Clean Technol., Vol. 22, No. 1, March 2016, pp

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1 lean echnl., Vl., N. 1, Mach 016, pp 청정에너지기술 mpaisn between Wate and N-etadecane as Insulatin Mateials thugh Mdeling and Simulatin f Heat ansfe in Pacaging Bx f Vaccine Shipping Van-Dung Da 1, I-Kyu Jin, H Hu 3, and H-Su hi 1,, 1 Depatment f hemical Engineeing, hungnam Natinal Univesity 99 Daeha-, Yuseng-gu, Daejen , Kea Gaduate Schl f Advanced icuit Substate Engineeing, hungnam Natinal Univesity 99 Daeha-, Yuseng-gu, Daejen , Kea 3 Depatment f Fie Safety Management, Mwn Univesity 88 Danbu-, Se-gu, Daejen 30-80, Kea (Received f eview Januay 5, 016; Revisin eceived Januay 11, 016; Accepted Januay 18, 016) Abstact his study epts n the mdeling and simulatin f heat tansfe in pacaging bxes used f vaccine shipping. Bth wate and n-tetadecane ae used as pimay insulatin mateials inside a multi-slab system. he ne-dimensinal mdel, which is a spheical mdel using a adius equivalent t the ectangula gemety f cntaine, is applied in this study. N-tetadecane with lw themal diffusivity and ppe phase tansitin tempeatue exhibits highe heat tansfe esistance duing bth heating and cling pcesses cmpaed t wate. hus, n-tetadecane is a bette candidate as an insulating mateial f pacaging cntaines f vaccine shipping. Futheme, the develped methd can als becme a apid and ecnmic tl f sceening apppiate phase change mateials used as insulatin mateials with suitable ppeties in lgistics applicatins. Keywds : ld chain, Mdelling, Simulatin, Heat tansfe, N-etadecane, Wate 1. Intductin Due t the ecent signing f the fee tade ageements between cunties, the imptance f the lgistics industy t tanspt a wide ange f pducts has emeged. Vaius instuctins have been made with the type f pduct t ensue eliable tanspt f the pduct. In the case f tempeatue-sensitive dugs lie vaccines, the Wld Health Oganizatin (WHO) has enacted the Guidelines n the intenatinal pacaging and shipping f vaccines [1] and ecmmended that the guidelines shuld be included in the technical specificatins and equiements. he WHO has classified each type f vaccine and indicated the minimum and maximum allwable tempeatue t which vaccines may be expsed duing intenatinal lgistics time f at least 48 hus. hus, all vaccine manufactues ae expected t ensue that thei pacaging cmplies with the citeia specified in the guidelines. In de t satisfy the guidelines, bth active system and passive system have been used f vaccine pacaging and shipping. Unlie the active system t eep a cnstant tempeatue by using electic pwe, the passive system is using nly pue physical ppeties f pacaging mateials cmpsed f insulatin and efigeants t maintain the tempeatue. hugh the use f the phase change mateials (PMs), which ae ec-fiendly, nn-txic and ecyclable, the pefmance f the passive system can be impved as much as the pefmance f the active system. heefe, the insulatin pacage using the PM has been actively develped. he PM, which has a melting pint f t 8, is useful f the pacaging and shipping f vaccines. Recently, paaffin waxes have becme emeging candidate mateials t be used as PMs since they d nt shw a tendency t segegate, ae chemically stable, safe, nn-eactive, cmpatible with all metal cntaines, and can easily be incpated int a heat stage system with a high heat f fusin []. Futheme, they als exhibit n tendencies t supe cling. hus, nucleating agents ae nt equied. In this study, we fcus n pedicting the intenal tempeatue changes that ccu duing vaccine pacage tanspt via the whm cespndence shuld be addessed. hchi@cnu.ac.; el: ; Fax: di: /sct pissn eissn his is an Open-Access aticle distibuted unde the tems f the eative mmns Attibutin Nn-mmecial License ( by-nc/3.0) which pemits unesticted nn-cmmecial use, distibutin, and epductin in any medium, pvided the iginal w is ppely cited. 45

2 46 Van-Dung Da ㆍ I-Kyu Jin ㆍ H Hu ㆍ H-Su hi mdeling and simulatin f heat tansfe in an insulated bx cntaining PMs. Bth n-tetadecane and wate ae used as PMs. he heat tansfe accmpanying the phase tansitin has been egaded as a difficult pblem because the nn-linea phasetansitin bunday is mving with time. Seveal techniques such as finite diffeence methd (FDM), finite element methd (FEM), cntl vlume, and the appaching bunday element methd have been epted [3-1] with the use f themal enegy equatins [13]. In u pevius study, we used wate in the mdeling and simulatin f heat tansfe inside a pacaging cntaine utilized f vaccine shipping. he simulatin esults shwed gd ageement with expeimental data duing the cling pcess, but the mdel did nt successfully simulate the heating pcess. Althugh a basic algithm f simulating heat tansfe thugh multi-slabs cmbined with diffeent mateials including phase-change mateial (PM) has been successfully develped, the esults shw that wate is nt suitable f use due t its lwe melting tempeatue (~0 ). hus, this study pves the effectiveness f using n-tetadecane as a PM inside a pacaging cntaine utilized f vaccine shipping.. Mateials and methd.1. Mateials N-tetadecane (99%) was puchased fm Kant chemical., Inc. Ethyl alchl was eceived fm Samchun Pue hemical., Ltd. Wate was gt fm J.. Bae. -histy methd was pefmed in a chille (HS-05 WL, Han Bse St., Ltd.) and ecded by est 175 H. Plyuethane fam (PUR, hem Safe Mdel N. E36) was used as cntaine in this study. Figue 1. Phase change tempeatue f n-tetadecane. able 1. Physical ppeties f simulatin hemal cnductivity Heat capacity, p Latent heat Density, Mateial (W m -1 K -1 ) (J g -1 K -1 ) (g m -3 ) (J g -1 ) Phase Slid Liquid Slid Liquid Slid Liquid n tetadecane [17] [17] PM- etadecane Wate [17] 7.63 [17] [17] [17] PM- Wate Inne Space Measuement We fist measued the them-physical ppeties f n- tetadecane and ethyl alchl. he them-physical ppeties f n-tetadecane wee chaacteized using an impved -histy methd [15] in a chille in the tempeatue ange fm 6 t 0 with a themcuple (length f 110 mm, diamete f 0.4 mm), tubes (PM length f 10 mm, tube length f 150 mm, tube diamete f 1 mm), and ecde. Ethyl alchl was used as the efeence mateial [16]. he slidificatin cuves f n- tetadecane and ethyl alchl ae shwn in Figue 1. he phasechange tempeatue f n-tetadecane can easily be deduced fm the impved -histy methd cuve, with elevant paametes being summaized in able 1. Figue illustates a mdel pacaging cntaine f vaccine shipping. w insulating cntaines f diffeent sizes wee used tgethe in this study. he insulating cntaine used in this study is depicted in Figue, and its desciptin is tabulated in able. We nte that the space thicness between the tw cntaines is 0.03 m. Figue. Mdel pacaging cntaine f mdeling and simulatin. able. Desciptins f insulating cntaines used in this study ntaine Inne dimensins Oute dimensins (L W H) (m) (L W H) (m)

3 mpaisn between Wate and N-etadecane as Insulatin Mateials f Vaccine Shipping Mathematical mdeling he heat tansfe accmpanying the phase tansitin is a mving bunday pblem in which the nn-linea phase-tansitin bunday is mving with time. In de t effectively slve this pblem, we used the enegy methd [13]. his methd used enegy and tempeatue as tw vaiables in the heat tansfe equatin. he intenal enegy and tempeatue f mateials have the fllwing elatin: able 3. ntaine gemety ntaine vlume (m 3 ) Equivalent adius (m) Dimensinless adius (m) ( e) m ( e e0 ) H[ e e0 ] ( e e0 λ) H[ e e0 λ] p, s p, l (1) he veall heat tansfe equatin can be witten with the use f the fllwing equatins. he heat tansfe equatin at each sectin f the pacaging cntaine is witten as fllws: whee is the tempeatue, m is a melting pint, e is the enegy, p,s is a heat capacity f slid, p,l is a heat capacity f liquid, λ is a latent heat, and H is a step functin. MS- Ftan Pwe Statin, which was incpated with an Intenatinal Mathematical and Statistical Libaies (IMSL) subine, was used f the simulatin f heat tansfe inside the pacaging cntaine. he mdeling was pefmed fllwing a pevius study. pvide a bief veview f the pcess, the cntaines thee-dimensinal ectangula gemety was cnveted int a ne-dimensinal spheical mdel. he cnvesin was caied using the fllwing Equatin (): 4 3 1/ π () bx vlume 4π (bx vlume) Meanwhile, the basic assumptins f this mdeling ae summaized via the thee fllwing desciptins. Fist, all the ectangles inside the cntaine wee cnveted int equivalent sphees. Secnd, heat tansfe in the inne space f the cntaine was assumed t ccu via themal cnductin. hid, althugh the physical ppeties such as the heat cnductivity, themal capacity, and density actually vay with espect t tempeatue, they wee assumed t have cnstant values. he scheme descibing u simple mdel is shwn in Figue 3, and the gemetical desciptin f the actual cntaine is tabulated in able 3. Inne space ai: whee I: whee PM: whee whee ai ai ai (3) ai, ai I I I (4) I, I SlidPM SlidPM SlidPM at mb SlidPM p, SlidPM anspm anspm anspm anspm mf λ mb at < (5) mb (6) mf LiquidPM Figue 3. One-dimensinal mdel f heat tansfe simulatin. whee LiquidPM LiquidPM at LiquidPM p, LiquidPM mf < (7)

4 48 Van-Dung Da ㆍ I-Kyu Jin ㆍ H Hu ㆍ H-Su hi II: II PM: SlidPM whee II II (8) II, II In the abve Equatins f (5) t (7), we cnside the phase tansitin f a PM afte dividing the PM int thee egins such as a slid state (SlidPM), a tansitin state (anspm), and a liquid state (LiquidPM), with espect t tempeatue. In paticula, the PM at a tansitin state epesents the change f themal heat capacity duing phase tansitin as a functin f latent heat. Using Equatin (1), the effect f latent heat n heat tansfe can be eflected in the heat tansfe accmpanying phase tansitin. he initial and bunday cnditins f slving these equatins ae as fllws: Initial cnditin: at t 0 and all Bunday cnditins: 0 at 0 and all t ( t) wall at 4 and all t at at at < mb (11) anspm mb mf (1) LiquidPM mf < (13) II: (14) he cespnding initial and bunday cnditins ae als ewitten as fllws: Initial cnditin: 1 at t 0 and all Dimensinless vaiables ae used f slving the abve equatins. hese vaiables ae defined as fllws: mb 4 mb 0 t mf t ( 4 / ) 0 mf 0 ai ai SlidPM wall ( ) wall 0 anspm anspm LiquidPM SlidPM LiquidPM t nsequently, the heat tansfe equatins ae ewitten using the dimensinless vaiables as belw: Inne space ai: I: ai (9) (10) Bunday cnditins: ling pcess at 0 and all t wall at 1 3. Results and all t We fistly investigate the tempeatue pfiles at vaius time dmains duing the cling pcess. he tempeatue pfiles at diffeent times ae shwn in Figue 4. his simulatin was pefmed with the fllwing initial and melting cnditins: 7 0 and -5 mb.48 and mf 5.64 whee 0 epesents the initial intenal tempeatue, the extenal tempeatue side tempeatue, mb the tempeatue at which melting begins, and mf the tempeatue at which melting ends. hese values f 0 and wee fixed, while the values f mb and mf wee measued via the impved -histy methd. Figue 4 shws the tempeatue change with espect t vaius psitins (with the distance being measued

5 mpaisn between Wate and N-etadecane as Insulatin Mateials f Vaccine Shipping 49 Figue 4. empeatue change with espect t vaius psitins inside the bx: (a) n-tetadecane (lines fm tp t bttm at diffeent times: 0.35, 1.39, 3.13, 5.56, 8.70, 1.5, 17.04,.6, 8.17, 34.78, 4.09, 50.09, 58.79, 68.18, 78.7, 89.05, h) and (b) wate (lines fm tp t bttm at diffeent times: 0.35, 1.39, 3.13, 5.56, 8.70, 1.5, 17.04,.6, 8.17, 34.78, 4.09, 50.09, h). fm the cente t the wall, as seen in Figue 3) in the bx calculated at vaius times duing the cling pcess. he lines fm tp t bttm indicate tempeatue pfiles calculated at vaius times. Each line cespnds t a tempeatue pfile within the cntaine. In de f the bx t be used as a cntaine suitable f the pacaging and shipping f vaccines, the phasechange mateials must be fistly equied t have a melting tempeatue in the ange f t 8. Secndly, the cldest tempeatue f the vaccine is nt belw with cntinuus expsue at an extenal tempeatue f -5 f a peid f at least 48 h [1]. Figue 4 shws the tempeatue pfiles in the bx calculated at vaius times f bth n-tetadecane (Figue 4(a)) and wate (Figue 4(b)). Fm Figue 4(a), we nte that the tempeatue pfiles d nt change at psitins in the ange fm 0 t 7.3 cm. Hweve, beynd 7.3 cm, the tempeatue quicly deceases t -5 due t heat tansfe thugh the diffeent insulatin mateials in the bx (Figue 3). In the beginning stage up t 0.35 h, thee ae n bvius tempeatue changes with change in the psitin f bth n-tetadecane and wate. Hweve, in the case f n-tetadecane, the inside tempeatue measued belw 7.3 cm gadually deceases fm 7 t.84 until 78 h, while the side tempeatue measued f distances geate than 7.3 cm stats t quicly decease up t -5 until 8.7 h, as can be bseved fm Figue 4(a). his esult indicates that the bx can be an apppiate insulatin candidate duing the cling pcess f pacaging and shipping f vaccines. hese esults ae in gd ageement with -histy data in Figue 1. In the case f wate, bth the inside and side tempeatues in the bx als decease in a patten simila t that exhibited by n-tetadecane. Hweve, the inside tempeatue quicly eaches 1 even at 8.7 h. his esult indicates that the cling ate inside is cnsideably faste up t 8.7 h, unlie in the case f n-tetadecane (Figue 4(b)). Fm Figue 4(b), we als nte that thee is n maed diffeence in the inside tempeatue f psitins f < 5 cm duing the cling pcess fm 1.5 t 4.09 h. his is because f the heat tansfe esistance due t the phase change f wate. his esult indicates that wate cannt be a ppe insulatin mateial duing the cling pcess in pacaging and shipping f vaccines as pe WHO guidelines. In de t futhe investigate the tempeatue change with espect t time, we pltted the tempeatue histy calculated at thee epesentative psitins f 0.15, 6.754, and 30.8 cm, which cespnd t the inside, PM, and side psitins, espectively. he simulated data ae pesented in Figue 5. Fm Figue 5(a), we bseve that the tempeatue gadually deceases fm 7 t.85 at the psitin f 0.15 cm. It taes 80 h f the tempeatue t each.85 stating fm 7, and thee is a damatic dp dwn t -5 afte 80 h. his esult is in gd ageement with the tempeatue change with espect t psitin in Figue 4(a). Futheme, the cling ate at the psitin f cm is slightly faste than that at the psitin f 0.15 cm, while the cling ate at the psitin f cm is slwe than that at the psitin f 30.8 cm. his phenmenn can be explained by tw facts. he fist ne is the diffeence in the distance fm the heat sin. Indeed, the psitins f 0.15, 6.754, and 30.8 cm ae assigned t the inside fam, PM, and side fam, espectively. A shte distance f measuement indicates a cespndingly lnge distance fm the extenal heat sin. he secnd fact is the diffeence in mateials, which esults in diffeent them-physical ppeties. F example, fm Figue 5(a), we bseve that the

6 50 Van-Dung Da ㆍ I-Kyu Jin ㆍ H Hu ㆍ H-Su hi tempeatue cnditins f 43 [1]. In de t investigate the change in inside tempeatue with espect t time duing the heating pcess, the initial cnditins wee set as fllws: 7 and mb.48 and mf 5.64 whee the initial inside and side tempeatues wee 7 and 43, espectively. he phase change ccus fm.48 t 5.64 f n-tetadecane and fm - 0. t 0. f wate. We nte that the slid tempeatue f n-tetadecane is assumed t be 1, while the ice tempeatue is assumed t be -1. he simulatin esults ae shwn in Figues 6 and 7. Figue 6 shws the tempeatue change with espect t the psitins in Figue 5. empeatue change with espect t time (inne cntaine: psitin, cm) f (a) n-tetadecane and (b) wate. Nte that ( ) 0.15 cm, (Ο) cm, and (Δ) 30.8 cm. tempeatue at the psitin f 30.8 cm, which cespnds t the side fam, damatically educes t ze within ab 10 h, while the tempeatue at the psitin f cm emains at aund 1 until 80 h. hese esults indicate that the elease f latent heat due t phase change f n-tetadecane effectively aids in esisting heat lss t the side. Meve, the esults als indicate that the heat tansfe esistance f fam is nt sufficient f maintaining a cnstant inside tempeatue f lng peids f time. Unlie the case f n-tetadecane, in the case f wate (Figue 5(b)), the tempeatues calculated at all thee psitins quicly dp dwn t nealy 0 within ab 10 h, and the inside tempeatue emains at aund 0 until 45 h. 3.. Heating pcess It is nwn that the highest tempeatue inside f the insulated pacage shuld be less than 30 f 48 h unde side Figue 6. empeatue change with espect t vaius psitins inside the bx: (a) n-tetadecane (lines fm bttm t tp at diffeent times: 0.35, 1.39, 3.13, 5.56, 8.70, 1.5, 17.04,.6, 8.17, 34.79, 4.09, 50.09, 58.79, 68.18, 78.7, 89.05, , 11.71, 15.58, , , , , 184.0, 00.37, h) and (b) wate (lines fm bttm t tp at diffeent times: 0.35, 1.39, 3.13, 5.56, 8.70, 1.5, 17.04,.6, 8.17, 34.79, 4.09, h).

7 mpaisn between Wate and N-etadecane as Insulatin Mateials f Vaccine Shipping 51 afte h, thus indicating that n-tetadecane is an apppiate insulatin candidate duing the heating pcess f the pacaging and shipping f vaccines. Figue 6(a) clealy eveals that the n-tetadecane lcated at the psitin f 6 cm acts as an excellent themal esistance, unlie the case f wate (Figue 6(b)). On the the hand, in the case f wate, the tempeatue eaches 30 afte nly 1.5 h. his esult indicates that wate is nt a suitable insulatin candidate duing the heating pcess as a PM in the pacaging and shipping f vaccines. futhe claify the le f the PM duing heating pcess, we simulated the tempeatue histy f the system at thee diffeent psitins f 0.15, 6.75, and 30.3 cm. he simulated data ae pesented in Figue 7. Fm Figue 7(a), we bseve that the tempeatue histy at the psitin f 0.15 cm is stable aund 6 until 0 h. Subsequently, it gadually inceases t 30 until a simulatin time f 50 h. Figue 7(a) als eveals that the time f maintaining cnstant tempeatue is shtened with incease in the psitin fm 6.75 t 30.3 cm while the heating ate inceases. he diffeence in heat esistance due t the diffeence in mateials can be used t explain this phenmenn, as mentined peviusly. he tempeatue histy f wate shws a tend simila t that f n-tetadecane, as can be bseved fm Figue 7(b). Hweve, the lngest time inteval equied f eaching 30 is nly ab 1 h. his inteval is shte than that f n-tetadecane and the WHO index. hus, wate is nt a suitable candidate duing the heating pcess as a PM in the pacaging and shipping f vaccines. 4. Discussin It is well nwn that the heat tansfe ate f n-tetadecane is less than that f wate. Futheme, the themal diffusivity,, can be calculated by using the fllwing expessin: Figue 7. empeatue change with espect t time (inne cntaine: psitin, cm) f (a) n-tetadecane and (b) wate. Nte that ( ) 0.15 cm, (Ο) 6.75 cm, and (Δ) 30.3 cm. the bx calculated at vaius times duing the heating pcess. Each time inteval cespnds t a diffeent tempeatue pfile. Fm Figue 6, we bseve that the heating pfile is quite diffeent fm the cling pfile (Figue 4) f bth n-tetadecane and wate. Futhe, we bseve that the tempeatue pfile fm 0 t 0.5 cm is almst cnstant, paticulaly f the case f n-tetadecane, because the pacaging aea is filled with inet ai, which has a lw themal diffusivity. Hweve, the tempeatue significantly changes with espect t psitins in the ange fm 0.5 t 34.7 cm. Fm Figue 6(a), we bseve that the tempeatue f n-tetadecane gadually inceases fm.84 t ~ 30 / (15) whee dentes the themal cnductivity, the density, and the specific heat capacity. We bseve that the themal diffusivity values (calculated fm data in able 1) in bth the slid and liquid phases f n-tetadecane wee less than thse f wate. In the slid phase, the themal diffusivity f n-tetadecane was m s -1, while this value f wate was m s -1. In the liquid phase, the themal diffusivities f n-tetadecane and wate wee m s -1 and m s -1, espectively. A high value f themal diffusivity indicates a high themal cnductivity lw themal heat capacity,. A lw themal cnductivity in tun indicates a lw heat tansfe ate thugh mateials. A high heat capacity indicates a lage amunt f heat absbed. hus, the ate f heat tansfe in the case f wate was highe than that f n-tetadecane, as can be bseved fm Figues 5 and 7. his intepetatin is in gd ageement with u simulatin esults. 5. nclusins In this study, we successfully accmplished the mdeling and simulatin f heat tansfe in a cntaine used f the pacaging

8 5 Van-Dung Da ㆍ I-Kyu Jin ㆍ H Hu ㆍ H-Su hi and shipping f vaccines, with n-tetadecane being utilized as a PM. hugh applying a simple ne-dimensinal mdel, which is a spheical mdel with a adius equivalent t the ectangula gemety f the cntaine, we develped a basic algithm f simulating cmplex heat tansfe pcess thugh multi-slabs cmbined with diffeent mateials including PM. he simulatin esults shwed that n-tetadecane, having a lw themal diffusivity and a ppe phase tansitin tempeatue, can be suitably used f pacaging and shipping f vaccines duing bth the heating and cling pcesses. he simulatin using the algithm develped can be a apid and ecnmic tl f sceening apppiate PMs used as insulatin mateials with lw themal diffusivity and suitable phase tansitin tempeatue in lgistics applicatins. Acnwledgments his eseach was suppted by the NU Reseach Pgam thugh the hungnam Natinal Univesity f Kea ( ). Refeences 1. n the Intenatinal Pacaging and Shipping f Vaccines, WHO/IVB/05.3. (005).. Shama, S. D., and Sagaa, K., Latent Heat Stage Mateials and Systems: A Review, Int. J. Geen Ene.,, 1-56 (005). 3. an, J., and Gupta, R. S., A Methd f Slving Mving Bunday Pblems in Heat Flw using ubic Splines Plynmials, IMA J. Appl. Math., 10, (197). 4. Gupta, R. S., Mving Gid Methd with Inteplatins, mp. Meth. Appl. Mech. Engg., 4, (1973). 5. Patana, S. V., Numeical Heat ansfe and Fluid Flw, Flw, McGaw-Hill, New Y (1980). 6. Gupta, R. S., and Kuma, D., A Mdified Vaiable ime Step Methd f One-Dimensinal Stefan Pblem, mp. Meth. Appl. Mech. Engg., 3, 101 (1980). 7. an, J., Hw t Deal with Mving Bundaies in hemal Pblems, In: Lewis, R. W., Mgan, K., Edits. Numeical Methds in Heat tansfe, Jhn Wiley & Sns, New Y (1981). 8. Pham, Q., A Fast Uncnditinally Stable Finite-Diffeence Scheme f Heat nductin with Phase hange, Int. J. Heat. Mass. ansfe., 8, 079 (1985). 9. ace, K. H., Discetizatin f the Explicit Enthalpy Methd f Plana Phase hange, Int. J. Num. Methds Eng., 1, 543 (1985). 10. Piie, D., On Numeical Methds used in Mathematical Mdeling f Phase hange in Liquid Metals, J. Heat ansfe., 110, 56 (1988). 11. Ozisi, N. M., Finite Diffeence Methds in Heat ansfe, R Pess, Flida (1994). 1. Keta, P. S., Numeical hemal Analysis, New Y: ASME (1999). 13. Saya, S., Heat ansfe Duing Melting and Slidificatin in Hetegeneus Mateials, Ph.D. hesis, Viginia Plytechnic Institute and State Univesity, Viginia (000). 14. Da, V. D., hi, H. S., Lee, S.., and Bae, Y. S., Mdeling and Simulatin f Heat ansfe Inside the Pacaging Bx f Vaccine Shipping, Kean hem. Eng. Res., 46, 604 (008). 15. Hng, H., Pa,. H., hi, J. H., and Pec, J. H., Impvement f the -histy Methd t Measue Heat f Fusin f Phase hange Mateials, Int. J. Ai-nditining Refig. 11, 3 (003). 16. Zhang, Y., Qian, J., and hen, F., Pepaatin f Bidegadable Phase-hange Refigeant Used in Insulating Pacing, Appl. Mech. Mate., 00, 437 (01). 17. Vagafti, N. B., Handb f Physical Ppeties f Liquids and Gas-Pue Substances and Mixtues, Mva (197).