Applied Energy 94 (2012) 295–302

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Applied Energy

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Combined heat transfer in multi-layered radiation shields for vacuum insulationpanels: Theoretical/numerical analyses and experiment

Jongmin Kim, Choonghyo Jang, Tae-Ho Song ⇑School of Mechanical, Aerospace and Systems Engineering, Korea Advanced Institute of Science and Technology, Guseong-dong 373-1, Yuseong-gu, Daejeon, Republic of Korea

a r t i c l e i n f o

Article history:Received 29 November 2011Received in revised form 30 January 2012Accepted 30 January 2012Available online 23 February 2012

Keywords:Multi-layered radiation shieldDepthwise conductionVacuum insulation panelVacuum guarded hot plate

0306-2619/$ - see front matter � 2012 Elsevier Ltd. Adoi:10.1016/j.apenergy.2012.01.072

⇑ Corresponding author. Tel.: +82 42 350 3032; faxE-mail address: thsong@kaist.ac.kr (T.-H. Song).

a b s t r a c t

Radiation and conduction heat transfer in stacked radiation shields to be used in the VIP (vacuum insula-tion panel) is investigated. Test radiation shields are multi-layered films of 32 nm Al, 12 lm PET and 32 nmAl thicknesses, folded with regular span and stacked in staggered manner. Radius of curvature of the foldedparts is measured by a three-dimensional scanner and the contact radius is calculated using Hertz contacttheory. Depthwise conduction around the contact spot and two-dimensional radial conduction models areadopted for the theoretical and the numerical analyses, together with measured surface emissivity. Mea-surement of the effective thermal conductivity of radiation shields is conducted using a vacuum guardedhot plate apparatus. Measurements show very low values between 0.3 and 1.0 mW/m K. Theoretical andnumerical results agree with measurements with maximum relative error of 29.1% and 18.3%, respectively.A simplified conduction model is also proposed and shown to be very useful for practical applications. Wefind that the stacked radiation shields have very high insulation performance, the numerical model is fairlyreliable and finally, conduction is negligibly small compared with radiation for this shield.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Buildings are the biggest contributor to energy consumption, asthey account for up to 45% of total energy consumption worldwide[1]. For this reason, various technologies such as heat pumps, heatrecovery ventilation begin to be applied to save building energyconsumption [2]. However, thermal insulation is a key factor to in-crease energy efficiency of buildings because space heating andcooling of buildings take a major portion of total energy consump-tion [3] due to poor thermal insulation of building fabric. Usingconventional insulators for high level of thermal insulation re-quires very large volume of insulation materials. For example, toreduce U-value of buildings to around 0.1 W/m K [4], 30–40 cm-thick conventional insulators are needed. It is hardly practicalnot only for new buildings but also for renovation of existing ones.Accordingly, super insulation materials which have much lowerthermal conductivity than the conventional insulators are needed.A vacuum insulation panel (VIP) generally has 5–10 times higherthermal resistance than the conventional insulators [5] thanks toevacuated inner space like the Dewar flask. A VIP is composed ofan envelope and a core. The envelope covers the core to maintainvacuum, the core is placed inside of the envelope and stands theexternal atmospheric pressure [6]. Often a gas absorbent isinstalled to absorb the residual gas in the VIP.

ll rights reserved.

: +82 42 350 3210.

Heat transfer in the VIP is often dominated by solid conductionthrough the core. The core is generally made of bulk materials likepowder and foam, however, artificial structures such as pillar maybe more functional. Kwon et al. [7] theoretically investigate solidconduction of various kinds of the core materials such as powder,foam, fiber and artificial staggered beam structure. Gaseous con-duction by residual gas is another heat transfer mode of the VIP.Usually gaseous conduction is negligible in the early stage of theVIP when the inner pressure is at a high vacuum level. However,aging usually makes the gaseous conduction a dominant heattransfer mode. The rarefied gas model [8] is generally applied toestimate the gaseous conduction when the mean free path of gasis still larger than the pore size of core material. Since the envelopeof the VIP consists of metallic and polymer films, conductionthrough the envelope is considerable [9] and can be reduced byembedded in expanded polystyrene foam [10]. Such edge effectis entirely related with the envelope, not the core, therefore it isnot treated in this paper. The last heat transfer mode is radiation.If an interstitial medium with large optical thickness is used asthe core to suppress the radiative transfer, radiation heat transferthrough the core material can be expressed by the diffusionapproximation [11]. On the other hand when artificial core struc-ture such as staggered beam or pillar is used as the core, large por-tions of hot and cold surfaces are directly facing each other. Tosuppress radiation, radiation shields with highly reflecting surfacesmay be employed like in cryogenic tanks of spacecrafts. Fig. 1 isshowing the concept of this VIP. Note that the pillars are needed

Nomenclature

A areaE Young’s modulus of elasticity (N/m2)F exerting force on a contact spot (N)H height of a specimen (m)k thermal conductivity (W/m K)k⁄ equivalent thermal conductivity (W/m K)L half span of folded radiation shieldP pressure (Pa)R thermal resistance (K/W)r radiusri inner radiusro outer radiusq heat transfer rate (W)T temperaturet thickness

Greek symbolsd mean distance between radiation shields (mm)e emissivity

/ pore size (m)m Poisson’s ratior Stefan–Boltzmann constant

SubscriptsAl aluminumc contactcomb combinedcond conductivecurv curvatureDC depthwise conductioneff effectiveg gaseousm meanpet PETrad radiativeRC radial conductiontot total

Fig. 1. Concept of the VIP with radiation shields.

296 J. Kim et al. / Applied Energy 94 (2012) 295–302

to withstand the atmospheric pressure. Reduction of radiation isgenerally proportional to the number of radiation shields. How-ever, increasing radiation shields naturally increases contacts be-tween them. It can seriously increase the solid conductionthrough the shields. Jang et al. [12] theoretically study the com-bined heat transfer of conduction and radiation in single-layeredradiation shields. They have tested several different solutions forthe effective thermal conductivity using depthwise conduction,contact resistance and two-dimensional radial conduction models.From the experiments using stainless steel 304 plates, they con-clude that the depthwise conduction is the most suitable conduc-tion model for stacked radiation shields. In reality, however,single-layered radiation shields such as aluminum foils are notwidely used due to the high conduction. Instead, multi-layeredshields using layers of polymer and aluminum coating arefrequently used.

The objective of this study is to find the effective thermal con-ductivity of aforementioned multi-layered radiation shield. Wefirstly apply theoretical solutions of Jang et al. to the multi-layeredshield. Numerical analysis is then applied to calculate the solidconductivity with depthwise and two-dimensional conductionmodels. Results of theoretical and numerical analyses are verifiedby experiment. The practical insulation performance is also exam-ined together with the validity of the analysis tools.

Fig. 2. Stacked radiation shields (2L: span, d: mean distance between shields).

2. Theoretical and numerical analysis

2.1. Multi-layered radiation shields

The test radiation shield has a triple-layer structure of 32 nmAl-coating/12 lm polyethylene terephthalate (PET)/32 nm Al-coat-ing. When the thickness of a layer is very thin like in the Al-coating,

the thermal conductivity is different from that of bulk material be-cause of the grain boundary and surface effects [13]. Accordingly,in-plane directional thermal conductivity of Al-layer is adoptedas 99.8 W/m K from the literature [14]. To avoid the randomnessof contact spot locations between two neighboring shields, theyare folded at a regular span 2L and stacked in an alternating-direc-tion staggered manner (Fig. 2). This configuration maximizes theconduction resistances through the shield. The maximum half spanis 20 mm because the shield cannot stand its self-weight beyondthis limit. Also, possible minimum half span folded by hand is5 mm. For this reason, 20 mm and 5 mm are selected as the halfspan L. Gap size d can be adjusted by number of shields insertedin the support structure. For example, d is 1 mm when 10 shieldsare inserted in the support structure of 10 mm height.

The contact between the shields is nearly pointwise with con-tact radius rc. The radiation shield is not transparent and rc is smallso that rc cannot be measured directly. Instead, Hertz contact the-ory can be applied to calculate it assuming that folded region has aconstant radius of curvature rcurv. This curvature can be measuredusing a 3-dimensional scanner (ATOS� from GOM mbH). Averagercurv is measured to be 337 lm for L = 20 mm, and 476 lm forL = 5 mm. Standard deviation is 95.6 lm for L = 20 mm, and86 lm for L = 5 mm. With this rcurv, rc is calculated from the Hertzcontact theory [15] as

rc ¼3F rcurvð1� m2

AlÞ2EAl

� �1=3

; ð1Þ

where mAl and EAl are Poisson’s ratio (0.36) and Young’s modulus ofaluminum (68 GPa), respectively, and F is the external force exerted

J. Kim et al. / Applied Energy 94 (2012) 295–302 297

on a contact spot. Let us assume that the shield is placed horizon-tally and the force is uniformly distributed to each spot by theweight of the shield. Then F can be calculated from the shield mass(1.92 � 10�2 kg/m2), span and number of shields N. As an example,when N = 7, rc is 1.85 lm for L = 20 mm, and 0.82 lm for L = 5 mm.

2.2. Theoretical analysis

When temperature difference is imposed across the stackedshields, conduction heat transfer occurs through the contact spotsand radiation heat transfer occurs between the facing surfaces.Heat transfer due to gas is temporarily ignored assuming high levelof vacuum. The stacked shields has a repeated geometry thus it canbe idealized as a unit cell of planes (Fig. 3). Planes in the unit cellhave size of 2L � 2L. Contacts between shields have uniformtemperature.

In a plane, conduction occurs from a contact spot of dimension-less temperature T = 0 to the surrounding four spots of T = 1 in atwo-dimensional manner (Fig. 4). The isothermal line of T = 1/2can be re-modeled as a circle with equivalent radius r0 which isequal to

ffiffiffiffiffiffiffiffiffi2=p

p� L. When rc is smaller than the total thickness ttot

(as is often the case), there will be a vertical temperature gradientand thus depthwise conduction occurs near the contact spot. Tem-perature variation in depthwise direction is occasionally largearound the contact spot but it is small away from the contact spotand finally becomes uniform over the depth. It means that conduc-tion often occurs in two-dimensional manner in the vicinity of thecontact spot. When temperature becomes nearly uniform acrossthe thickness within 10�5 variation at r = ri (>rc), conduction occursnearly radially. Consequently, the whole region can be conceptuallydivided into the depthwise conduction (DC) region (r < ri) and theradial conduction (RC) region (ri 6 r 6 ro) (Fig. 5), though the quan-titative border is not presented in this study. For theoretical analy-sis, we adopt solutions of Jang et al. [12] which are derived forsingle-layered radiation shield. However, since triple-layeredshield is treated in this study, the equivalent in-plane thermalconductivity k⁄ is used instead of k as

k� ¼ 2ðkAl � tAlÞ þ ðkPET � tPETÞttot

; ð2Þ

where kAl and kPET are the thermal conductivities of aluminum layerand PET layer, and tAl and tPET are thicknesses of aluminum layer andPET layer, respectively. Using exact solutions of Jang et al. combinedand separate analyses are compared (Table 1) and they show onlymarginal difference (below 1%). Since the separate analysis issimpler than combined analysis, it is reasonable to use the separateanalysis for the multi-layered radiation shield at hand. It still leavesa question regarding the properness of employing k⁄ for the multi-layer. It will be treated later in Section 4.1.

2.3. Numerical analysis

Here, numerical analysis is conducted using a commercial code,Fluent� to calculate the solid conductivity. Radiation is neglected

Fig. 3. Idealized conduction heat transfer of stacked radiation shield; perspective v

here; it will be handled separately later. Fig. 5b shows boundarycondition for the numerical analysis. PET layer is placed at the cen-ter, upper and bottom surfaces make contact with aluminum lay-ers. Temperature of contact area is set as arbitrary temperatureT0 and right wall is set as 0.5T0. Upper and bottom surfaces areinsulated and the left boundary is the symmetric axis. The resultshows large temperature difference in depthwise direction aroundthe contact spot (that is, the DC region) and uniform temperaturedistribution in the RC region (Fig. 6). The radius ri is set in the sameway as before (10�5 temperature variation in depthwise direction).It is usually smaller than 0.02L, which shows that the DC region isvery limited near the contact spot. Since radiation heat transfer isroughly proportional to the surface area, it may be safely neglectedin the small DC region, leaving the DC region conduction dominant.Thermal resistance of DC region RDC is then calculated as

RDC ¼T0 � Ti

q; ð3Þ

where Ti is temperature at r = ri and q is heat transfer rate. Thermalresistance of RC region RRC is expressed as

RRC ¼lnðro=riÞ2pk�ttot

; ð4Þ

In Eqs. (3) and (4), Ti, q and ri can be found from the numerical re-sult. Since RDC and RRC are serially connected, total conduction resis-tance of the shield Rcond over the 2L by 2L area is calculated as

Rcond ¼ 2 � ðRDC þ RRCÞ; ð5Þ

and the effective solid conductivity kcond over the gap d is expressedfrom

q ¼ kcond � ð2LÞ2 DTd

¼ DTRcond

ð6Þ

so that

kcond ¼d

Rcondð2LÞ2: ð7Þ

Radiative conductivity can be calculated using surface radiationtheory [11]. Actually, the surface of the upper shield is facing itselfpartly as well as the surface of the lower shield. Considering everyradiative heat exchanges could make the problem very compli-cated. Since the configuration factor between surfaces of upperand lower shields is dominant (around 0.9), it is assumed to beunity for simplicity and radiative conductivity krad can be esti-mated as

krad ¼4rT3

m2e � 1

d; ð8Þ

where r is Stefan–Boltzmann constant, Tm is mean temperature ofthe shields. Mean distance d is the total height divided by numberof shields. Surface emissivity of the radiation shield is measured

iew (a) and side view (b) (vertical dotted lines are contacts between shields).

Fig. 4. Two-dimensional lateral conduction modeling the radiation shield (a) and approximated boundary isothermal line (b) (dotted lines are isotherms).

Fig. 5. Depthwise and radial conduction in the radiation shield (a) and boundary condition of the numerical analysis (b).

Table 1Comparison of combined and separate theoretical analyses.

Case 1 Case 2

L 20 mm 5 mmrc 1.85 lm 0.82 lmk⁄ 0.788 W/m Kqcomb 0.4129 mW 0.0268 mWqsepa 0.4122 mW 0.0266 mW

298 J. Kim et al. / Applied Energy 94 (2012) 295–302

to be 0.088 using the measurement method of Kim et al. [16]. Addi-tion of Eqs. (7) and (8) to obtain the total effective conductivity keff

may be justified if RDC� RRC. When this is the case, the conductionprevails intensively around the small contact area and the radiationdoes away from the contacts. This reasoning gives us the justifica-tion in part, and further justifications will be provided later inSection 4.2.

3. Experiments

3.1. Measurement apparatus

The effective thermal conductivity keff of stacked radiationshields is measured to verify the theoretical and the numericalanalyses. Among various measurement methods, the GHP (guarded

hot plate) method is known to be most accurate when measuringvery low thermal conductivity [17]. Measurement has to be con-ducted in vacuum to eliminate the residual gas conduction. For thispurpose a VGHP (vacuum GHP) is manufactured following ASTMstandard [18] as shown in Fig. 7.

The heater block is made of pure copper and equipped with anelectric heater. The guard is also made of pure copper and sur-rounds the heater block across a narrow gap. Bottom of the heaterblock and the guard is insulated following the ASTM standard. Thehot plate and the guard are connected to a bath-circulator to main-tain their temperatures to be the same as the heater block. Five-pairs of T-type thermopiles are attached to control temperatures.The cold plate is also connected to a bath-circulator to maintainit colder than the heater block. Specimen is placed between theheater block and the cold plate. The effective thermal conductivityof the specimen keff can be measured as

keff ¼qheater � HAeff � DT

; ð9Þ

where qheater is the electrically generated heat from the heater block,H is height of the specimen, Aeff is effective area of the specimen andDT is temperature difference between the heater block and the coldplate. A vacuum chamber and other vacuum components can main-tain a vacuum level below 10�4 Pa during the measurement. A pres-sure pad exerts external force on the specimen when needed.

Fig. 8. Stacked radiation shields (dotted lines) and support structure (solid lines).

Table 2Effective thermal conductivity from theoretical/numerical analyses and experiment.

L (mm) d (mm) keff (mW/m K)Theoretical analysis Numerical analysis Experiment

20 1 0.30 0.33 0.341.17 0.36 0.39 0.421.4 0.48 0.49 0.562 0.65 0.70 0.772.5 0.87 0.95 0.99

5 1 0.32 0.36 0.361.17 0.37 0.44 0.491.4 0.48 0.55 0.672 0.68 0.79 0.772.33 0.93 1.10 0.93

Fig. 6. Temperature of layers 1 and 2 from the numerical analysis of Fig. 5.L = 20 mm (a), L = 5 mm (b).

J. Kim et al. / Applied Energy 94 (2012) 295–302 299

3.2. Specimen and measurement condition

The radiation shield is so flexible that it cannot maintain itsshape against the weight of the cold plate (13 kg) in the VGHP.Thus a support structure made of polycarbonate is installed sur-rounding the shields as shown in Fig. 8. According to Eqs. (7) and(8), conduction and radiation are highly affected by the half spanL and gap size d, respectively.

Fig. 7. Schematic feature of the VGHP.

Mean temperature of the specimen is maintained at 298 K with308 K for the heater block and 288 K for the cold plate.

4. Results and discussions

4.1. Results and uncertainty analysis

There are ten cases as mentioned earlier; 20 mm and 5 mm of Land five different d’s. Results of theoretical, numerical analyses andexperiments are tabulated in Table 2 and illustrated in Fig. 9. It isimpressive that keff lies between 0.3 and 1.0 mW/m K, which is sig-nificantly smaller than keff of most VIPs (note, however, that lateron, conduction through the pillar of Fig. 1 should be also addedin the real VIP, which is expected to occupy a significant portionin the total keff).

When comparing with the experimental result, the theoreticaland numerical analyses show maximum relative error of 29.1%,18.3%, respectively. Relative error between results of theoreticaland numerical analyses is 7.3% at most.

Uncertainty of measurement can be quantitatively estimatedusing Eq. (9) and following equation [19].

dkeff

keff¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi@keff

@Aeff

dAeff

keff

� �2

þ @keff

@ðDTÞdðDTÞ

keff

� �2

þ @keff

@HdHkeff

� �2

þ @keff

@qheater

dqheater

keff

� �2s

:

ð10Þ

Uncertainties from Aeff, DT and H are 0.03%, 0.4% and 0.2%, respec-tively. Uncertainty from qheater is 11%, which is the dominant one.It comes from the electric power of the power supply; it is main-tained at a very low level (20–30 mW) and it brings relatively largeuncertainty. When summarizing up the whole terms, measure-ments have approximately 11% of uncertainties.

Meanwhile, theoretical and numerical analyses are based on rc

and it is calculated using rcurv of the shield. Measured rcurv has28% of deviation and it brings approximately 3% of uncertainty torc. This gives uncertainty of 3.8% to the kcond, 0.33% to the keff whenL = 20 mm. When L = 5 mm, it brings 0.51% of uncertainty to kcond,however, keff is hardly affected. Thus, we can say that the uncer-tainty from rc is not significant. Rather than rc, surface emissivityof the shield can affect to the results. Measured surface emissivityof the shield has 8% of uncertainty [16] and it gives maximum 7% ofuncertainty to keff. Furthermore, aluminum layer of the shield ispossibly damaged when the shield is folded because its thicknessis very thin. If it is so, the surface emissivity could have been

Fig. 9. Result of analyses and measurement. L = 20 (a), L = 5 mm (b).

300 J. Kim et al. / Applied Energy 94 (2012) 295–302

underestimated and accordingly, keff from theoretical/numericalanalyses can be smaller than reality. The fact that most of experi-mental results are higher than theoretical/numerical results sup-ports this reasoning.

Relatively large error of theoretical results may indicate theinappropriateness of using the theoretical analysis for multi-layeredradiation shields. As stated previously, the theoretical analysismethod is for single-layered shields. Thus applying the method totriple-layered shields, the shields are assumed to be single-layeredand its thermal conductivity is estimated to be k⁄ as defined in Eq.(2). It might be proper in the RC region because conduction occursradially there, but not in the DC region. Due to the ambiguity ofthe thermal conductivity, the theoretical analysis has suspiciousvalidity in this case. Therefore it is recommended to use the numer-ical analysis for multi-layered radiation shields.

4.2. Comparison of conduction and radiation

Effective thermal conductivity is nearly proportional to d inboth L = 20 mm and 5 mm (Fig. 9). It implies that the radiation isthe dominant heat transfer mode. From the numerical analysis,the portion of conduction and radiation can be found quantita-tively. For L = 20 mm, conduction across the shield takes less than1% of total heat transfer for all d’s and for L = 5 mm, it takes around10% but still much smaller than the radiation. It means that con-duction resistance across the major shield area is much larger than

radiation resistance Rrad. As shown in Eq. (5), conduction resistanceRcond is twice the sum of RRC and RDC. Due to small contact radius rc,depthwise conduction arises in much smaller area than radial con-duction (ri/ro � 0.6–2%), and RDC is much larger than RRC, that is,RDC > RRC > Rrad. Fig. 10 illustrates the heat transfer process of theradiation shields. The total thermal resistance between A and Bin Fig. 10 is ðR�1

rad þ R�1condÞ

�1 so that effective thermal conductivitykeff is krad + kcond.

4.3. Approximation of the conduction resistance

The conduction resistance has been derived using numericalanalysis. A commercial code is used which takes quite a long timefor convergence and needs further processes to find Ti, and ri in Eqs.(3) and (4). For this reason, we seek an approximation of the con-duction resistance without using a numerical code.

In the numerical analysis, ri is chosen (later found to be about100rc) when the temperature difference in depthwise direction isbelow 10�5. However, sum of RDC and RRC is rarely changed within1% even if the DT criterion in depthwise direction is increased to10�1 (then ri � 10rc) because RDC is increased while RRC is decreased(Table 3). For this mutually compensating effect, RDC + RRC is notvery dependent on the choice of depthwise temperature unifor-mity requirement, and thus, also on the choice of ri.

To model the conduction phenomena, let us assume that con-duction resistance is comprised of horizontal radial resistancesR1, R2 and Rm and vertical resistances RD1 and RD2 (Fig. 11). Here,RD1 and RD2 are resistances of two cones in series, middle radiusrm1 (arbitrarily given) and bottom radius rm2 being equalto 2rm1–rc. Each resistance can be expressed as

R1 ¼2pkAltAl

lnðro=rcÞ

� ��1

; ð11Þ

Rm ¼2pkPET tPET

lnðro=rm1

� ��1

; ð12Þ

R2 ¼2pkAltAl

ro=rm2

� ��1

; ð13Þ

RD1 ¼tPET=2

kPETprcrm1; ð14Þ

and

RD2 ¼tPET=2

kPETprm1rm2: ð15Þ

The composition of resistances can be simplified as Fig. 11b and thetotal conduction resistance Rmodel is derived as

Rmodel ¼ 2 � R�11 þ fRD1 þ ½R�1

m þ ðRD2 þ R2Þ�1�g�1D E�1

: ð16Þ

From Eqs. (11)–(16), Rmodel is a function of rm1, which is an optimi-zation parameter to determine. When rm1 ¼ 20:78 1000�tPET

L

� �1:21rc ,

Rmodel is best-fitted to Rcond of the numerical analysis within 9% ofrelative error. Note that, however, it is uncertain whether this rm1

can be universally applied. Using Rmodel, the solid conductivity canbe found as

kmodel ¼d

Rmodelð2LÞ2; ð17Þ

and the effective thermal conductivity keff, model can be derived bysumming kmodel and krad from Eq. (8). The resulting solid conductiv-ities and effective thermal conductivities from numerical analysesand approximations are tabulated in Table 4. Solid conductivitiesand effective thermal conductivities show 8.8% and 0.6% of average

Fig. 10. Equivalent circuit of heat transfer between shields (a) and between A and B (b).

Table 3Conduction resistance according temperature difference in depthwise direction.

L DT criterion in depthwise direction ri/rc Ti/T0 RDC (K/W) RRC (K/W) RDC + RRC (K/W)

20 mm 10�1 11 0.773 90,992 111,327 202,31910�3 32 0.734 106,626 93,840 200,46610�5 53 0.712 115,300 85,166 200,466

5 mm 10�1 24 0.773 122,650 88,853 211,50310�3 70 0.734 142,521 71,026 213,54710�5 121 0.712 151,615 61,947 213,562

Fig. 11. Approximation of total resistance (a) and its electric analogy (b).

J. Kim et al. / Applied Energy 94 (2012) 295–302 301

relative errors, respectively. Such small relative error in the effec-tive thermal conductivity is due to the dominance of krad; in otherwords, relative error in the solid conductivity is moderated by thekrad because it is much larger than kcond and kmodel.

4.4. Stacked radiation shield as the core of VIP

Widely used core materials such as PU foam or glass wool haveeffective thermal conductivity of 3–8 mW/m K at high vacuum[20]. On the contrary, stacked radiation shields have approximately1/10 of effective thermal conductivity. Therefore, if stacked radia-tion shields are applied as a core of the VIP, insulation performanceof the VIP would be greatly improved. Two technical barriers, how-ever, are still ahead.

The first is the thermal resistance of the support structure. Asshown in Fig. 1, stacked radiation shields need support structuresuch as pillars to maintain its shape against the external atmo-spheric pressure. The support structure brings additional heattransfer through it. Hence new support structure, especially pillarwith large thermal resistance has to be developed prior to usingstacked radiation shields.

The second is the large pore size that is vulnerable to perfor-mance deterioration at moderate vacuum. Gaseous conductivitykg due to residual gas in the VIP is expressed as [21]

kg ¼kg0

1þ 0:032P/

ð18Þ

where kg0 is thermal conductivity of air at normal state, P is vacuumlevel in Pa and / is pore size (m) of the core. According to theEq. (18), smaller / has lower kg when P is fixed. In other words,the VIP can have high insulation performance even in low level ofvacuum if the core has small /. Therefore / is a crucial factor tothe service life of the VIP. For this reason, common core materialssuch as fumed silica and glass wool show tens of nm to severallm of / [22]. However pore size of stacked radiation shields ismuch larger than other core materials consequently, kg is seriouslyincreased when the vacuum level slightly increases. To decrease /of stacked radiation shields, filling materials with small / such asfumed silica may be added to the gap between shields or inserting

Table 4Solid conductivity and effective thermal conductivity from numerical analysis and approximation.

L (mm) d (mm) Solid conductivity (W/m K) Effective thermal conductivity (W/m K)kcond kmodel R.E (%) keff, numerical keff, model R.E (%)

20 1 2.42 � 10�6 2.70 � 10�6 11.4 3.25 � 10�4 3.25 � 10�4 0.01.17 2.88 � 10�6 3.03 � 10�6 5.1 3.91 � 10�4 3.91 � 10�4 0.01.4 3.58 � 10�6 3.48 � 10�6 2.8 4.87 � 10�4 4.87 � 10�4 0.02 5.11 � 10�6 4.97 � 10�6 2.8 6.96 � 10�4 6.95 � 10�4 0.12.5 6.73 � 10�6 6.05 � 10�6 10.0 9.46 � 10�4 9.46 � 10�4 0.0

5 1 3.96 � 10�5 4.56 � 10�5 15.3 3.62 � 10�4 3.68 � 10�4 1.61.17 4.72 � 10�5 5.16 � 10�5 9.4 4.43 � 10�4 4.48 � 10�4 1.11.4 5.88 � 10�5 5.94 � 10�5 1.1 5.52 � 10�4 5.53 � 10�4 0.22 8.39 � 10�5 8.49 � 10�5 1.2 7.89 � 10�4 7.90 � 10�4 0.22.33 1.15 � 10�4 9.71 � 10�5 15.3 1.10 � 10�3 1.08 � 10�3 1.6

302 J. Kim et al. / Applied Energy 94 (2012) 295–302

many radiation shields in the structure. These propose new techni-cal challenges. The study is under way by the authors. Indeed, a newmethod to assure high vacuum for a long time, like the doubleenveloping by Kwon et al. [23], can be the best way to solve theproblem.

One last comment regarding the stacked radiation shield is that,when kg from Eq. (18) is significantly large, its effect on keff can beeasily found by simply adding kg to krad of Eq. (8). This means thegaseous conduction is simply added to the radiation exchange be-tween the neighboring shields. The numerical analysis method isperfectly useful for this case too.

As the final remark, though stacked radiation shields are notcurrently applied as the core, but it still has a high potential withvery low effective thermal conductivity.

5. Conclusions

In this paper, conduction and radiation heat transfer in stackedradiation shields for the VIP application is investigated. The shieldshave triple-layered structure of aluminum, PET and aluminum.They are folded with regular span and stacked in a staggered man-ner. Solid and radiative conductivities are derived separately in thetheoretical and numerical analyses. Depthwise conduction andtwo-dimensional radial conduction models are applied to calculatethe solid conductivity. Radiative conductivity is estimated underthe assumption of surface radiation between two surfaces. Theo-retically and numerically calculated keff’s are compared to experi-mental result. The VGHP apparatus is used for the experimentand its uncertainty is expected to be 11%. Numerical and theoret-ical results show at maximum 18.3% and 29.1% of relative errorcompared to the experimental results. The conclusions of the re-search are as follows:

The overall keff’s of stacked radiation shields are found to be assmall as 0.3–1.0 mW/m K showing great potential as the core offuture VIP. It is recommended to use numerical separate analysis to esti-

mate keff of the multi-layered radiation shield rather than thetheoretical analysis for a single-layered shield. A simplified conduction model is also proposed and shown to be

very useful for practical applications.

Acknowledgments

This work was supported by the National Research Foundationof Korea (NRF) grant funded by the Korea government (MEST) (No.

2011-0027642) and the second stage of the Brain Korea 21 Projectin 2011.

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