice, Hemisphee, Washington, DC, [13] Tepsta, M., and Van Veen, J. G., Heat Pipes: Constuction and Application, Elsevie Applied Science, New Yok, [14] Peteson, G. P., An Intoduction to Heat Pipes: Modeling, Testing, and Applications, John Wiely, New Yok, [15] Noui-Boujedi, A., and Layeghi, M., A Numeical Analysis of Vapo Flow in Concentic Annula Heat Pipes, ASME Jounal of Fluids Engineeing, vol. 126, pp , [16] Faghi, A., and Thomas S., Pefomance Chaacteistics of a Concentic Annula Heat Pipe, Pat I: Expeimental Pediction and Analysis of the Capillay Limit, Jounal of Heat Tansfe, vol. 111, pp , [17] Cotte, T. P., Theoy of Heat Pipes, Los Alamos National Laboatoy Repot no. LA-3246-MS, The Univesity of Califonia, Los Alamos, NM, [18] Chisholm, D., The Heat Pipe, Mills and Boon, London, England, [19] Tien, C. L., Fluid Mechanics of Heat Pipes, Annual Review of Fluid Mechanics, vol. 2, pp , [20] Feldman, K. T., The Heat Pipe: Theoy, Design and Applications, Technology Application Cente, Univesity of New Mexsico, Albuqueque, NM, [21] Faghi, A., Pefomance Chaacteistics of a Concentic Annula Heat Pipe Pat II: Vapo Flow Analysis, Jounal of Heat Tansfe, vol. 111, pp , [22] Faghi, A., and Pavani, S., Numeical Analysis of Lamina Flow in a Double-Walled Annula Heat Pipe, Jounal of Themophysics and Heat Tansfe, vol. 2, no. 2, pp , [23] Faghi, A., Vapo Flow Analysis in a Double-Walled Concentic Heat Pipe, Numeical Heat Tansfe,vol. 10, no. 6, pp , [24] Fezige, J. H., and Peíc, M., Computational Methods fo Fluid Dynamics, 2nd ed., Spinge-Velag, Belin, Heidelbeg, [25] Beaves, G., and Josef, D. D., Bounday Conditions at a Natually Pemeable Wall, Jounal of Fluid Mechanics, vol. 30, pp , [26] Neale, G., and Nade, W., Pactical Significance of Binkman s Extension of Dacy s Law: Coupled Paallel Flows within a Channel and a Bonding Poous Medium, Can. J. Chem. Engg., vol. 52, pp , [27] Vafai, K., and Thiyagaaja, R., Analysis of Flow and Heat Tansfe at the Inteface Region of a Poous Medium, Intenational Jounal of Heat Mass Tansfe, vol. 30, pp , [28] Vafai, K., and Kim, S. J., Fluid Mechanics of the Inteface Region Between a Poous Medium and a Fluid Laye An Exact Solution, Intenational Jounal of Heat Fluid Flow, vol. 11, pp , [29] Poulikakos, D., and Kazmieczak, M., Foced Convection in a Duct Patially Filled with a Poous Mateial, Jounal of Heat Tansfe, vol. 109, pp , [30] Vafai, K., and Kim, S. J., Analysis of Suface Enhancement by a Poous Substate, Jounal of Heat Tansfe, vol. 112, pp , [31] Kim, S. J., and Choi, C. Y., Convection Heat Tansfe in Poous and Ovelying Layes Heated fom Below, Intenational Jounal Heat Mass Tansfe, vol. 39, pp , [32] Ochoa-Tapia, J. A., and Whitake, S., Heat Tansfe at the Bounday between a Poous Medium and a Homogeneous Fluid, Intenational Jounal of Heat Mass Tansfe, vol. 40, pp , [33] Sahaoui, M., and Kaviany, M., Slip and No Slip Tempeatue Bounday Conditions at the Inteface of Poous, Plain Media: heat tansfe engineeing vol. 26 no

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