The effects of PE additive on the performance of polystyrene vacuum insulation panels

The effects of PE additive on the performance of polystyrene vacuum

insulation panels

P.C. Tseng, H.S. Chu

*

Department of Mechanical Engineering, National Chiao Tung University, Hsinchu 30049, Taiwan, ROC

a r t i c l e

i n f o

Article history:

Received 21 January 2008

Received in revised form 29 January 2009 Accepted 29 January 2009

Available online 21 March 2009 Keywords:

Broken cell ratio PS foam insulation Solid volume fraction

a b s t r a c t

The effects of adding polyethylene (PE) in polystyrene (PS) foaming material on the cell structure and the heat transfer of vacuum insulation panels (VIPs) are examined in this study. Several parameters are pro-posed to describe the foam structure, namely, the broken cell ratio, the average cell size and the solid vol-ume fraction. Adding 2% PE was effective in altering the cell structure and reducing the heat transfer, while adding 5% PE did not improve the performance further. The lowest thermal conductivity found in this study is 4.4 mW m1_K1_{, which is among the best published performances of VIP.}

Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Vacuum insulation panel (VIP) features extremely low thermal conductivity and is suitable for numerous energy conservation applications, such as refrigerator insulation. It is constituted of por-ous material enclosed in evacuated non-permeable package that is normally made of metal foil envelope. Evacuating the package to a vacuum effectively eliminates the heat transfer by gas convection and conduction. Combining the vacuum with the low thermal con-ductivity of the porous material, which acts as the VIP’s structural support, can greatly reduce overall heat transfer. Commercially available VIPs have currently reached an effective thermal conduc-tivity that is two to six times lower than ordinary foam insulation. The porous cells in the materials must be largely open, that is, bro-ken and connected forming a network so that all the gases can be effectively evacuated. Further reduction in the heat transfer relies on the balance between solid conductive and radiative heat trans-fer, as we have proposed in an earlier study[1]. Nevertheless, con-trolling the material structures to obtain optimum performance VIPs is currently still a challenge.

Many previous studies have attempted to determine the heat transfer of solid conduction [2–5], gaseous conduction [5] and thermal radiation[6–18]in porous medium. Most of the studies assumed all closed-cell or all open-cell structures in their analyses. Our earlier work[1]has attempted to characterize the geometrical parameters in VIPs with cell structures in-between all closed-cell and all open-cell, which means that part of the cells are closed

and contain gases. It was found that broken cell ratio and cell size have been the deciding factors in reducing thermal transfer. The present study examines the possibility of increasing broken cell ra-tio by adding polyethylene (PE) into polystyrene in manufacturing the porous materials of VIP. Polyethylene has a higher solidifica-tion temperature and becomes hardened when the temperature is still above the melting point of polystyrene. Solidified PE parti-cles could exert shear forces on surrounding molten PS to augment the breaking of closed cells during their expansion in the foaming process. Furthermore, the possibility of modulating cell sizes through PE additives is also examined in detail. Small cell size im-plies greater solid conduction routes, while large cell size leads to enhanced radiation transport. It is believed there is an optimal cell size that can render the lowest total heat transfer[1]. Adding PE provides a possibility of modulating the cell size and reducing the total heat transfer.

A total of 42 samples with different PE contents, namely, 0 wt%, 2 wt% and 5 wt%, are fabricated in this study. Their heat transfer rates are measured and analyzed. The results will be helpful in manufacturing VIP with improved performance.

2. Experiments 2.1. Sample fabrication

The samples were prepared by the following procedure. A mix-ture of polystyrene, polyethylene, carbon black, and calcium stea-rate were put into a batch die of 400 mm diameter and subjected to a 40-ton press. After mixing with the molten mixture, foaming was performed by introducing CO2and R-134a into the die to form 0017-9310/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ijheatmasstransfer.2009.01.033

*Corresponding author. Tel.: +886 3 571 2121x55115; fax: +886 3 572 7930. E-mail address:hschu@cc.nctu.edu.tw(H.S. Chu).

Contents lists available atScienceDirect

International Journal of Heat and Mass Transfer

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j h m t

a supercritical fluid. The high pressure gas in the die was released after 6 h, forming a plain board measuring 250 mm long  250 mm wide  6–26 mm thick. After about an hour of heating, the mate-rial was enclosed by a metal foil envelope, which was sealed after the enclosed air was evacuated to 104_{torr. Experiments were} de-signed to vary the cell geometry of the samples by modulating die temperature and gas pressure. Heaters controlled the die temper-ature, and maintained a fixed temperature ranging from 398 K to 408 K with a stability of ±0.5 °C throughout the process. Fig. 1

shows the dual pressure control system that was able to separately control the pressure and the amount of CO2and R-134a. During the forming process, the gas pressure normally ranged between 2500 psi and 3300 psi. InFig. 1, the booster pressurizes mixture gas into two pressure tanks. One tank steadily supplies the super critical fluid to liquid tank by the pressure regulator, the other one is as the spare tank.Fig. 2a–c show typical SEM pictures of material samples with 0 wt%, 2 wt% and 5 wt% PE, respectively. The structure typically consists of struts, cell membranes, broken cells and unbroken cells. The average cell size of each sample was calculated by a method in accordance with ASTM standard D 3576-77, using a SEM picture of the sample. The average cell size

is 119

l

m inFig. 2a for PE0L4, 211

l

m inFig. 2b for PE2L1, and 262

l

m inFig. 2c for PE5L3.

2.2. Measurements and data reduction

The following method measured radiation’s contribution to thermal conductivity. The dimensionless optical thickness of a PS sample is evaluated by multiplying is geometrical thickness from its mean extinction coefficient[19]. For considering optically thick condition, the value has to be far greater than 1. The minimum optical thickness of all the samples in this study is 45, thereby pre-vailing an optically thick medium that can be treated as a diffusion process. The radiant transfer is simply[20],

qr¼ krrT ¼ ðð16

r

T

3

mÞ=ð3

r

eÞÞ

r

T ð1Þ

where the equivalent thermal conductivity is defined as

kr¼ ð16

r

T3mÞ=ð3

r

eÞ ð2Þ

where Tmis the arithmetic mean of the boundary temperatures. The Rosseland mean extinction coefficient (

r

e) is defined as

Foaming equipment Pressure reguator Check valve HFC (R134a) Valve Valve 2 CO Valve Valve Pressure reguator Valve

Liquid tank Valve Booster Valve Pressure guage Check valve 2nd. pressure tank 1St. pressure tank Valve Valve Safety valve

Fig. 1. The schematic process of dual pressure control system for modulating the forming pressure[1]. Nomenclature

dc cell size,

l

m

eb total emissive power of a blackbody, W m2 ekb spectral emissive power, W m2

l

m1sr1 fs solid volume fraction, Vs/Vt

fs+g volume fraction of combined solid and gas ik spectral intensity of radiant energy ikð0Þ spectral intensity of incident radiation ikðsÞ spectral radiation intensity of a path length s

ks+g the equivalent thermal conductivity of combined solid and gas

kr the thermal radiation conductivity kt the equivalent total thermal conductivity m the weight of the sample

qs+g the heat flux of combined solid and gas qr radiation heat flux

qt total heat flux

T the absolute temperature of the surface, K

Vb the broken cell volume Vs the volume of solid

Vs+g the volume of combined solid and gas in the unbroken cell

Vt the apparent volume (total volume) Vtb the volume of all the cells

Vub the volume of gas in the unbroken cell Greek symbols

q

f apparent density or foam density, kg m3

q

s the density of the solid, 991.96 kg m3

q

s+g the density of the combined solid and gas in the unbro-ken cells, kg m3

r

Stefan–Boltzmann constant, 5.67  108_{W m}2_K4

r

e Rosseland mean extinction coefficient, Eq.(3)

r

ek spectral extinction coefficient, Eq.(4)

1

r

e¼ Z 1 0 1

r

ek @ekb @eb dk ð3Þ

where ekbis the spectral emissive power, and ebis the total emissive power of a blackbody. By neglecting the emission terms and in-scat-tering terms of a cold homogeneous medium under the influence of a relatively strong but unidirectional beam of radiant energy, the radiation intensity is governed by Beer’s law,

dik=ds ¼ 

r

ekikðsÞ ð4Þ

where

r

ek¼ ð

r

akþ

r

skÞ is the spectral extinction coefficient. The transmittance is defined as

s

k¼ ikðsÞ=ikð0Þ ¼ expð

r

eksÞ ð5Þ

The local energy flux (qt) in VIPs is composed of the transfer by combined gas conduction and solid conduction (qs+g), and by radia-tion (qr),

qt¼ ðqsþgþ qrÞ ¼ ðksþgþ ð16

r

T3mÞ=ð3

r

eÞÞ

r

T ð6Þ

Then, the concept of equivalent thermal conductivity applies,

kt¼ ksþgþ kr ð7Þ

where kt is the equivalent total thermal conductivity, ks+g is the equivalent thermal conductivity of combined solid and gas, and kr is the fraction of equivalent thermal conductivity induced by ther-mal radiation. An EKO model HC-072 conductivity meter was used in this study to measure ktand keep the temperature difference on both sides of the sample at 0.1 K during the measurements. The equivalent thermal conductivities of all the samples were measured

at a hot side temperature of 30 °C and a cold side temperature of 0 °C. The equivalent thermal conductivity is calculated by

kt¼ ðE  LÞ=ðS 

D

TÞ ð8Þ

where E is the output of the heat-flow meters, L is the thickness of the sample, S is the sensitive of heat-flow meter, andDT is the tem-perature difference between the hot and the cold plate. The equiv-alent thermal conductivity uncertainty of the data of sample L3 is estimated by ðdk=ktÞ ¼ ½ðkt=qtÞ 2 dq2 tþ ðkt=SÞ 2 dS2 þ ðkt=

D

TÞ 2 d

D

T2 0:5=kt ¼ ½ð6:6=23:34Þ2ð0:02Þ2þ ð6:6=0:00646Þ2ð0:00005Þ2 þ ð6:6=22:8Þ2ð0:1Þ20:5=6:6 ¼ ð0:05896=6:6Þ ¼ 0:0089 ð9Þ

Thus, conductivity measurement uncertainty was controlled to within 0.89%, as estimated by the method of Wu et al.[12].

This study uses a Perkin-Elmer Spectrum 2000 Fourier Trans-form Infrared Spectrometer to measure the spectral transmittance of each sample. A thinly sliced foam specimen was subjected to normal incident irradiation in the wavelength range of 2.5– 25

l

m for the measurement. The moisture and volatile organic gas contents of specimens were first removed by an oven. The spectral extinction coefficient ð

r

ekÞ is calculated by Eq. (5) with the measured transmittance. By substituting

r

ekinto Eq.(3), the term

r

eis then calculated. kris subsequently obtained by Eq.(2). With the knowledge of krand kt, ks+gcan be inferred from Eq.(7). Note that krand ks+greveal the contribution by radiation and com-bined solid and gas, respectively. To further distinguish the contri-bution by solid and by gas, this study employs a broken cell Fig. 2. (a) SEM of sample PE0L4 for PS core material without PE additive[1]. (b) SEM of sample PE2L1 for PS core material with 2% PE additive. (c) SEM of sample PE5L3 for PS core material with 5% PE additive.

ratio, /, representing the ratio of broken cell volume to the total cell volume /¼Vb Vtb ¼Vt ðm=

q

sþgÞ Vt ðm=

q

sÞ ¼ðm=

q

fÞ  ðm=

q

sþgÞ ðm=

q

fÞ  ðm=

q

sÞ ¼

q

s

q

_sþg ð

q

sþg

q

fÞ ð

q

s

q

fÞ ð10Þ where Vbor the broken cell volume is the vacuum volume inside the VIP (which actually contains air in extremely low pressure), Vtbis the volume of all the cells, Vtis the apparent volume (total volume), m is the weight of the sample,

q

s+g= m/Vs+g= m/(Vub+ Vs) is the density of the combined solid and gas in the unbroken cells, Vs+gis the volume of combined solid and gas in the unbroken cell, Vubis the volume of gas in the unbroken cell, and Vsis the volume of solid. The apparent density, or foam density,

q

f= m/Vt, was measured using the ASTM D-1622 method. Note that this ap-proach disregards the weight of the extremely low-pressure gas in the vacuum. Subtracting the broken cell volume from the total volume produces Vs+g. The former was measured by an AccuPyc 1330 Pycnometer with an accuracy of 0.03%. The term

q

s is the density of the solid, taken as the density of the raw polystyrene, which is 991.96 kg m3_.

The solid volume fraction, fs, is the ratio of solid volume to the total volume and is readily obtained by dividing the foam density of the sample by the polystyrene density.

fs¼ Vs=Vt¼ 1  ½ð1  fsþgÞ=/ ð11Þ

3. Results and discussion

Table 1summarizes the measurement results of the samples without PE additive. The samples fall into two distinct groups with different solid volume fraction. The first group, referred to as PE0L, has a lower solid volume fraction, and includes PE0L1 to PE0L6 with 0.0413 < fs< 0.0494. The second group, referred to as PE0H, has a higher solid volume fraction and includes PE0H1 to PE0H8 with 0.065 < fs< 0.0706. Similar results of samples with 2.0 wt% and 5.0 wt% PE additive are also listed inTable 1, respectively. Sim-ilar to the samples without PE additive inTable 1, each PE additive contains two distinct groups with different solid volume fraction. The groups with higher solid volume fraction are designated as PE2H and PE5H, and the groups with lower solid volume fraction are designated as PE2L and PE5L, for the 2% and 5% PE samples, respectively. Note that all solid volume fractions in the 42 investi-gated samples are extremely low (less than 0.07), indicating a good foaming process. Nevertheless, the distinction between high and low solid volume fractions in each table is sharp and allows us to investigate the effects of solid volume fraction.

Figs. 3 and 4show examples of spectral transmittance and spec-tral extinction coefficient, respectively. Note that the spectra do not reveal any CO2 absorption, which could occur at 2.7

l

m,

Table 1

The characteristics of PS core material with 0%PE, 2%PE and 5%PE in vacuum insulation panel.

No. of samples qf(kg m3) qf+g(kg m3) fs / dc(lm) re(m1) kr(mW m1K1) ks+g(mW m1K1) kt(mW m1K1) PE0L1 49 704 0.0494 0.9787 143 5397 1.336 5.46 6.8 PE0L2 47 623 0.0474 0.9705 138 5999.2 1.202 5.50 6.7 PE0L3 44 565 0.0444 0.9649 130 6653.1 1.084 5.52 6.6 PE0L4 43 486 0.0433 0.9528 119 9645.9 0.749 5.75 6.5 PE0L5 42 388 0.0423 0.9312 100 13818.1 0.519 6.48 7.0 PE0L6 41 347 0.0413 0.9198 85 21887.6 0.327 7.37 7.7 PE0H1 70 812 0.0706 0.9832 374 5231.8 1.368 6.73 8.1 PE0H2 69 782 0.0696 0.9799 369 5999.2 1.187 6.71 7.9 PE0H3 68 736 0.0686 0.9744 330 6291.2 1.132 6.67 7.8 PE0H4 65 709 0.0655 0.9720 318 6750.3 1.059 6.64 7.7 PE0H5 64 692 0.0645 0.9701 305 7677.3 0.928 6.67 7.6 PE0H6 63 626 0.0635 0.9604 250 10758.7 0.664 7.24 7.9 PE0H7 62 561 0.0625 0.9488 175 15149.4 0.472 7.83 8.3 PE0H8 61 450 0.0615 0.9211 110 20886.1 0.341 8.66 9.0 PE2L1 30 675 0.0302 0.9854 211 11535.9 0.713 3.89 4.6 PE2L2 29 627 0.0292 0.9825 196 12862.9 0.639 3.86 4.5 PE2L3 28 560 0.0282 0.9776 175 14643.3 0.561 3.84 4.4 PE2L4 26 502 0.0262 0.9737 152 15842.2 0.518 4.48 5.0 PE2L5 25 448 0.0252 0.9686 140 17153.1 0.479 4.82 5.3 PE2H1 52 761 0.0524 0.9832 252 12825.8 0.640 4.66 5.3 PE2H2 51 732 0.0514 0.9808 238 13729.1 0.598 4.60 5.2 PE2H3 49 695 0.0494 0.9778 212 14920.2 0.552 4.55 5.1 PE2H4 48 668 0.0484 0.9753 191 15482.9 0.531 5.07 5.6 PE2H5 47 637 0.0474 0.9723 177 16655.2 0.495 5.31 5.8 PE5L1 49 762 0.0494 0.9843 264 5488.4 1.497 5.90 7.4 PE5L2 49 695 0.0492 0.9778 263 5545.8 1.484 5.72 7.2 PE5L3 48 579 0.0476 0.9637 262 6081.8 1.352 5.85 7.2 PE5L4 47 540 0.0465 0.9584 245 6959.4 1.181 5.92 7.1 PE5L5 46 473 0.0464 0.9466 240 8643.4 0.953 6.05 7 PE5L6 46 452 0.0454 0.9419 239 8664.4 0.949 6.05 7 PE5L7 46 382 0.0451 0.9224 220 9669.6 0.849 5.95 6.8 PE5L8 45 334 0.0444 0.9064 180 15161.5 0.540 6.56 7.1 PE5L9 44 319 0.0436 0.9021 145 16771.1 0.488 7.11 7.6 PE5H1 65 706 0.0655 0.9716 302 6420 1.279 6.62 7.9 PE5H2 64 655 0.0649 0.9645 296 6750.7 1.214 6.49 7.7 PE5H3 64 523 0.0647 0.9592 276 6891.5 1.189 6.51 7.7 PE5H4 63 509 0.0638 0.9357 251 9658.9 0.850 6.45 7.3 PE5H5 63 476 0.0635 0.9265 226 11612.5 0.707 6.49 7.2 PE5H6 62 460 0.0626 0.9229 241 12452.4 0.658 6.44 7.1 PE5H7 61 440 0.0617 0.9178 217 13162.3 0.624 6.68 7.3 PE5H8 61 431 0.0616 0.9147 197 14666.1 0.599 6.9 7.5 PE5H9 60 393 0.0604 0.9019 140 18567.8 0.441 7.56 8.0

4.3

l

m, 9.4

l

m, 10.4

l

m, and 15

l

m, or H2O absorption, which could occur at 2.7

l

m and 6.3

l

m. This indicates that the amount

of CO2and H2O trapped in the unbroken cells is insignificant in terms of influencing radiation heat transfer. This is reasonable since most of the cells in the samples are broken and evacuated.

Fig. 5plots the broken cell ratio versus the cell size. Each group shows an almost linear dependence of cell size on open cell ratio. Higher solid volume fraction is typically associated with larger cell size for a given PE additive weight percentage. The trend can be ex-plained by the fact that a higher solid volume allows the cells to expand further before breaking. In the meantime, in order to obtain a higher broken cell ratio, more of the unbroken cells must be ex-panded further until they are broken, which also increases the average cell size. Different slopes of the relationship between bro-ken cell ratio and cell size for different PE additive weight percent-ages inFig. 5are attributed to the effects of PE on the strength of cell membranes. These effects are also responsible for the larger cell sizes of PE2 and PE5 when compared to PE0. PE0H is an excep-tion because its solid volume fracexcep-tion is too high, which leads to large cell size as explained earlier. PE’s high melting temperature makes them more likely to solidify than PS during the cooling pro-cess in foaming and create membrane shear stress when the cells are growing, which helps to raise the broken cell ratio. If the PE additive is too much, however, the cell membrane strength could be augmented too much and the cells would grow larger without becoming broken. It will become evident in the following discus-sion that 2% PE is appropriate in terms of balancing cell size and broken cell ratio, while 5% PE leads to larger cell size and lower broken cell ratio. To summarize, cell size is influenced by three parameters, the broken cell ratio, the solid volume fraction and the PE additive. Among which, the PE additive is the easiest one to control and is an effective way to modify cell morphology.

Figs. 6 and 7 plot the Rosseland mean extinction coefficient against variations in cell size and broken cell ratio, respectively. The extinction coefficient in VIP consists of two parts, the absorp-tion part,

r

a, and the scattering part,

r

s, that is,

r

e=

r

a+

r

s. The former represents the absorption effect of solid material and de-pends largely on the solid volume fraction. The latter is affected by the morphology of the porous foam structure, which is charac-terized by the average cell size and the broken cell ratio. Smaller cell size implies a shorter mean free path and a larger scattering coefficient for thermal radiation. The mean extinction coefficient therefore increases as the cell size decreases, as evident inFig. 6. For a given PE additive percentage,Fig. 7, the group with higher so-lid volume fraction exhibits only a slight increase in extinction coefficient compared with the lower solid volume fraction group,

5 10 15 20 25

Wavelength,

λ

(

μ

m)

0 10 20 30 40

Transmittance,

τ

λ

(%)

PE2H2 (157

μ

m) PE2H3 (137

μ

m) PE2H4 (110

μ

m)

Fig. 3. Spectral transmittance varied with wavelength on PE2H samples.

5 10 15 20 25

λ

(

μ

m)

8000 12000 16000 20000 24000 28000

σ

eλ

(m

-1

)

PE2H4 (110

μ

m) PE2H2 (157

μ

m) PE2H3 (137

μ

m)

Fig. 4. Spectral extinction coefficient varied with wavelength on PE2H samples.

0 100 200 300 400

d

c

(

μ

m)

0.90 0.92 0.94 0.96 0.98 1.00

φ

PE0L PE2L PE5L PE0H PE2H PE5H

Fig. 5. Relationship between cell sizes and broken cell ratio on various PE additives

with high and low solid volume fraction. 0 100 200 300 400

dc (

μ

m)

4000 8000 12000 16000 20000 24000

σ

e

(m

-1

)

PE0L PE0H PE2L PE2H PE5L PE5H

Fig. 6. Rosseland mean extinction coefficient varied with cell sizes with/without PE additives on high and low solid volume fraction.

although the average solid volume fractions of the two groups dif-fer significantly. This can be explained by the fact that the solid volume fraction of all the samples are so small that the extinction is dominated by scattering and the solid absorption contribution is relatively insignificant. Extinction coefficients generally decrease as the broken cell ratio increases, as shown inFig. 7, due to reduced scattering by closed cell membrane. Although radiation extinction is a complex process influenced by cell morphology, the broken cell ratio proposed in this study is a suitable parameter to correlate the extinction coefficient for a given PE additive percentage. Adding 2% PE is effective in increasing the extinction coefficient, due mainly to the alteration of cell morphology. Increasing the PE additive to 5% does not increase the extinction further. On the contrary, the extinction at the same broken cell ratio drops to a lower amount than the case without PE additive. This can be explained partly by the fact that the cell size has grown too large in 5% PE samples. The trend inFigs. 6 and 7should be examined carefully, as the cell size, the solid volume fraction and the broken cell ratio all appear to influence the extinction coefficient. Nevertheless, the apparent higher extinction coefficient for higher solid volume fraction shown inFig. 6can be explained by the lower broken cell ratio associated with higher solid volume fraction, as evident inFig. 5.

Fig. 8shows the equivalent thermal conductivities of samples without PE additive, including the total thermal conductivity, kt, the thermal conductivity by solid/gas conduction, ks+g, and the thermal conductivity by radiation, kr. The total thermal conductiv-ity of the lower solid volume fraction group, PE0L is generally low-er than that of the highlow-er solid volume fraction group, PE0H. This difference is mainly caused by a change in solid/gas conduction, which accounts for more than 80% of the heat transfer in the sam-ples. Also, solid/gas conduction increases as the cell sizes decrease, which is associated with lower broken cell ratio and creates more conduction transport routes in the material. On the other hand, radiation decreases as the cell size decreases. Note that the de-crease in radiation (inde-crease in extinction coefficient) is attribut-able to the change in broken cell ratio, as explained earlier. Consequently, there is a best cell size (best broken cell ratio), which leads to the lowest total thermal conductivity after combin-ing ks+gand krfor each group of samples. InFig. 8, the lowest total thermal conductivity is around 6.5 mW m1_K1_{, which occurs in} the PE0L group at a broken cell ratio of approximately 0.95 corre-sponding to a cell size of about 100

l

m.Figs. 9 and 10shows the equivalent thermal conductivities of PE2 and PE5 groups, respec-tively, with trends similar to that in Fig. 7. The best cell size of

0.8 0.84 0.88 0.92 0.96 1

φ

4000 8000 12000 16000 20000 24000

σ

e

(m

-1

)

PE0L PE0H PE2L PE2H PE5L PE5H

Fig. 7. Rosseland mean extinction coefficient varied with broken cell ratio with/ without PE additives on high and low solid volume fraction.

0 100 200 300 400

dc (

μ

m)

0 2 4 6 8 10

k (mW/mK)

PE0L kr ks kt PE0H kr ks kt

Fig. 8. The relation between equivalent thermal conductivity and cell sizes for PS core material without PE additive.

120 160 200 240 280

dc (

μ

m)

0 2 4 6

k (mW

/mK)

PE2L kr ks kt PE2H kr ks kt

Fig. 9. The relation between equivalent thermal conductivity and cell sizes for PS core material with 2% PE additive.

120 160 200 240 280 320

dc (

μ

m)

0 2 4 6 8

k (mW/mK)

PE5L kr ks kt PE5H kr ks kt

Fig. 10. The relation between equivalent thermal conductivity and cell sizes for PS core material with 5% PE additive.

the 2% PE group,Fig. 9, falls at around 170

l

m, resulting in a total thermal conductivity of 4.4 mW m1_K1_{, which is the lowest in all} the samples investigated in this study. Increasing the PE additive to 5% does not reduce the total thermal conductivity further. Both so-lid/gas conduction and radiation are enhanced in the 5% PE groups when compared to 2% PE group. The enhanced radiation could be explained by the alteration in cell morphology and the enhanced solid/gas conduction is explained by the lower broken cell ratios of the 5% PE groups, as discussed earlier.

4. Conclusions

This study analyzes heat transfer in practical VIP, that is, VIP with a broken cell ratio higher than 90%. The structure of these non-black-body VIP foams consists of struts, closed cells and open cell residue membranes. PE additive is used as a way to alter the foam structure and the heat transfer. Two parameters, namely, the broken cell ratio and the average cell size, are proposed to char-acterize the structure. The experimental samples are further grouped based on their solid volume fraction to reveal the influ-ence of the solid material on heat transfer. Some conclusions derived from the experimental findings may help improve VIP per-formance, as summarized below.

1. Under a specific solid volume fraction, a best cell size (best bro-ken cell ratio) leads to the lowest total thermal conductivity. 2. Radiation heat transfer, as manifested by the mean extinction

coefficient, is influenced predominantly by broken cell ratio. The effects of solid volume fraction upon radiation are relatively insignificant in the samples investigated in this study. PE2 sam-ples have smaller cell size and therefore higher extinction than PE5 samples.

3. An appropriate amount of PE additive has proven to be effective in tuning the cell structure and improving the VIP performance. The best PE content among the three additive percentages investigated in this study was 2%.

4. Solid volume could affect the absorption coefficient in radia-tion transfer, but the effects are not obvious because the solid volume fraction is extremely low in this study, and the extinc-tion coefficient is dominated by scattering. However, the solid volume fraction has a crucial effect on solid conduction, which is the dominant heat transfer mechanism in VIP. A rule of thumb to improve VIP permeance can be derived from the findings in this study. Firstly, the solid volume fraction must be kept low to diminish the solid conduction. Secondly, the cell size and broken cell ratio must be carefully controlled to an optimum value to produce the lowest total thermal con-ductivity. A high broken cell ratio may cause high radiation

transfer, and does not necessarily imply low total thermal con-ductivity. In contrast to conventional closed-cell foam, where a small cell size reduces the heat transfer of trapped gas, the best cell size in practical VIP with high broken cell ratio ranges from 100 to 300

l

m. The lowest thermal conductivity obtained in this study reached 4.4 mW m1_K1_{, and was among the} best when previously compared to published VIP performance results.

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