A Review of Concentric Annular Heat Pipes


 Sharon Carroll
 1 years ago
 Views:
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. NOURIBORUJERDI 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 steadystate esponse of a CAHP to vaious heat fluxes in the evapoato and condense sections ae discussed. Twodimensional 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 NavieStokes 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 twophase 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 mid1800s [1, 2]. These patents descibe a device efeed to as the Pekins tube, which utilizes eithe single o twophase 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. NouiBoujedi, School of Mechanical Engineeing, Shaif Univesity of Technology, P.O. Box , Azadi Ave., Tehan, Ian. 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 lowtempeatue cyogenic) heat pipes to lithium, potassium, o sodium fo vey hightempeatue 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. NOURIBORUJERDI 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 twophase 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 twophase 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 twophase 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 heatgeneating 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 cosssection 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 liquidflow cosssectional 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 dyout 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 nonconventional heat pipes, howeve, the dynamics of
3 A. NOURIBORUJERDI 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, twophase 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 twodimensional 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, NouiBoujedi 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 lowtempeatue 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 lowtempeatue 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. NOURIBORUJERDI 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 steadystate 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 dyout of the evapoato wick occus. Fo a CAHP, the dyout 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 dyout phenomenon occus at least in one of the CAHP wicks, and the maximum capillay limit is the maximum amount of heat addition in which dyout phenomenon occus in both wicks. The capillay limit is appoximately detemined using a simple onedimensional 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 steadystate 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 counteflow diection ove the liquidsatuated 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 dyout of the evapoato. Fo low to modeatetempeatue 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 lowtempeatue 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. NOURIBORUJERDI 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 NavieStokes 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 NavieStokes 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 twodimensional, 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. NOURIBORUJERDI 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 twodimensional 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 volumeaveaged velocities ove a cosssection 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. NOURIBORUJERDI 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 steadystate 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 volumeaveaged 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 FochheimeExtended 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 OchoaTapia 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. NOURIBORUJERDI 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. OchoaTapia 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]. OchoaTapia and Whitake [41] have pesented anothe shea stess jump bounday condition whee the inetia effects become impotant. Futhe same investigation by OchoaTapia 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 nonequilibium 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 cosssection, 2.16 meteslong 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: waveinduced, 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 steadystate befoe adding moe powe. When the steadystate 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 dyout 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 dyout 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 bunout 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 coolout. 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. NOURIBORUJERDI 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 oxygenfee 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 lowtempeatue 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 lowtempeatue 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. NOURIBORUJERDI 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. Lowtempeatue 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 feezedegassing. 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. Feezedegassing may be caied out on the heat Schematic of two diffeent typical filling igs fo lowtempeatue 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. NOURIBORUJERDI AND M. LAYEGHI 55 Downloaded By: [Canadian Reseach Knowledge Netwok] At: 07:56 5 Septembe 2010 The mateial of constuction fo pipewok is geneally eithe glass o stainless steel. Glass has advantages when handling liquids in that the pesence of liquid doplets in the ductwok can be obseved and thei vapoization unde vacuum noted. Stainless steel has obvious stength benefits and must be used fo all hightempeatue wok, togethe with hightempeatue packless valves such as HokeBellows valves. The ig that is shown in Figue 6 is fo lowtempeatue 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 metalloaded 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 Ts diagams. They analyzed both tansient and steadystate 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 cosssectional 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. VapoLiquid Coupling and NonDacian Tanspot Zhu and Vafai [51] pesented a twodimensional analytical model fo lowtempeatue cylindical heat pipes. They obtained a closed fom solution that incopoated vapo liquid intefacial hydodynamic coupling and nondacian 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 hydodynamic 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 closedfom analytical solutions povided a quick, accuate pediction method fo lowtempeatue 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 twodimensional 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 gavityassisted 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. NOURIBORUJERDI 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 sidebyside 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, longlife 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 NavieStokes 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 steadystate vapo flow and heat tansfe in a CAHP. A twodimensional 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 lowtempeatue CAHP ae vey simila to those fo a conventional heat pipe. The most impotant one is the capillay limit. Duing steadystate 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 steadystate woking fluid ciculation and the elated themodynamic constaints can be analyzed by themodynamic Ts diagams. Entopy geneation and the effects of vapo liquid coupling and nondacian 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. NOURIBORUJERDI 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] NouiBoujedi, 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. LA3246MS, 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 DoubleWalled Annula Heat Pipe, Jounal of Themophysics and Heat Tansfe, vol. 2, no. 2, pp , [23] Faghi, A., Vapo Flow Analysis in a DoubleWalled 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., SpingeVelag, 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] OchoaTapia, 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
14 58 A. NOURIBORUJERDI AND M. LAYEGHI Downloaded By: [Canadian Reseach Knowledge Netwok] At: 07:56 5 Septembe 2010 Convection, Intenational Jounal of Heat Mass Tansfe, vol. 37, pp , [34] OchoaTapia, J. A., and Whitake, S., Momentum Tansfe at the Bounday between a Poous Medium and a Homogeneous Fluid I: Theoetical Development, Intenational Jounal of Heat Mass Tansfe, vol. 38, pp , [35] OchoaTapia, J. A., and Whitake, S., Momentum Tansfe at the Bounday between a Poous Medium and a Homogeneous Fluid II: Compaison with Expeiment, Intenational Jounal of Heat Mass Tansfe, vol. 38, pp , [36] Kuznetsov, A. V., Analytical Investigation of the Fluid Flow in the Inteface Region between a Poous Medium and a Clea Fluid in Channels Patially Filled with a Poous Medium, Applied Scientific Reseach, vol. 56, pp , [37] Kuznetsov, A. V., Influence of the Stess Jump Condition at the PoousMedium/CleaFluid Inteface on a Flow at a Poous Wall, Intenational Communications Heat Mass Tansfe, vol. 24, pp , [38] Kuznetsov, A. V., Analytical Investigation of Coette Flow in a Composite Channel Patially Filled with a Poous Medium and Patially Filled with a Clea Fluid, Intenational Jounal of Heat Mass Tansfe, vol. 41, pp , [39] Kuznetsov, A. V., Analytical Study of Fluid Flow and Heat Tansfe duing Foced Convection in a Composite Channel Patially Filled with a BinkmanFochheime Poous Medium Flow, Tubulence Combustion, vol. 60, pp , [40] Kuznetsov, A. V., Fluid Mechanics and Heat Tansfe in the Inteface Region between a Poous Medium and a Fluid Laye: A Bounday Laye Solution, Jounal of Poous Media, vol. 2, no. 3, pp , [41] OchoaTapia, J. A., and Whitake, S., Momentum Jump Condition at the Bounday between a Poous Medium and a Homogeneous Fluid: Innetial Effects, Jounal of Poous Media, vol. 1, pp , [42] OchoaTapia, J. A., and Whitake, S., Heat Tansfe at the Bounday between a Poous Medium and a Homogeneous Fluid: The OneEquation Model, Jounal of Poous Media, vol. 1, pp , [43] Alazmi, B., and Vafai, K., Analysis of Vaiants within the Poous Media Tanspot Models, Jounal of Heat Tansfe, vol. 122, pp , [44] Alazmi, B., and Vafai, K., Analysis of Fluid Flow and Heat Tansfe Intefacial Conditions between a Poous Medium and a Fluid Laye, Intenational Jounal of Heat Mass Tansfe, vol. 44, pp , [45] Tien, C. L., and Chung, K. S., Entainment Limits in Heat Pipes, AIAA Jounal, vol. 17, no. 6, pp , [46] Kim, B. H., and Peteson, G. P., Analysis of the Citical Webe Numbe at the Onset of Liquid Entainment in CapillayDiven Heat Pipes, Intenational Jounal of Heat Mass Tansfe, vol. 38, no. 8, pp , [47] Faghi, A., Pefomance Chaacteistics of an Annula Heat Pipe, in Expeiments in Heat Tansfe and Themodynamics, ed. R. A. Gange, Cambidge Univesity Pess, London, [48] Colwell, G.T., and Chang, W.S., Measuements of the Tansient Behavio of a Capillay Stuctue unde Heavy Themal Loading, Intenational Jounal Heat Mass Tansfe, vol. 27, no. 4, pp , [49] Zuo, Z. J., and Faghi, A., A Netwok Themodynamic Analysis of the Heat Pipe, Intenational Jounal of Heat Mass Tansfe, vol. 41, no. 11, pp , [50] Khalkhali, H., Faghi, A., and Zuo, Z. J., Entopy Geneation in a Heat Pipe System, Applied Themal Engineeing, vol. 19, pp , [51] Zhu, N., and Vafai, K., Analysis of Cylindeical Heat Pipes Incopoating the Effects of Liquid Vapo Coupling and NonDacian Tanspot A Closed Fom Solution, Intenational Jounal of Heat Mass Tansfe, vol. 42, pp , [52] Khustalev, D., and Faghi, A., Coupled Liquid and Vapo Flow in Miniatue Passages with Mico Gooves, ASME Jounal of Heat Tansfe, vol. 121, pp , [53] Zhang, J. T., and Wang, B. X., Effect of Capillaity at Vapo Liquid Inteface on Phase Change without Sufactant, Intenational Jounal of Heat Mass Tansfe, vol. 45, pp , [54] Joudi, K. A., and Wiwit A. M., Impovements of GavityAssisted Wickless Heat Pipes, Enegy Convesion & Management, vol. 41, pp , Ali NouiBoujedi is a pofesso of Mechanical Engineeing at Shaif Univesity of Technology in Tehan, Ian. He eceived his Ph.D. degee fom the Univesity of Wisconsin at Madison, and he joined Shaif Univesity of Technology in He has authoed o coauthoed moe than foty publications in the field of heat tansfe, computational fluid dynamics, poous media, and twophase flow, including boiling and condensation, and acts as consultant to vaious industies. Mohammed Layeghi is a Ph.D. student in the division of Themal/ Fluid Sciences of Mechanical Engineeing Depatment at Shaif Univesity of Technology, Tehan, Ian. He eceived his Maste s degee fom Ian Univesity of Science and Technology in 1998 and his B.Sc degee fom Shaif Univesity of Technology in His eseach inteest is in the analysis and simulation of concentic annula heat pipes. heat tansfe engineeing vol. 26 no
Chapter 6. GraduallyVaried Flow in Open Channels
Chapte 6 GaduallyVaied Flow in Open Channels 6.. Intoduction A stea nonunifom flow in a pismatic channel with gadual changes in its watesuface elevation is named as gaduallyvaied flow (GVF). The backwate
More informationVISCOSITY OF BIODIESEL FUELS
VISCOSITY OF BIODIESEL FUELS One of the key assumptions fo ideal gases is that the motion of a given paticle is independent of any othe paticles in the system. With this assumption in place, one can use
More informationAn Introduction to Omega
An Intoduction to Omega Con Keating and William F. Shadwick These distibutions have the same mean and vaiance. Ae you indiffeent to thei iskewad chaacteistics? The Finance Development Cente 2002 1 Fom
More informationFXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it.
Candidates should be able to : Descibe how a mass ceates a gavitational field in the space aound it. Define gavitational field stength as foce pe unit mass. Define and use the peiod of an object descibing
More informationPhysics 235 Chapter 5. Chapter 5 Gravitation
Chapte 5 Gavitation In this Chapte we will eview the popeties of the gavitational foce. The gavitational foce has been discussed in geat detail in you intoductoy physics couses, and we will pimaily focus
More informationON NEW CHALLENGES FOR CFD SIMULATION IN FILTRATION
ON NEW CHALLENGES FOR CFD SIMULATION IN FILTRATION Michael Dedeing, Wolfgang Stausbeg, IBS Filtan, Industiestasse 19 D51597 MosbachLichtenbeg, Gemany. Oleg Iliev(*), Zaha Lakdawala, Faunhofe Institut
More informationStructure and evolution of circumstellar disks during the early phase of accretion from a parent cloud
Cente fo Tubulence Reseach Annual Reseach Biefs 2001 209 Stuctue and evolution of cicumstella disks duing the ealy phase of accetion fom a paent cloud By Olusola C. Idowu 1. Motivation and Backgound The
More information2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses,
3.4. KEPLER S LAWS 145 3.4 Keple s laws You ae familia with the idea that one can solve some mechanics poblems using only consevation of enegy and (linea) momentum. Thus, some of what we see as objects
More informationIntroduction to Fluid Mechanics
Chapte 1 1 1.6. Solved Examples Example 1.1 Dimensions and Units A body weighs 1 Ibf when exposed to a standad eath gavity g = 3.174 ft/s. (a) What is its mass in kg? (b) What will the weight of this body
More informationSIMULATION OF GAS TURBINES OPERATING IN OFFDESIGN CONDITION
SIMULAION OF GAS URBINES OPERAING IN OFFDESIGN CONDIION Analdo Walte: awalte@fem.unicamp.b Univesity of Campinas Dept. of Enegy DE/FEM/Unicamp P.O. Box 6122  ZIP code 13083970  Bazil Abstact. In many
More information(3) Bipolar Transistor Current Sources
B73 lectonics Analysis & Design (3) Bipola Tansisto Cuent Souces Leaning utcome Able to descibe and: Analyze and design a simple twotansisto BJT cuentsouce cicuit to poduce a given bias cuent. Analyze
More informationNUCLEAR MAGNETIC RESONANCE
19 Jul 04 NMR.1 NUCLEAR MAGNETIC RESONANCE In this expeiment the phenomenon of nuclea magnetic esonance will be used as the basis fo a method to accuately measue magnetic field stength, and to study magnetic
More informationLearning Objectives. Decreasing size. ~10 3 m. ~10 6 m. ~10 10 m 1/22/2013. Describe ionic, covalent, and metallic, hydrogen, and van der Waals bonds.
Lectue #0 Chapte Atomic Bonding Leaning Objectives Descibe ionic, covalent, and metallic, hydogen, and van de Waals bonds. Which mateials exhibit each of these bonding types? What is coulombic foce of
More informationGauss Law. Physics 231 Lecture 21
Gauss Law Physics 31 Lectue 1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing
More informationQuestions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing
M13914 Questions & Answes Chapte 10 Softwae Reliability Pediction, Allocation and Demonstation Testing 1. Homewok: How to deive the fomula of failue ate estimate. λ = χ α,+ t When the failue times follow
More informationRevision Guide for Chapter 11
Revision Guide fo Chapte 11 Contents Student s Checklist Revision Notes Momentum... 4 Newton's laws of motion... 4 Gavitational field... 5 Gavitational potential... 6 Motion in a cicle... 7 Summay Diagams
More informationMagnetic Bearing with Radial Magnetized Permanent Magnets
Wold Applied Sciences Jounal 23 (4): 495499, 2013 ISSN 18184952 IDOSI Publications, 2013 DOI: 10.5829/idosi.wasj.2013.23.04.23080 Magnetic eaing with Radial Magnetized Pemanent Magnets Vyacheslav Evgenevich
More informationHeat transfer has direction as well as magnitude. The rate of heat conduction
HEAT CONDUCTION EQUATION CHAPTER 2 Heat tansfe has diection as well as magnitude. The ate of heat conduction in a specified diection is popotional to the tempeatue gadient, which is the ate of change in
More informationStrength Analysis and Optimization Design about the key parts of the Robot
Intenational Jounal of Reseach in Engineeing and Science (IJRES) ISSN (Online): 23209364, ISSN (Pint): 23209356 www.ijes.og Volume 3 Issue 3 ǁ Mach 2015 ǁ PP.2529 Stength Analysis and Optimization Design
More informationDeflection of Electrons by Electric and Magnetic Fields
Physics 233 Expeiment 42 Deflection of Electons by Electic and Magnetic Fields Refeences Loain, P. and D.R. Coson, Electomagnetism, Pinciples and Applications, 2nd ed., W.H. Feeman, 199. Intoduction An
More informationThe Role of Gravity in Orbital Motion
! The Role of Gavity in Obital Motion Pat of: Inquiy Science with Datmouth Developed by: Chistophe Caoll, Depatment of Physics & Astonomy, Datmouth College Adapted fom: How Gavity Affects Obits (Ohio State
More informationSoftware Engineering and Development
I T H E A 67 Softwae Engineeing and Development SOFTWARE DEVELOPMENT PROCESS DYNAMICS MODELING AS STATE MACHINE Leonid Lyubchyk, Vasyl Soloshchuk Abstact: Softwae development pocess modeling is gaining
More informationGauss Law in dielectrics
Gauss Law in dielectics We fist deive the diffeential fom of Gauss s law in the pesence of a dielectic. Recall, the diffeential fom of Gauss Law is This law is always tue. E In the pesence of dielectics,
More informationXIIth PHYSICS (C2, G2, C, G) Solution
XIIth PHYSICS (C, G, C, G) 6 Solution. A 5 W, 0 V bulb and a 00 W, 0 V bulb ae connected in paallel acoss a 0 V line nly 00 watt bulb will fuse nly 5 watt bulb will fuse Both bulbs will fuse None of
More informationINVESTIGATION OF FLOW INSIDE AN AXIALFLOW PUMP OF GV IMP TYPE
1 INVESTIGATION OF FLOW INSIDE AN AXIALFLOW PUMP OF GV IMP TYPE ANATOLIY A. YEVTUSHENKO 1, ALEXEY N. KOCHEVSKY 1, NATALYA A. FEDOTOVA 1, ALEXANDER Y. SCHELYAEV 2, VLADIMIR N. KONSHIN 2 1 Depatment of
More informationLAL Update. Letter From the President. Dear LAL User:
LAL Update ASSOCIATES OF CAPE COD, INCORPORATED OCTOBER 00 VOLUME 0, NO. Lette Fom the Pesident Dea LAL Use: This Update will claify some of the statistics used with tubidimetic and chomogenic LAL tests.
More informationSmart Antenna Array Calibration Procedure Including Amplitude and Phase Mismatch and Mutual Coupling Effects
Smat Antenna Aay alibation Pocedue Including Amplitude and Phase Mismatch and Mutual oupling Effects Kapil R. Dandeka, Hao Ling, and Guanghan Xu Univesity of Texas at Austin, Dept. of Elec. And omp. Eng.
More informationComparing Availability of Various Rack Power Redundancy Configurations
Compaing Availability of Vaious Rack Powe Redundancy Configuations By Victo Avela White Pape #48 Executive Summay Tansfe switches and dualpath powe distibution to IT equipment ae used to enhance the availability
More informationThe transport performance evaluation system building of logistics enterprises
Jounal of Industial Engineeing and Management JIEM, 213 6(4): 194114 Online ISSN: 213953 Pint ISSN: 2138423 http://dx.doi.og/1.3926/jiem.784 The tanspot pefomance evaluation system building of logistics
More information2  ELECTROSTATIC POTENTIAL AND CAPACITANCE Page 1
 ELECTROSTATIC POTENTIAL AND CAPACITANCE Page. Line Integal of Electic Field If a unit positive chage is displaced by `given by dw E. dl dl in an electic field of intensity E, wok done is Line integation
More informationDesign and Analysis of a Classical Controller to the Residual Oil in a Small Scale Semibatch Extractor
Euopean Symposium on Compute Aded Aided Pocess Engineeing 15 L. Puigjane and A. Espuña (Editos) 25 Elsevie Science B.V. All ights eseved. Design and Analysis of a Classical Contolle to the Residual Oil
More informationEpisode 401: Newton s law of universal gravitation
Episode 401: Newton s law of univesal gavitation This episode intoduces Newton s law of univesal gavitation fo point masses, and fo spheical masses, and gets students pactising calculations of the foce
More informationUNIT 21: ELECTRICAL AND GRAVITATIONAL POTENTIAL Approximate time two 100minute sessions
Name St.No.  Date(YY/MM/DD) / / Section Goup# UNIT 21: ELECTRICAL AND GRAVITATIONAL POTENTIAL Appoximate time two 100minute sessions OBJECTIVES I began to think of gavity extending to the ob of the moon,
More informationExperiment MF Magnetic Force
Expeiment MF Magnetic Foce Intoduction The magnetic foce on a cuentcaying conducto is basic to evey electic moto  tuning the hands of electic watches and clocks, tanspoting tape in Walkmans, stating
More information1.4 Phase Line and Bifurcation Diag
Dynamical Systems: Pat 2 2 Bifucation Theoy In pactical applications that involve diffeential equations it vey often happens that the diffeential equation contains paametes and the value of these paametes
More informationdz + η 1 r r 2 + c 1 ln r + c 2 subject to the boundary conditions of noslip side walls and finite force over the fluid length u z at r = 0
Poiseuille Flow Jean Louis Maie Poiseuille, a Fench physicist and physiologist, was inteested in human blood flow and aound 1840 he expeimentally deived a law fo flow though cylindical pipes. It s extemely
More informationCarterPenrose diagrams and black holes
CatePenose diagams and black holes Ewa Felinska The basic intoduction to the method of building Penose diagams has been pesented, stating with obtaining a Penose diagam fom Minkowski space. An example
More informationSupplementary Material for EpiDiff
Supplementay Mateial fo EpiDiff Supplementay Text S1. Pocessing of aw chomatin modification data In ode to obtain the chomatin modification levels in each of the egions submitted by the use QDCMR module
More informationSELFINDUCTANCE AND INDUCTORS
MISN0144 SELFINDUCTANCE AND INDUCTORS SELFINDUCTANCE AND INDUCTORS by Pete Signell Michigan State Univesity 1. Intoduction.............................................. 1 A 2. SelfInductance L.........................................
More informationInternational Journal of Heat and Mass Transfer 43 (2000) 1391±1398
Intenational Jounal of Heat and Mass Tansfe 43 (2) 1391±1398 Condensation on the outside suface of a small/mini diamete tube fo vapo owing though a hoizontal annulus suound by an adiabatic concentic tube
More informationIlona V. Tregub, ScD., Professor
Investment Potfolio Fomation fo the Pension Fund of Russia Ilona V. egub, ScD., Pofesso Mathematical Modeling of Economic Pocesses Depatment he Financial Univesity unde the Govenment of the Russian Fedeation
More informationGravitational Mechanics of the MarsPhobos System: Comparing Methods of Orbital Dynamics Modeling for Exploratory Mission Planning
Gavitational Mechanics of the MasPhobos System: Compaing Methods of Obital Dynamics Modeling fo Exploatoy Mission Planning Alfedo C. Itualde The Pennsylvania State Univesity, Univesity Pak, PA, 6802 This
More informationYARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH
nd INTERNATIONAL TEXTILE, CLOTHING & ESIGN CONFERENCE Magic Wold of Textiles Octobe 03 d to 06 th 004, UBROVNIK, CROATIA YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH Jana VOBOROVA; Ashish GARG; Bohuslav
More informationThe Electric Potential, Electric Potential Energy and Energy Conservation. V = U/q 0. V = U/q 0 = W/q 0 1V [Volt] =1 Nm/C
Geneal Physics  PH Winte 6 Bjoen Seipel The Electic Potential, Electic Potential Enegy and Enegy Consevation Electic Potential Enegy U is the enegy of a chaged object in an extenal electic field (Unit
More informationProgress In Electromagnetics Research Letters, Vol. 11, , 2009
Pogess In Electomagnetics Reseach Lettes, Vol. 11, 93 102, 2009 COMPUTATIONAL MODELING OF INDUCTION HEATING PROCESS M. H. Tavakoli, H. Kabaschi, and F. Samavat Physics Depatment BuAli Sina Univesity Hamedan
More informationSamples of conceptual and analytical/numerical questions from chap 21, C&J, 7E
CHAPTER 1 Magnetism CONCEPTUAL QUESTIONS Cutnell & Johnson 7E 3. ssm A chaged paticle, passing though a cetain egion of space, has a velocity whose magnitude and diection emain constant, (a) If it is known
More informationUSB True Emulation for KVM Switches. Transparent and reliable USB KVM switching technology.
Tanspaent and eliable KVM switching technology. 0118 7247465500 965 6000 www.blackbox.co.uk blackbox.com Table of Contents Intoduction... 3 Enumeated Switching... 4 Emulated Switching... 5 Tue Emulation...
More informationSTUDENT RESPONSE TO ANNUITY FORMULA DERIVATION
Page 1 STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION C. Alan Blaylock, Hendeson State Univesity ABSTRACT This pape pesents an intuitive appoach to deiving annuity fomulas fo classoom use and attempts
More informationProblems of the 2 nd International Physics Olympiads (Budapest, Hungary, 1968)
Poblems of the nd ntenational Physics Olympiads (Budapest Hungay 968) Péte Vankó nstitute of Physics Budapest Univesity of Technical Engineeing Budapest Hungay Abstact Afte a shot intoduction the poblems
More informationON THE (Q, R) POLICY IN PRODUCTIONINVENTORY SYSTEMS
ON THE R POLICY IN PRODUCTIONINVENTORY SYSTEMS Saifallah Benjaafa and JoonSeok Kim Depatment of Mechanical Engineeing Univesity of Minnesota Minneapolis MN 55455 Abstact We conside a poductioninventoy
More informationStudy on Insitu Capacitive Sensor for Monitoring Engine Lubricant Oil Debris
8th Euopean Wokshop On Stuctual Health Monitoing (EWSHM 016), 58 July 016, Spain, Bilbao www.ndt.net/app.ewshm016 Study on Insitu Capacitive Senso fo Monitoing Engine Lubicant Oil Debis Moe info about
More informationInfinitedimensional Bäcklund transformations between isotropic and anisotropic plasma equilibria.
Infinitedimensional äcklund tansfomations between isotopic and anisotopic plasma equilibia. Infinite symmeties of anisotopic plasma equilibia. Alexei F. Cheviakov Queen s Univesity at Kingston, 00. Reseach
More information81 Newton s Law of Universal Gravitation
81 Newton s Law of Univesal Gavitation One of the most famous stoies of all time is the stoy of Isaac Newton sitting unde an apple tee and being hit on the head by a falling apple. It was this event,
More informationExperiment 6: Centripetal Force
Name Section Date Intoduction Expeiment 6: Centipetal oce This expeiment is concened with the foce necessay to keep an object moving in a constant cicula path. Accoding to Newton s fist law of motion thee
More informationDYNAMICS AND STRUCTURAL LOADING IN WIND TURBINES
DYNAMIS AND STRUTURAL LOADING IN WIND TURBINES M. Ragheb 12/30/2008 INTRODUTION The loading egimes to which wind tubines ae subject to ae extemely complex equiing special attention in thei design, opeation
More informationSimple Harmonic Motion
Simple Hamonic Motion Intoduction Simple hamonic motion occus when the net foce acting on an object is popotional to the object s displacement fom an equilibium position. When the object is at an equilibium
More informationVoltage ( = Electric Potential )
V1 of 9 Voltage ( = lectic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage
More informationest using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years.
9.2 Inteest Objectives 1. Undestand the simple inteest fomula. 2. Use the compound inteest fomula to find futue value. 3. Solve the compound inteest fomula fo diffeent unknowns, such as the pesent value,
More informationThe Critical Angle and Percent Efficiency of Parabolic Solar Cookers
The Citical Angle and Pecent Eiciency o Paabolic Sola Cookes Aiel Chen Abstact: The paabola is commonly used as the cuve o sola cookes because o its ability to elect incoming light with an incoming angle
More informationEXPERIENCE OF USING A CFD CODE FOR ESTIMATING THE NOISE GENERATED BY GUSTS ALONG THE SUN ROOF OF A CAR
EXPERIENCE OF USING A CFD CODE FOR ESTIMATING THE NOISE GENERATED BY GUSTS ALONG THE SUN ROOF OF A CAR Liang S. Lai* 1, Geogi S. Djambazov 1, Choi H. Lai 1, Koulis A. Peicleous 1, and Fédéic Magoulès
More informationModal Characteristics study of CEM1 SingleLayer Printed Circuit Board Using Experimental Modal Analysis
Available online at www.sciencediect.com Pocedia Engineeing 41 (2012 ) 1360 1366 Intenational Symposium on Robotics and Intelligent Sensos 2012 (IRIS 2012) Modal Chaacteistics study of CEM1 SingleLaye
More informationUNIVERSITY OF CANTABRIA
Failue Assessment Diagam  Cack Diving Foce Diagam COMPATIBILITY UNIVERSITY OF CANTABRIA Novembe 1997 J. Ruiz Ocejo F. GutiéezSolana M.A. GonzálezPosada I. Goochategui Depatamento de Ciencia e Ingenieía
More informationHow to select.
How to select a Specialty Gas Regulato STEP 1 Detemine gas and mateial compatibility Mateial compatibility between the puposed gas and the egulato's mateials of constuction is essential. Regulato components
More informationInstituto Superior Técnico Av. Rovisco Pais, 1 1049001 Lisboa Email: virginia.infante@ist.utl.pt
FATIGUE LIFE TIME PREDICTIO OF POAF EPSILO TB30 AIRCRAFT  PART I: IMPLEMETATIO OF DIFERET CYCLE COUTIG METHODS TO PREDICT THE ACCUMULATED DAMAGE B. A. S. Seano 1, V. I. M.. Infante 2, B. S. D. Maado
More informationPAN STABILITY TESTING OF DC CIRCUITS USING VARIATIONAL METHODS XVIII  SPETO  1995. pod patronatem. Summary
PCE SEMINIUM Z PODSTW ELEKTOTECHNIKI I TEOII OBWODÓW 8  TH SEMIN ON FUNDMENTLS OF ELECTOTECHNICS ND CICUIT THEOY ZDENĚK BIOLEK SPŠE OŽNO P.., CZECH EPUBLIC DLIBO BIOLEK MILITY CDEMY, BNO, CZECH EPUBLIC
More informationDatabase Management Systems
Contents Database Management Systems (COP 5725) D. Makus Schneide Depatment of Compute & Infomation Science & Engineeing (CISE) Database Systems Reseach & Development Cente Couse Syllabus 1 Sping 2012
More informationComparing Availability of Various Rack Power Redundancy Configurations
Compaing Availability of Vaious Rack Powe Redundancy Configuations White Pape 48 Revision by Victo Avela > Executive summay Tansfe switches and dualpath powe distibution to IT equipment ae used to enhance
More informationForces & Magnetic Dipoles. r r τ = μ B r
Foces & Magnetic Dipoles x θ F θ F. = AI τ = U = Fist electic moto invented by Faaday, 1821 Wie with cuent flow (in cup of Hg) otates aound a a magnet Faaday s moto Wie with cuent otates aound a Pemanent
More informationChapter 13 Gravitation. Problems: 1, 4, 5, 7, 18, 19, 25, 29, 31, 33, 43
Chapte 13 Gavitation Poblems: 1, 4, 5, 7, 18, 19, 5, 9, 31, 33, 43 Evey object in the univese attacts evey othe object. This is called gavitation. We e use to dealing with falling bodies nea the Eath.
More informationNUMERICAL STUDY OF TURBULENT HEAT TRANSFER ALONG A HEATED ROD IN AN ANNULAR CAVITY
NUMERICAL STUDY OF TURBULENT HEAT TRANSFER ALONG A HEATED ROD IN AN ANNULAR CAVITY Abstact A. Batta, A. Class, M. Daubne S. Gniese R. Stieglit Foschungsentum Kalsuhe GmbH Institut fü Ken und Enegietechnik
More information2008 QuarterFinal Exam Solutions
2008 Quatefinal Exam  Solutions 1 2008 QuateFinal Exam Solutions 1 A chaged paticle with chage q and mass m stats with an initial kinetic enegy K at the middle of a unifomly chaged spheical egion of
More informationChapter 4: Fluid Kinematics
Oveview Fluid kinematics deals with the motion of fluids without consideing the foces and moments which ceate the motion. Items discussed in this Chapte. Mateial deivative and its elationship to Lagangian
More informationmv2. Equating the two gives 4! 2. The angular velocity is the angle swept per GM (2! )2 4! 2 " 2 = GM . Combining the results we get !
Chapte. he net foce on the satellite is F = G Mm and this plays the ole of the centipetal foce on the satellite i.e. mv mv. Equating the two gives = G Mm i.e. v = G M. Fo cicula motion we have that v =!
More informationFluids Lecture 15 Notes
Fluids Lectue 15 Notes 1. Unifom flow, Souces, Sinks, Doublets Reading: Andeson 3.9 3.12 Unifom Flow Definition A unifom flow consists of a velocit field whee V = uî + vĵ is a constant. In 2D, this velocit
More information(a) The centripetal acceleration of a point on the equator of the Earth is given by v2. The velocity of the earth can be found by taking the ratio of
Homewok VI Ch. 7  Poblems 15, 19, 22, 25, 35, 43, 51. Poblem 15 (a) The centipetal acceleation of a point on the equato of the Eath is given by v2. The velocity of the eath can be found by taking the
More informationLab M4: The Torsional Pendulum and Moment of Inertia
M4.1 Lab M4: The Tosional Pendulum and Moment of netia ntoduction A tosional pendulum, o tosional oscillato, consists of a disklike mass suspended fom a thin od o wie. When the mass is twisted about the
More informationConverting knowledge Into Practice
Conveting knowledge Into Pactice Boke Nightmae srs Tend Ride By Vladimi Ribakov Ceato of Pips Caie 20 of June 2010 2 0 1 0 C o p y i g h t s V l a d i m i R i b a k o v 1 Disclaime and Risk Wanings Tading
More informationCIRCUITS LABORATORY EXPERIMENT 7
CIRCUITS LABORATORY EXPERIMENT 7 Design of a Single Tansisto Amplifie 7. OBJECTIVES The objectives of this laboatoy ae to: (a) Gain expeience in the analysis and design of an elementay, single tansisto
More informationFinancing Terms in the EOQ Model
Financing Tems in the EOQ Model Habone W. Stuat, J. Columbia Business School New Yok, NY 1007 hws7@columbia.edu August 6, 004 1 Intoduction This note discusses two tems that ae often omitted fom the standad
More information9:6.4 Sample Questions/Requests for Managing Underwriter Candidates
9:6.4 INITIAL PUBLIC OFFERINGS 9:6.4 Sample Questions/Requests fo Managing Undewite Candidates Recent IPO Expeience Please povide a list of all completed o withdawn IPOs in which you fim has paticipated
More informationAN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM
AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM Main Golub Faculty of Electical Engineeing and Computing, Univesity of Zageb Depatment of Electonics, Micoelectonics,
More informationTHERMAL ISOLATION TECHNIQUES FOR CURE MONITORING USING FBG OPTICAL SENSORS
THERMAL OLATION TECHNIQUES FOR CURE MONITORING USING FBG OPTICAL SENSORS E.K.G. Boateng, P.J. Schubel, N.A. Waio Polyme Composites Goup Division of Mateials, Mechanics and Stuctues Faculty of Engineeing
More informationLecture 16: Color and Intensity. and he made him a coat of many colours. Genesis 37:3
Lectue 16: Colo and Intensity and he made him a coat of many colous. Genesis 37:3 1. Intoduction To display a pictue using Compute Gaphics, we need to compute the colo and intensity of the light at each
More informationPhysics 202, Lecture 4. Gauss s Law: Review
Physics 202, Lectue 4 Today s Topics Review: Gauss s Law Electic Potential (Ch. 25Pat I) Electic Potential Enegy and Electic Potential Electic Potential and Electic Field Next Tuesday: Electic Potential
More informationAn Epidemic Model of Mobile Phone Virus
An Epidemic Model of Mobile Phone Vius Hui Zheng, Dong Li, Zhuo Gao 3 Netwok Reseach Cente, Tsinghua Univesity, P. R. China zh@tsinghua.edu.cn School of Compute Science and Technology, Huazhong Univesity
More informationResearch on Risk Assessment of the Transformer Based on Life Cycle Cost
ntenational Jounal of Smat Gid and lean Enegy eseach on isk Assessment of the Tansfome Based on Life ycle ost Hui Zhou a, Guowei Wu a, Weiwei Pan a, Yunhe Hou b, hong Wang b * a Zhejiang Electic Powe opoation,
More informationChapter 3 Savings, Present Value and Ricardian Equivalence
Chapte 3 Savings, Pesent Value and Ricadian Equivalence Chapte Oveview In the pevious chapte we studied the decision of households to supply hous to the labo maket. This decision was a static decision,
More informationDetermining solar characteristics using planetary data
Detemining sola chaacteistics using planetay data Intoduction The Sun is a G type main sequence sta at the cente of the Sola System aound which the planets, including ou Eath, obit. In this inestigation
More informationChapter 26  Electric Field. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University
Chapte 6 lectic Field A PowePoint Pesentation by Paul. Tippens, Pofesso of Physics Southen Polytechnic State Univesity 7 Objectives: Afte finishing this unit you should be able to: Define the electic field
More informationOPERATIONAL CHARACTERISTICS OF BRUSHLESS DC MOTORS
OPERATIONAL CHARACTERISTICS OF BRUSHLESS DC MOTORS Ronald De Fou Depatment of Electical & Compute Engineeing, The Univesity of the West Indies St. Augustine, Tinidad defou@eng.uwi.tt Emily Ramouta Univesity
More informationVector Calculus: Are you ready? Vectors in 2D and 3D Space: Review
Vecto Calculus: Ae you eady? Vectos in D and 3D Space: Review Pupose: Make cetain that you can define, and use in context, vecto tems, concepts and fomulas listed below: Section 7.7. find the vecto defined
More information12. Rolling, Torque, and Angular Momentum
12. olling, Toque, and Angula Momentum 1 olling Motion: A motion that is a combination of otational and tanslational motion, e.g. a wheel olling down the oad. Will only conside olling with out slipping.
More informationPerformance Analysis of an Inverse Notch Filter and Its Application to F 0 Estimation
Cicuits and Systems, 013, 4, 1171 http://dx.doi.og/10.436/cs.013.41017 Published Online Januay 013 (http://www.scip.og/jounal/cs) Pefomance Analysis of an Invese Notch Filte and Its Application to F 0
More informationSTABILITY ANALYSIS IN MILLING BASED ON OPERATIONAL MODAL DATA 1. INTRODUCTION
Jounal of Machine Engineeing, Vol. 11, No. 4, 211 Batosz POWALKA 1 Macin CHODZKO 1 Kzysztof JEMIELNIAK 2 milling, chatte, opeational modal analysis STABILITY ANALYSIS IN MILLING BASED ON OPERATIONAL MODAL
More informationManual ultrasonic inspection of thin metal welds
Manual ultasonic inspection of thin metal welds Capucine Capentie and John Rudlin TWI Cambidge CB1 6AL, UK Telephone 01223 899000 Fax 01223 890689 Email capucine.capentie@twi.co.uk Abstact BS EN ISO 17640
More informationLab #7: Energy Conservation
Lab #7: Enegy Consevation Photo by Kallin http://www.bungeezone.com/pics/kallin.shtml Reading Assignment: Chapte 7 Sections 1,, 3, 5, 6 Chapte 8 Sections 14 Intoduction: Pehaps one of the most unusual
More informationGAUSS S LAW APPLIED TO CYLINDRICAL AND PLANAR CHARGE DISTRIBUTIONS ` E MISN0133. CHARGE DISTRIBUTIONS by Peter Signell, Michigan State University
MISN0133 GAUSS S LAW APPLIED TO CYLINDRICAL AND PLANAR CHARGE DISTRIBUTIONS GAUSS S LAW APPLIED TO CYLINDRICAL AND PLANAR CHARGE DISTRIBUTIONS by Pete Signell, Michigan State Univesity 1. Intoduction..............................................
More informationEAS Groundwater Hydrology Lecture 13: Well Hydraulics 2 Dr. Pengfei Zhang
EAS 44600 Goundwate Hydology Lectue 3: Well Hydaulics D. Pengfei Zhang Detemining Aquife Paametes fom TimeDawdown Data In the past lectue we discussed how to calculate dawdown if we know the hydologic
More informationChapter 22. Outside a uniformly charged sphere, the field looks like that of a point charge at the center of the sphere.
Chapte.3 What is the magnitude of a point chage whose electic field 5 cm away has the magnitude of.n/c. E E 5.56 1 11 C.5 An atom of plutonium39 has a nuclea adius of 6.64 fm and atomic numbe Z94. Assuming
More information