• 沒有找到結果。

An experimental study of the heat transfer in PS foam insulation

N/A
N/A
Protected

Academic year: 2021

Share "An experimental study of the heat transfer in PS foam insulation"

Copied!
8
0
0

加載中.... (立即查看全文)

全文

(1)

O R I G I N A L

An experimental study of the heat transfer in PS foam insulation

Pen-Chang TsengÆ Hsin-Sen Chu

Received: 11 June 2007 / Accepted: 4 June 2008 / Published online: 7 October 2008 Ó Springer-Verlag 2008

Abstract Heat transfer mechanisms in 14 samples of vacuum insulation panels (VIPs) are examined to reveal the influence of porous foam structure on VIP performance. The samples were produced by in-house equipment that was able to vary the foam structure by modulating the process temperature and pressure. Two parameters are proposed to describe the foam structure, namely, the bro-ken cell ratio and the average cell size. Under a specific solid volume fraction, the average cell size shows a linear dependence on the broken cell ratio. Furthermore, the radiation and conduction heat transport data correlate well with these parameters. Radiation heat transfer increases as the broken cell ratio (cell size) increases, but solid con-duction decreases as the broken cell ratio (cell size) increases. Consequently, an optimum broken cell ratio (cell size) exists such that the total heat transport is minimum under a specific solid volume fraction. However, the majority of VIP heat transfer is solid conduction. Solid conduction accounts for more than 80% of the total heat transport and is largely affected by the solid volume frac-tion. A rule of thumb for improving VIP performance is to reduce the solid volume fraction as much as possible to eliminate solid conduction, and maintain the cell size at an optimum value that is dependent on the solid volume fraction.

List of symbols dc cell size (lm)

fs solid volume fraction (Vs/Vt)

fs?g volume fraction of combined solid and gas

ik spectral intensity of radiation

ks thermal conductivity of solid

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

Tm the arithmetic mean of the boundary temperatures

(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

qf apparent density or foam density (kg m-3)

qs the density of the solid, 991.96 (kg m -3

)

qs?g the density of the combined solid and gas in the

unbroken cells (kg m-3) r Stefan–Boltzmann constant,

5.67 9 10-8W m-2K-4

re Rosseland mean extinction coefficient, Eq. (7)

rek spectral extinction coefficient, sk, spectral

transmittance, Eq. (8)

/ broken cell ratio, Vb/Vtb, Eq. (9) P.-C. Tseng H.-S. Chu (&)

Department of Mechanical Engineering, National Chiao Tung University, HsinChu 300, Taiwan, ROC e-mail: hschu@cc.nctu.edu.tw P.-C. Tseng

e-mail: PenChangTseng@itri.org.tw DOI 10.1007/s00231-008-0417-1

(2)

1 Introduction

A vacuum insulation panel (VIP), which is constituted of a core porous material enclosed in an evacuated non-per-meable package (normally made of metal foil envelopes), features extremely low thermal conductivity and relatively low production cost. These benefits make VIPs suitable for numerous energy conservation applications, such as refrigerator insulation. If the porous cells in the materials are largely open, that is, broken and connected forming a network, evacuating the package to a vacuum could effectively eliminate the gas content and heat transfer by gas convection and conduction. Combining a vacuum with the low conductivity 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 conductivity as low as 4– 10 (mW m-1K-1), which is two to six times lower than ordinary foam insulation. However, further reductions in the heat transfer of VIPs require a detailed knowledge of heat transfer mechanisms in the material.

Previous studies have attempted to determine heat transfer in porous foam, including solid conduction [1–5], radiation [6–18] and gaseous conduction [19]. Some of these studies are relevant to VIP applications, and are cited below. Glicksman and Torpey [8] considered a black body strut with an efficiency factor of unity without scattering, and predicted radiation heat transfer in foam using foam density and average cell size. Kamiuto [10] adopted the Dul’nev cubic unit cell model to predict the thermal and radiative properties of open-cellular porous materials for applications in high-temperature heat transfer augmenta-tions. Quenard and Giraud [19] developed an experimental procedure to measure the micro-structural geometrical parameters of a packing of cellular pellets such as EPS foam. A critical value of foam density exists for any given cell size which minimizes effective thermal conductivity. Placido et al. [11] studied the dependence of radiative and conductive properties on the geometrical parameters of closed-cell foam, including mean wall thickness, mean strut diameter, and mean cell diameter. Coquard and Baillis [14] simulated the closed-cell structure of EPS by dodecahedrons and cubes. By solving one-dimensional (1D) steady state coupling equations of radiative and conductive transfer, he found the following parameters pertinent to heat transport, which are listed in order from higher influence to lower influence: foam density, mean cell diameter, inter-bead porosity, and mean bead diameter. Micco and Aldao [15] derived radiative heat transfer rates using a geometrical model and concluded that the geo-metrical model produced results more similar to experimental values than the Rosseland mean extinction coefficient derivation. Zhao et al. [16, 17] measured the

radiative heat transfer of FeCrAlY alloy foam with a high porosity (larger than 95%) and various cell diameters. The extinction coefficients decreased as the cell diameter increased, which has little influence on reflectivity. Both the extinction coefficient and the reflectivity were found to increase as the operation temperature increased.

Most of the studies above assumed all closed-cell or all open-cell structures in their analyses. However, practical applications are far more complicated since the cells in VIPs are not 100% broken, which means that some cells are closed. A cell breaks when forming agents induce enough internal pressure to overcome the cell membrane strength, which depends largely on the viscosity of the material, and therefore on the glass transition temperature (Tg). The material viscosity is relatively high at

tempera-tures above the Tg, but the material hardens immediately

when the temperature falls below the Tg. Both features

hinder the cell from breaking. It is very difficult to control the material temperature and simultaneously break all the cells inside the material. The positions and number of the unbroken, i.e., closed, cells are hard to control. Neverthe-less, cell geometry, including the struts and the residue membranes, plays a key role in both solid conduction and radiative heat transfer in VIPs. Further enhancement of VIP performance requires determining the influence of cell geometry on conduction and radiation, and using this knowledge to improve the manufacturing process. This paper deals with heat transfer in VIPs with partially open cell structures, focusing on VIPs with most of the cells broken. Specifically, more than 90% of the cells are broken and less than 10% of the cells are closed. This high ratio of broken cells is necessary and common in VIPs with satis-factory performance. A total of 14 samples with different cell geometries are produced, and their heat transfer rates are measured and analyzed. The results will be helpful in describing heat transfer in VIPs and serve as a basis for improving VIP performance in the future.

2 Experiments 2.1 Sample fabrication

The samples were prepared by the following procedure. A mixture of polystyrene (97% in weight), carbon black, and calcium stearate were put into a batch die of 400 mm diameter and subjected to a 40-ton press. Foaming was performed by introducing CO2and R-134a into the die to

form a supercritical fluid after mixing with the molten polystyrene. The high pressure gas in the die was released after 6 h, forming a plain board measuring 250 mm long 9 250 mm wide 9 6–26 mm thick. After about an hour of heating, the board was enclosed by a metal foil

(3)

envelope, which was sealed after the enclosed air was evacuated to 10-4torr. Experiments were designed to vary the cell geometry of the samples by modulating die tem-perature and gas pressure. Die temtem-perature is controlled by heaters and is maintained at a fixed temperature with a stability of 0.5°C throughout the foaming process. Figure1 shows the dual pressure control system which was able to separately control the pressure and the amount of CO2and

R-134a. During the forming process, the gas pressure normally ranged between 2,500 and 3,300 psi. Figure2 shows a SEM picture of the material sample. The structure typically consists of struts, cell membranes, broken cells, and unbroken cells. A total of 14 samples were produced for analysis in this study, all with partially open cell structures and broken cell ratios (see the definition below) ranging from 90 to 98%.

2.2 Measurements and data reduction

The heat flux (qt) in VIPs can be divided into the transfer

by conduction of solid and gas (qs?g), and by radiation (qr),

qt¼ ðqrþ qsþgÞ: ð1Þ

The concept of equivalent thermal conductivity applies,

kt¼ krþ ksþg ð2Þ

where kt is the equivalent total thermal conductivity, kris

the fraction of equivalent thermal conductivity induced by thermal radiation, and ks?g is the equivalent thermal

conductivity of combined solid and gas. In this study, it is further assumed that ks& ks?gsince the contribution by

gas conduction is relatively small in the samples with broken cell ratio higher than 90%. Note that the heating before sealing and evacuating also helped to eliminate the gases enclosed in closed cells. The equivalent total thermal conductivity was measured by a commercial thermal conductivity meter (EKO HC-072), which was designed in accordance with industrial standards JIS A 1412 and

ASTM 518. The device consists of a hot and a cold plate, thin-film heat-flow meters and a thickness measurement sensor. The temperature of the center of hot and cold plates was measured by the thermocouples. The 250 mm long 9 250 mm wide 9 (6–26) mm thick samples were clapped between the hot and the cold plate with integrated heat flow meters. The following formula is used to calculate the equivalent thermal conductivity.

kt¼

EL

SDT ð3Þ

Where S is the sensitivity of heat-flow meter, DT is the temperature difference between the hot and the cold plate, E is the output of the heat-flow meters, and L is the thickness of the sample. The uncertainty was estimated based on the data of Sample L3,

Dk¼ kt qt  2 dq2t þ kt s  2 ds2þ kt DT  2 dDT2 " #0:5 ¼ 6:6 23:34  2 ð0:02Þ2þ 6:6 0:00646  2 ð0:00005Þ2 " þ 6:6 22:8  2 ð0:1Þ2 #0:5 ¼ 0:05896 ðmW mK1Þ: ð4Þ

Therefore, the equivalent total thermal conductivity uncertainty can be calculated by, ðDk=ktÞ ¼ ð0:05896=

6:6Þ ¼ 0:0089: That is, the uncertainty of measuring specimen total thermal conductivity can be controlled to within 0.89%, as estimated by the method of Wu et al. [13]. The contribution to the equivalent thermal conductivity by radiation is evaluated by the following method. The solid volume fractions of the samples are normally less than 0.06. For the solid phase, over 97% material is polystyrene, which has a refractive index of 1.55. Therefore, if one estimates the refractive index of the foam by weighing the

Fig. 1 The dual pressure control system used to modulate the foaming pressure

(4)

ratio of solid to void volume, the result would be around 1.03, which is very close to the refractive index of air and vacuum and is neglected in the calculation. The dimensionless optical thickness of a PS sample is evaluated by multiplying its geometrical thickness by its mean extinction coefficient [18]. To be considered optically thick, the value has to be far greater than 1. All the samples in this study obtained the minimum optical thickness of 45. It is therefore satisfactory to assume all samples are optically thick and use the Rosseland mean extinction coefficient, re, by which the radiation heat flux

of an absorbing, emitting, and isotropically scattering medium can be written as [20],

qr¼ krrT ¼ 

16rT3 m

3re

rT ð5Þ

where the equivalent thermal conductivity is defined as kr ¼

16rT3 m

3re

ð6Þ where Tm is the arithmetic mean of the boundary

temperatures and r is the Stefan–Boltzmann constant. The Rosseland mean extinction coefficient, re, is defined as

[20] 1 re ¼ Z1 0 1 rek oekb oe dk: ð7Þ

The radiative heat transfer is 1D for a homogeneous planar system, in which the spectral intensity of radiation is governed by the equation of transfer. For the case of a cold homogeneous medium, the emission terms and in-scattering terms are negligible under the influence of a relatively strong but unidirectional beam of radiant energy, and the solution is given by Beer’s law. The transmittance is defined as

sk¼ expðreksÞ ð8Þ

where rek¼ ðrakþ rskÞ is the spectral extinction

coefficient.

The spectrum transmittances of the samples were mea-sured by a Perkin Spectrum 2000 Fourier Transform Infrared Spectrometer. For the measurement, a thinly sliced foam specimen was subjected to normal incident irradia-tion in the wavelength range of 2.5–25 lm. The specimen was first put into an oven to remove its moisture and volatile organic gas contents. With the measured trans-mittance, the spectral extinction coefficient is calculated by Eq. (8). The term reis then calculated by substituting rek

into Eq. (7) and kr is subsequently obtained by Eq. (6).

With the knowledge of krand kt, ks?gcan be inferred from

Eq. (2). Note that kr and ks?g reveal the contribution by

radiation and combined solid and gas, respectively. To

further distinguish the contribution by solid and by gas, this study introduces a broken cell ratio, /, representing the ratio of broken cell volume to the total cell volume /¼ Vb Vtb ¼ Vtqm sþg Vtqm s ¼ m qf m qsþg m qf m qs ¼ qs qsþg ðqsþg qfÞ ðqs qfÞ ð9Þ

where m is the mass of the sample, Vt is the apparent

volume (total volume), Vs is the volume of solid, Vs?gis

the volume of combined solid and gas in the unbroken cell, Vub is the volume of gas in the unbroken cell, Vb is the

vacuum volume inside the VIP (which actually contains air in extremely low pressure) or the broken cell volume, and Vtbis the volume of all the cells. The apparent density, or

foam density, qf= m/Vt, was measured using the ASTM

D-1622 method. The value qs?g= m/Vs?g= m/(Vub? Vs)

is the density of the combined solid and gas in the unbroken cells. Note that this approach discards the mass of 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 qsis the

density of the solid, taken as the density of the raw poly-styrene, which is 991.96 (kg m-3).

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

Vt

¼ 1 ð1  fsþgÞ

/ : ð10Þ

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.

3 Results and discussions

Table1 summarizes the measurement results of the 14 samples. The samples fall into two distinct groups with different solid volume fraction. The first group has a lower solid volume fraction (referred to as LSFG) and includes L1–L6 with 0.0413 \ fs\ 0.0494. The second group has a

higher solid volume fraction (referred to as HSFG) and includes H1–H8 with 0.0615 \ fs\ 0.0706. The variation

of solid volume fraction exerts a profound influence on VIP heat transfer, as explained later. Figures 3 and 4 show examples of spectral transmittance and spectral extinction coefficient, respectively. Note that this spectrum does not reveal CO2absorption, which could occur at 2.7, 4.3, 9.4,

10.4, and 15 lm, or H2O absorption, which could occur at

2.7 and 6.3 lm. This indicates that the amount of CO2and

H2O trapped in the unbroken cells is insignificant in terms

(5)

since most of the cells in the samples are broken and evacuated.

Figure5plots the broken cell ratio versus the cell size of the 14 samples. The data visibly falls into two groups based on the solid volume fraction. The HSFG cell sizes are typically larger than LSFG cell sizes. Both groups show an almost linear dependence of cell size on open cell ratio. The trend in Fig.5 can be explained by the fact that a higher solid volume enables the cells to expand further before they are broken, and therefore they have a larger cell size after foaming. On the other hand, to obtain a higher broken cell ratio, some of the unbroken cells must be expanded further until they are broken. Consequently, this also increases the average cell size.

Figures6 and 7 plots the Rosseland mean extinction coefficient data against variations in cell size and broken cell ratio, respectively. All the extinction coefficient data falls into a single straight line when plotted against the broken cell ratio, as Fig.7 shows. This indicates that the broken cell ratio is the dominant factor in determining the extinction coefficient. The VIP extinction coefficient con-sists of two parts, the absorption part, ra, and the scattering

part, rs, that is, re= ra? rs. The former represents the

absorption effect of solid material and depends largely on the solid volume fraction. The latter is affected by the geometry of the porous foam structure, which is charac-terized by the average cell size and the broken cell ratio. For the 14 samples investigated in this study, the solid volume fraction plays a minor role in determining the extinction coefficient, as Fig.7indicates. The group with a higher solid volume fraction exhibits only a slight increase in extinction coefficient compared with the lower solid volume fraction group, although the average solid volume

Table 1 The experimental results of the 14 samples No. of samples qf (kg m-3) qf?g (kg m-3) fs / dc (lm) re(m-1) kr (mW m-1K-1) ks?g (mW m-1K-1) kt (mW m-1K-1) L1 49 704 0.0494 0.9787 143 5,397 1.336 5.46 6.8 L2 47 623 0.0474 0.9705 138 5,999.2 1.202 5.50 6.7 L3 44 565 0.0444 0.9649 130 6,653.1 1.084 5.52 6.6 L4 43 486 0.0433 0.9528 119 9,645.9 0.749 5.75 6.5 L5 42 388 0.0423 0.9312 100 13,818.1 0.519 6.48 7.0 L6 41 347 0.0413 0.9198 85 21,887.6 0.327 7.37 7.7 H1 70 812 0.0706 0.9832 374 5,231.8 1.368 6.73 8.1 H2 69 782 0.0696 0.9799 369 5,999.2 1.187 6.71 7.9 H3 68 736 0.0686 0.9744 330 6,291.2 1.132 6.67 7.8 H4 65 709 0.0655 0.9720 318 6,750.3 1.059 6.64 7.7 H5 64 692 0.0645 0.9701 305 7,677.3 0.928 6.67 7.6 H6 63 626 0.0635 0.9604 250 10,758.7 0.664 7.24 7.9 H7 62 561 0.0625 0.9488 175 15,149.4 0.472 7.83 8.3 H8 61 450 0.0615 0.9211 110 20,886.1 0.341 8.66 9.0

Fig. 3 The transmittance spectrums of several typical samples

(6)

fractions of the two groups differ by more than 44% (0.045–0.065). This can be explained by the fact that the solid volume fraction of the samples is so small that the extinction is dominated by scattering and the contribution of absorption is insignificant. The apparent dependence of extinction coefficient on cell size, as Fig.6shows, could be interpreted as the dependence on broken cell ratio, since cell size and broken cell ratio are well correlated under a specific volume fraction, as Fig.5 indicates.

Figure8shows the equivalent thermal conductivities of the lower solid volume group, including the total thermal conductivity, kt, the thermal conductivity by solid

con-duction, ks, and the equivalent thermal conductivity by

radiation, kr. Figure8shows that as the cell size decreases,

which creates more conduction transport routes in the solid material, solid conduction increases. On the other hand, radiation decreases as the cell size decreases. Note that the

decrease in radiation (increase in extinction coefficient) is attributable to the change in broken cell ratio, as explained earlier. Consequently, there is a best cell size (best broken cell ratio), which produces the lowest total thermal con-ductivity after combining ks and kr. In Fig.8, the lowest

total thermal conductivity is around 6.5 (mW m-1 K-1), which occurs at a broken cell ratio of approximately 0.95 and corresponds to a cell size of about 120 lm. Figure9 shows the thermal conductivities of the higher solid vol-ume fraction group, with a trend similar to that in Fig.8. The best broken cell ratio falls at around 0.97, corre-sponding to a cell size of 300 lm, and results in the lowest total thermal conductivity of 7.6 (mW m-1 K-1). Similar dependence of total thermal conductivity on cell size is found in the simulation work by Placido et al. [12], who assumed constant gas contribution in fully closed cell

Fig. 5 The relation between average cell size and broken cell ratio, under two different solid volume fractions

Fig. 6 The effects of average cell size on extinction coefficient, under two different solid volume fractions

Fig. 7 The effects of broken cell ratio on extinction coefficient, under two different solid volume fractions

Fig. 8 The influences of average cell size on the LSFG equivalent thermal conductivities

(7)

structures and concluded a best cell size of around 100 lm. However, they also concluded that the minimum total conductivity corresponds to the minimum radiative con-ductivity in fully closed cell structures [11], in contrast to the results of partially open cell structures in Figs.8and9. The total thermal conductivity of the lower solid volume fraction group (Fig.8) is generally lower than that of the higher solid volume fraction group (Fig.9). This difference is caused by a change in solid conduction, which accounts for more than 80% of the heat transfer in the samples (see Figs.8, 9). The equivalent thermal conductivity of radia-tion, which is generally responsible for less than 20% of the total heat transfer, shows a relatively weak dependence on the solid volume fraction, which is consistent with earlier observations in Fig.7. Our earlier study [12] of polyure-thane foams revealed the similar proportion of radiative contribution to total heat transfer, namely, 20% of the total heat transfer in vacuum are attributed to radiative transfer.

4 Conclusions

This study analyzes heat transfer in practical VIPs, i.e., VIPs with a broken cell ratio higher than 90%. The struc-ture of these non-black-body VIP foams consists of struts, closed cells, and open cell residue membranes. Two parameters, namely, the broken cell ratio and the average cell size, are proposed to characterize the cell structure. The experimental samples are further grouped based on their solid volume fraction to reveal the influence of the solid material on heat transfer. Some conclusions derived from the experimental findings are summarized below. 1. Radiation heat transfer, as manifested by the mean

extinction coefficient, is influenced predominantly by

the broken cell ratio. The effects of cell size and solid volume fraction upon radiation are relatively insignif-icant in the samples investigated in this study. 2. Under a specific solid volume fraction, the best broken

cell ratio (best cell size) leads to the lowest total thermal conductivity.

3. Solid volume could affect the absorption coefficient in radiation transfer, but the effects are not obvious because the solid volume fraction is extremely low in this study, and the extinction 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 performance 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 conductivity. A high broken cell ratio may cause high radiation transfer, and does not nec-essarily imply low total thermal conductivity. Experimental results of this study suggest a best cell size in the range of 100–300 lm for practical VIP with a high broken cell ratio.

References

1. Chu HS, Stretton AJ, Tien CL (1988) Radiative heat transfer in ultra-fine powder insulations. Int J Heat Mass Transf 31(8):1627– 1634

2. Tseng CJ, Yamaguchit M, Ohmorit T (1997) Thermal conduc-tivity of polyurethane foams from room temperature to 20 K. Cryogenics 37(6):305–312

3. Druma AM, Alam MK, Druma C (2004) Analysis of thermal conduction in carbon foams. Int J Thermal Sci 43:689–695 4. Giaretto V, Miraldi E, Ruscica G (1995/1996) Simultaneous

estimations of radiative and conductive properties in lightweight insulating materials. High Temp High Press 27/28:191–204 5. Kuhn J, Ebert HP, Arduini-Schuster MC, Buttner D, Fricke J

(1992) Thermal transport in polystyrene and polyurethane foam insulations. Int J Heat Mass Transf 35(7):1795–1801

6. Doermann D, Sacadura JF (1996) Heat transfer in open cell foam insulation. ASME J Heat Transf 118:88–93

7. Baillis D, Arduini-Schuster M, Sacadura JF (2002) Identification of spectral radiative properties of polyurethane foam from hemispherical and bi-directional transmittance and reflectance measurements. J Quant Spectrosc Radiat Transf 73:297–306 8. Glicksman LR, Torpey MR (1987) The influence of cell size and

foam density on the thermal conductivity of foam insulation. Polyurethanes World Congress, Aachen, Germany. 29 Septem-ber–2 October, pp 80–84

9. Glicksman LR, Marge AL, Moreno JD (1992) Radiation heat transfer in cellular foam insulation. ASME Paper HTD-203, Developments in Radiative Heat Transfer, pp 45–53

10. Kamiuto K (1997) Study of Dul’nev’s model for the thermal and radiative properties of open-cellular porous materials. JSME Int J Ser B 40(4):577–582

Fig. 9 The influences of average cell size on the HSFG equivalent thermal conductivities

(8)

11. Placido E, Arduini-Schuster MC, Kuhn J (2005) Thermal prop-erties predictive model for insulating foams. Infrared Phys Technol 46:219–231

12. Wu JW, Sung WF, Chu HS (1999) Thermal conductivity of polyurethane foams. Int J Heat Mass Transf 42:2211–2217 13. Caps R, Heinemann U, Fricke J, Keller K (1997) Thermal

con-ductivity of polymide foams. J Heat Mass Transf 40(2):269–280 14. Coquard R, Baillis D (2006) Modeling of heat transfer in

low-density EPS foams. ASME J Heat Transf 128:538–549 15. De Micco C, Aldao CM (2005) Radiation contribution to the

thermal conductivity of plastic foams. J Polym Sci [B] 43:190–192 16. Zhao CY, Lu TJ, Hodson HP (2004) Thermal radiation in ultra-light metal foams with open cells. Int J Heat Mass Transf 47:2927–2939

17. Zhao CY, Lu TJ, Hodson HP (2004) The temperature dependence of effective thermal conductivity of open-celled steel alloy foams. Mater Sci Eng A 367:123–131

18. O¨ zisik MN (1973) Radiative transfer and interactions with con-duction and convection. Wiley, New York

19. Quenard D, Giraud D (1998) Heat transfer in the packing of cellular pellets: microstructure and apparent thermal conductiv-ity. High Temp High Press 30(6):709–715

20. Siegel R, Howell JR (2002) Thermal radiation heat transfer, 4th edn. Taylor & Francis, New York

數據

Fig. 1 The dual pressure control system used to modulate the foaming pressure
Table 1 The experimental results of the 14 samples No. of samples q f (kg m -3 ) q f?g (kg m -3 ) f s / d c (lm) r e (m -1 ) k r (mW m -1 K -1 ) k s?g (mW m -1 K -1 ) k t (mW m -1 K -1 ) L1 49 704 0.0494 0.9787 143 5,397 1.336 5.46 6.8 L2 47 623 0.0474 0.9
Fig. 5 The relation between average cell size and broken cell ratio, under two different solid volume fractions
Fig. 9 The influences of average cell size on the HSFG equivalent thermal conductivities

參考文獻

相關文件

denote the successive intervals produced by the bisection algorithm... denote the successive intervals produced by the

Topics include properties of simple harmonic motion, waves and sound, heat, heat transfer, thermodynamics, light, lighting and

The continuity of learning that is produced by the second type of transfer, transfer of principles, is dependent upon mastery of the structure of the subject matter …in order for a

and Dagtekin, I., “Mixed convection in two-sided lid-driven differentially heated square cavity,” International Journal of Heat and Mass Transfer, Vol.47, 2004, pp. M.,

Based on Biot’s three-dimensional consolidation theory of porous media, analytical solutions of the transient thermo-consolidation deformation due to a point heat source buried in

Based on Biot’s three-dimensional consolidation theory of porous media, analytical solutions of the transient thermo-consolidation deformation due to a point heat source buried

The aim of this study is to investigate students in learning in inequalities with one unknown, as well as to collect corresponding strategies and errors in problem solving..

By comparing and analyzing the advantages and disadvantages of using the FRP molded panels and hard PS insulation material on roof insulation and waterproof with the