Heat transfer reduction in closed cell polyurethane foams

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HEAT TRANSFER REDUCTION IN CLOSED

CELL POLYURETHANE FOAMS

Proefschrift

ter verkrijging van de graad van doctor in de technische wetenschappen

aan de Technische Universiteit Delft, op gezag van de

Rector Magnificus, prof.dr. J.M. Dirken,

in het openbaar te verdedigen ten overstaan van

het College van Dekanen op dinsdag 23 september 1986 te 14.00 uur

door

RUDOLF BOETES

Natuurkundig ingenieur

geboren te 's-Gravenhage.

TR diss

1498

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prof.ir. C.J. Hoogendoorn

Acknowledgment

This work has been initiated by the "Stichting Ontwikkeling Koeltechniek" (Foundation for Development of Refrigeration Technology).

These investigations were supported in part by the Netherlands Foundation for Chemical Research (S.O.N.) with financial aid from the Netherlands Foundation for Technical Research (S.T.W.), the Netherlands Organization for the Advancement of Pure Research (Z.W.O.) and the "Stichting Ontwikkeling Koeltechniek".

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SUMMARY

This thesis considers closed cells polyurethane foam for the insulation of cooled spaces. In view of the great economic importance of improved insulation, Re investigated the heat transfer processes through the foam both theoretically and experimentally. The main objective has been to find guidelines for the production of polyurethane foams Rith a thermal conduc tivity coefficient ( M of 0.016 H/m. K or less, Rhich shoRs little ageing. In vied of the test-procedures for refrigerated lorries for long distance transport, the thermal conductivity coefficient should for that application remain bel OH the value of 0.016 H/m. K for at least 5 years.

Firstly thermal insulation in general is discussed. Some common prod uction processes are presented, including the foam chemistry and the blOH-ing principles. The heat transfer mechanisms in foams are described. Con ductive heat transfer is extensively discussed. An equation for the ther mal conductivity coefficient of a gas mixture is presented. Data about the A-value of the gases used in insulating foams (air, CO, , Refriger ant 11 (R11) and Refrigerant 12 (R12)) and about the A-value of solid polyurethane are also presented.

These data are used to calculate the effective thermal conductivity coeffi cient of a foam cell, the weighted average of the gas and the solid thermal conductivity. For that calculation a fen equations are presented, based on different cell models, such as the elongated rectangular cell model or the cubical cell model, or based on cell models such as the dodecahedron model. The differences betneen the numerical values of h found from these equa tions are presented. Por cubical cells Kith constant cell Rail thickness the tno most significant analytical equations (upper and loner limit) are compared with a numerical model. The A-values according to these three approaches differ very little, they are Hithin 1 % for normal insulating

3 foams ( 40 kg/m ).

The radiative heat transfer in foams is investigated, as well as the interaction of radiation with conduction. The radiative heat transfer is

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modelled by a lamellae model, in which a lamella, with a certain reflec tion-, transmission- and absorption-coefficient, represents a single layer of foam cells.

Both separate heat transfer mechanisms, radiation and conduction, would each individually establish different temperature profiles throughout the foam. The actual temperature profile, a result of the interaction of these two mechanisms, is calculated, using heat balances.

The measurements of the thermal conductivity coefficient of foam slabs have been discussed. Several different principles of these measurements and the corresponding apparatus are presented.

The heat flow meter apparatus, which we have used to perform relative meas urements, is described in more detail. An absolute calibration procedure for this apparatus is described in appendix 4. After a relative calibra tion the accuracy of the apparatus is 3 % in the absolute value of A.

Next, the important foam properties and the way to measure them are dis cussed. Examples are cell size (0.2-0.5 mm.), cell gas composition (air, CO, , R11 and R12), volume fractions of the gas components, and foam

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sity (35-45 kg/m ). Special attention is given to the radiative (infra red) properties of the solid polyurethane (lamella reflection « 0.03, lamella transmission « 0. 5 and lamella absorption ~ 0.47).

Simulations of the heat transfer in foams are presented. From these simulations we found some favourable properties of insulating foams.

- small cells, especially the dimension into the heat flux direction should be minimal.

3 - foam density should be approximately 30 to 40 kg/m

- the infra-red reflection should be large, and the transmission as low as possible.

- a well insulating fill gas should be used, for example R11.

The emission coefficients of the boundary surfaces hardly affect the appar ent thermal conductivity of the foam, for a foam thickness of 20 mm. or more.

The infra-red properties of a foam.will be difficult to alter, a study on the introduction of reflecting or absorbing shields in the foaa at regular intervals has been done. In this way a significant reduction of the appar ent thermal conductivity can be achieved, though this requires at least 10

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reflecting or absorbing shields in the foam. Of these reflecting shields are the most effective.

Some measurements of the apparent thermal conductivity coefficient of foams as a function of one or more parameters are presented. The trends that are predicted by the simulations of chapter 7 are verified.

For one foam the measured thermal conductivity coefficients in the tempera ture range -20 to 20 degrees Celsius are compared Kith those found from the simulations. The differences are maximally ± 13 %.

Also the ageing of foams has been investigated briefly. Due to the effusion of CO. and the infusion of air, thermal conductivity increases Rith time. The transient diffusion of gases is described and the effective diffusion coefficient of gases in polyurethane foams of different densities and at different temperatures are presented. From these data the rate of ageing of a foam can be estimated, «hen the foam is in contact Rith the environmental air.

However even in foams that are Hell protected against diffusion from or to the environment ageing can occur, due to selective absorption of the Ion A gas component in the solid polyurethane.

This is also investigated. Under almost stationary conditions the solubil ity of R11 in polyurethane is determined. It is shoRn that approximately 35 % of the original amount of R11 is dissolved in the solid, uithin about a month after production. The relevant temperature and pressure are 25*C

S

and 0.25x10 Pa. respectively.

Finally there is a general discussion and the conclusions are given. The investigations shoHed that noRadays polyurethane insulations can be made on a commercial scale Rith an initial A-value of 0.016 H/m. K. Such foams have a density of about 40 kg/m , a cell dimension of about 0. 3 mm. and a gas filling of about 30 mole % CO. and 70 mole % R11. Improvements are still possible in the field of radiation suppression, by using other chemicals for the polymer, or by using radiation shields in the foam. The prevention of ageing of the foam is also important.

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SAMENVATTING

Dit proefschrift beschrijft een onderzoek aan polyurethaanschuimen met gesloten celstruktuur, die gebruikt Horden als thermische isolatie in de koeltechniek. Een goede isolatie is van groot economisch belang. In dit onderzoek is langs theoretische en experimentele neg het Rarmtetransport door schuimen onderzocht. Het doel hierbij is te komen tot richtlijnen voor de produktie van verbeterde polyurethaan isolatiematerialen, met een Harmtegeleidingscoefficient (A ) van 0.016 H/m. K of minder, die niet ver ouderen. Het het oog op de testprocedures voor koelvoertuigen is het belangrijk dat deze lage A-Baarde ook na vijf jaar nog niet overschreden Rordt.

Allereerst Rordt thermisch isolatiemateriaal in zijn algemeenheid besproken. Enkele gebruikelijke produktieprocessen Borden gepresenteerd, gecombineerd met de bijbehorende chemie en de opschuim technieken. De Rarmtetransport mechanismen in schuimen «orden beschreven. Daarna volgt een uitgebreide behandeling van het geleidingstransport. Hier Rordt een uitdrukking gegeven waarmee de Harmtegeleidingscoefficient van een gasmeng sel berekend kan Horden. A-Raarden van de in polyurethaanschuim voorko mende gassen (lucht, CO , Refrigerant 11 ( R11) en Refrigerant 12 (R12)) Horden gegeven. Deze gegevens Horden gebruikt om de Harmtegeleidingscoef-ficient van een schuimcel te bepalen als een genogen gemiddelde van de gas en de vaste stof geleiding. Om dit te berekenen zijn er enkele vergelij kingen gegeven, die gebaseerd zijn op verschillende cel geometrieen, balk-vormig of kubisch, dannel gebaseerd op een dodecaeder model. Het verschil in de A-waarde tussen deze modellen Rordt gepresenteerd. Voor kubische cellen met een konstante celRand-dikte Horden de tnee belangrijkste verge lijkingen (een bovengrens en een ondergrens) vergeleken met een numeriek model. Het blijkt dat de berekende A-Raarden volgens deze drie benaderin gen op 1 % nauRkeurig identiek zijn, voor normale isolatie schuimen (40 kg/m3 ).

Het Rarmtetransport door straling is onderzocht, alsook de interaktie tussen geleiding en straling. Het stralingstransport Rordt gemodelleerd

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net behulp van een lamellen model, naarin een enkele lamel een cel voor stelt, net een bepaalde reflectie-, transmissie- en absorptiecoëfficiënt. Beide narmtetransportmechanismen apart, straling en geleiding, proberen een ander temperatuurprofiel te handhaven in het schuim. Het Kerkelijke tempe ratuurprofiel, een resultaat van de interaktie tussen geleiding en stra ling, Hordt berekend net behulp van Harmtebalansen.

De meetmethode voor de bepaling van de Harmtegeleidingscoefficient van schuimplaten wordt behandeld. Enkele meetprincipes alsook de bijbehorende meetapparatuur Horden besproken. Het Harmtestroommeter apparaat, dat in dit onderzoek gebruikt is als een relatieve meetmethode, uordt meer expli ciet besproken. Een methode voor absolute calibratie van dit apparaat is beschreven in appendix 4. Ha een relatieve calibratie is de onnauwkeurig heid van dit apparaat 3 % in de absolute A-Haarde.

Vervolgens Horden de belangrijke schuimparameters, en de manier waarop ze gemeten kunnen Horden, besproken. Voorbeelden zijn de celgrootte (0.2-0.5 mm.), celgas samenstelling (lucht, CO, , R11 en R12), volume

3 fracties van de gascomponenten en de schuimdichtheid (35-40 kg/m ). Speciale aandacht is gegeven aan de infrarood-stralingseigenschappen van het vaste polyurethaan (lamel reflectie » 0.03, lamel transmissie Ï 0,5 en lamel absorptie ~ 0. 47).

Simulaties van het warmtetransport in schuimen Horden gepresenteerd. Dit deze simulaties zijn enkele gunstige schuimparameters gevonden.

- kleine cellen, vooral de celgrootte in de richting parallel aan de narmtestroom richting moet klein zijn.

- de schuimdichtheid moet ongeveer 30 tot 40 kg/m zijn. - de infrarood reflectie moet zo groot mogelijk zijn, terwijl de

transmissie juist klein moet zijn.

- een goed isolerend vulgas moet gebruikt Horden, bijvoorbeeld Ril. De emissiecoefficient van de grensvlakken heeft naunelijks invloed op de effectieve Rarmtegeleidingscoefficient van het schuim, voor een schuimdikte van 20 mm. of «eer.

De infrarood eigenschappen van het schuim zijn moeilijk te veranderen. Een onderzoek naar het effekt van absorberende of reflekterende stralingsscher-aen in het schuim is verricht. Gebleken is dat met deze schermen een sig nificante reductie van de effektieve Rarmtegeleidingscoefficient bereikt kan Horden, hoewel hier nel 10 of meer reflekterende dan nel absorberende

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schermen in het schuim voor nodig zijn. Reflekterende schermen zijn hier het meest effektief.

Een aantal metingen van de effektieve narmtegeleidingscoefficient van schuimen oorden gepresenteerd als een funktie van een of meer parameters. De tendensen die op basis van theoretische beschouoingen voorspeld Herden zijn hier geverifieerd.

Voor een bepaalde schuimplaat is de gemeten narmtegeleidingscoefficient, bij temperaturen tussen -20 en 20*C, vergeleken met de simulatieresultaten. De verschillen bedragen maximaal 13 %, naar beide kanten.

Ook is de veroudering van schuimplaten kort onderzocht. Door het uit-diffunderen van CO en het in-uit-diffunderen van lucht neemt de narmtegelei dingscoef ficient toe. De tijdsafhankelijke diffusie van gas is beschreven en de effektieve diffusie coëfficiënten van gassen in polyurethaan schuim van verschillende dichtheden en bij verschillende temperaturen zijn gege ven. Het deze gegevens kan de snelheid naarmee de schuimplaten verouderen geschat Horden, indien het schuim aan alle zijden blootgesteld is aan lucht. Echter ook in schuimen die diffusiedicht verpakt zijn kan verouder ing optreden, veroorzaakt door een selectieve absorptie van gascomponenten in het polyurethaan. Dit is ook onderzocht. Onder min of meer stationaire omstandigheden is de oplosbaarheid van R11 in polyurethaan bepaald. Aange toond is dat ongeveer 35 % van de originele hoeveelheid R11 oplost in het polymeer, in ongeveer een maand tijd na de produktie, bij een druk van 0.25x10 Pa. en een temperatuur van 25"C.

Uiteindelijk volgen een algemene discussie en de conclusies. Dit het onderzoek is gebleken dat polyurethaan isolatiematerialen met een ini tiële A-Haarde van 0.016 R/m. K momenteel geproduceerd kunnen worden op

com-3 merciele schaal. Dit schuim heeft dan een dichtheid van ca.40 kg/m , een cel diameter van ca. 0. 3 mm. en een gassamenstelling van ongeveer 30 mol % CO en 70 mol % R11.

Verbeteringen zijn nog mogelijk op het gebied van stralings onderdrukking, via de chemie van het polymeer, of met gebruikmaking van stralingsschermen in het schuim.

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LIST OF SYMBOLS

a aspect ratio (-) 2

A area (m ) A matrix, defined in appendix 1 ( -)

b cell dimension (model) (m) b' cell diameter (foam) (m) B coefficient as defined in chapter 3 (-)

2

B vector, defined in appendix 1 (H/m c constants

C concentration (kg/m C matrix, defined in appendix 1 ( -)

d thickness (m) 2

D effective diffusion coefficient (m /s 2 D diffusion coefficient in the solid phase (m /s

s

2 D„ diffusion coefficient in the gas phase (m /s

2

D vector, defined in appendix 1 (H/m 2

E diffuse radiation per unit area (H/m Ê matrix, defined in appendix 1 (H/m. f gas specific correction factor (-)

F view factor (-) F matrix of view f a c t o r s (-) Fo F o u r i e r number (-) g c e l l n a i l t h i c k n e s s (m) Q a b s o r p t i o n f a c t o r ( - ) Q matrix of a b s o r p t i o n f a c t o r s (-) h c e l l dimension (model) (m) h' c e l l d i a m e t e r (foam) (m) 2 H v e c t o r d e f i n e d i n appendix 1 ( H/m i i n t e g e r (-) i imaginairy number (-) I integrator output (V. s)

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j integer (-) 2

J mass flux rate per unit area (kg/m . s) 2 J' mass flux per unit area (kg/m ) k integer ( -) k extinction coefficient ( -) K backscatter coefficient of tno-flux model (m )

2 L radiation in backward direction ( H/m )

2 L vector of backward radiations ( H/m )

m mass (kg) 2

M emitted radiation ( H/m )

M molecular Height (chapter 3 & 9) (kg/kmole) n refractive index ( -)

p pressure (Pa. ) P absorption coefficient of two-flux model (m ) P permeation coefficient defined by (9.12) (kg/m. s. Pa)

2 P' permeation coefficient defined by (9. 15) (m /s. Pa)

3 P" permeation coefficient defined by (9. 21) (m . s/kg)

2 q heat fIon rate per unit area (H/m )

2 q heat fIon rate per unit area, conductive part (H/m )

c

2 q heat fIon rate per unit area, interactive part (H/m )

2 q heat flow rate per unit area, radiative part (H/m )

r lamella or cell Rail reflection coefficient (-) r. boundary surface reflection coefficient ( -)

R universal gas constant ( J/mol. K) 2 R radiation in forward direction (H/m )

2 R vector of forward radiations (H/m ) s cell size into the heat flow direction (model) ( m)

s' cell diameter into the heat flow direction (foam) (m)

S Sutherland constant (K) t lamella or cell nail transmission coefficient (-)

t time (chapter 9) (s) T thermodynamic temperature (K)

Tc foam temperature at the cold side (K)

T_ foam cell temperature at the cold side (K) T„ foam temperature at the hot side (K)

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THc u ü V 9 V 0 z y z Z a a 0' R óx ay AZ s e £

o

ïf

PF H

e

A A e s A 9 AC *I XR A U V «

foam cell temperature at the hot side coordinate

voltage

porosity (fraction by volume of gas in the foam) volume

absorption plus backscatter coefficient in the two-flux coordinate in rectangular coordinate system

coordinate in rectangular coordinate system coordinate in rectangular coordinate system number of foam cells into the heat floo direction coefficient in the exponential grid definition. solubility (Bunsen coefficient)

partition coefficient strut thickness.

gridpoint distance in z-direction gridpoint distance in y-direction gridpoint distance in z-direction distance

lamella or cell nail emission coefficient boundary surface emission coefficient matrix, defined in appendix 3

matrix, defined in appendix 3 reflection coefficient Celsius temperature thermal conductivity

thermal conductivity of the cubical cell thermal conductivity of the solid

thermal conductivity of the void-gas thermal conductivity, conductive part thermal conductivity, interactive part thermal conductivity, radiative part wavelength viscosity relative frequency angle (K) (m) (V) (-) ( m3) model. (m) (m) (m) (-) (-) (kg/i (-) (m) (m) (m) (m) (m) (-) (-) (-) ( -) (-) C°C> (H/m. (H/m. ( H/m. (H/m. (H/m. (H/m. (H/m. (m) (m~1) n3. Pa) K) K) K) K) R) K) K) ( kg/m. s) (-) (-)

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p PI pg ps 0 T * cd * r x . a i r XC 0 2 XR 1 1 XR 1 2 X s Cl density insulation density gas density solid density Stephan-Boltzmann constant 4. n . k/A

heat flOH rate

heat flOH rate by conduction heat floR rate by radiation air volume fraction in the void CO, volume fraction in the void R11 volume fraction in the void R12 volume fraction in the void fraction of solid in the struts direction in the foam

gas gas gas gas (kg/m3) (kg/m3) (kg/m3) (kg/m3) (H/m2. K*) ( m- 1) (ff) (R) (R) (-) (-) (-) (-) (-) (-)

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CHAPTER 1 GENERAL INTRODUCTION

1.1 Background.

For international refrigerated road transport the fact that the standard pallets on which aost of the goods are loaded cannot econoaically be placed in a refrigerated lorry is a problea. This is due to a nisnatch of dimen sions of the standard pallets on the one hand (diaensions 1200 z 1000 an.) and of the aaziaua outside diaensions of a lorry on the other (aaziaua Ridth in Europe: 2500 ■■. ).

Hitbout theraal insulation tno pallets 1200 aa. long can be placed side by side in a lorry of 2500 aa. (outside) width.

For products that have to be cooled during transport the situation is dif ferent. The refrigerated lorry has to be insulated and this usually reduces the inside Ridth by aore than 100 aa. This leaves no rooa for tuo pallets side by side, so about half of thea are placed such that they occupy only 1000 aa. in the direction of the Ridth of the lorry. Unfortu nately this aeans that about 9 % of the transport capacity of a lorry (length about 12 aeters) is not used.

There are three Rays to solve this problea, but all three have their drawbacks.

- adapting the pallets to the inside diaensions of the lorry.

This is not a proper solution, because it will cause aajor probleas in other transport systeas, that are fully based on the ezisting standard diaensions.

- adapting the aaziaua outside diaensions of lorries.

This adjustaent will increase the useful inside voluae and certainly solves the problea. On the other hand it requires an adaptation of international (European Coaaunity) agreeaents and in practice this is hard to achieve.

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Recently a maximum width of 2600 mm. has been accepted in some Euro pean countries. It may be that the problem will be solved in this way in Europe in the near future.

- reducing insulation thickness.

Insulation thickness is not subject to any statutory standard, but there is an international regulation stating the maximum acceptable K-value for the total area surrounding the cooled 9pace, the Agreement on the International Carriage of Perishable Foodstuffs and on the Spe cial Equipment to be used for such carriage, in short ATP-agreement ( Accord relatif aux Transports internationaux des denrées Perissables et aux agents spéciaux a utiliser pour ces transports).

The K-value is defined as:

*

K = (1 1}

4 • <Tin- Tout>

where T^n = inside temperature (K)

TQ U t= outside temperature ( K) 2 A = total area of all walls, including roof and bottom (m )

* = heat flow rate (K) Hhen the refrigerated lorry is tested for an ATP-certificate the inside

temperature is kept constant at 35 *C. The outside temperature is 5"C. The K-value measured in this way, for stationary conditions, may not exceed

2

0.4 H/K. m , for the ATP-oertificate to be issued.

Hhen we realize that the heat flow rate (* ) is proportional to : ♦ - A/d

where A = the apparent thermal conductivity (H/m. K) and d = the insulation thickness (ro)

we see that a reduction of insulation thickness requires better insulators. The best available so far, with a thermal conductivity of about 0.023 H/m. C

2

in practice, are not enough to reach K < 0. 4 H/K. m for a desired side wall insulation thickness of about 35 mm.

In practice the insulation of the top, bottom, front and back walls of the lorry are much thicker, for example 100 mm., which reduces the demands for the thermal conductivity value of the side wall insulation. It is con cluded from this that refrigerated lorries need a 35 mm. thick insulation

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for the side «alls with a thermal conductivity of 0.016 H/o. K or less, when a small number of cold bridges in the construction are also taken into account. Sandwiched between two solid layers this will form a 40 mm. thick insulated side wall of the required quality, which leaves a useful inside width of 2420 mm. (two pallets plus 20 mm. for manoeuvre and ventilation). At the time this project started the latter solution seemed to be the most promising, and our research concentrated on this.

The final goal for research was to find guidelines for the production of insulating foams, to be used in refrigeration technology, with thermal conductivities as low as 0.016 H/m. K. He have investigated these foams under conditions of more or less normal use: an average temperature of -20 to +70*C, a temperature difference over the insulation of 20 to 40°C and a foam thickness of 20 to 50 mm. In this way the temperatures consid ered are only slightly different from those used for the ATP-test proce dure.

& significant aspect of foam insulation is that the thermal conductivity tends to increase with time, due to an infusion of air and an effusion of the blowing agents. This is called 'ageing'. For an insulated lorry this ageing process has to be avoided because 5 years later, when the lorry again has to be tested for the ATP-certificate, ageing might cause the lorry to fail the test. For economic reasons it is highly desirable that

2 the K-value of the lorry at that time will still be below 0.4 R/K. m

He are thus searching for a foam insulation with A = 0.016 H/m. K or less, which does not exceed this value for at least 5 years.

These foams, once developed, will also be useful for other purposes, such as insulation of cold stores and refrigerators, in order to save energy. This general applicability further justifies research in the insu lation field because of its great economic importance.

This thesis describes such investigations into closed cells polyure-thane foams. These investigations were supported in part by the Netherlands Foundation for Chemical Research ( S. 0. N. ) with financial aid from the Neth erlands Organization for Technical Research (S. T. R. ), the Netherlands Organisation for the Advancement of Pure Research (Z.H. 0. ) and the Nether lands Foundation for Development of Refrigeration Technology (Stichting Ontwikkeling Koeltechniek).

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1.2 Aia and topics of this study.

The aia of this study is to develop guidelines for the aanufacturing of insulating foaas with low theraal conductivity. To achieve this we have to understand the heat transfer aechanisas in theraal insulations.

In this study a physical aodel has been set up to calculate the heat fluxes in foaa slabs by conduction and radiation.

The aodel allows us to search for a foaa with a low theraal conductivity coefficient by changing aaterial and other properties of the foaa in the physical aodel. On this basis only the aost proaising foaas have to be aanufactured in order to investigate thea ezperiaentally.

The foaa aanufacturing itself was no part of this research project, but in cooperation with the S. 0. t. soae special saaples were supplied by partici pating industries.

Hhen siaulating the heat transfer process in foaas by use of the physi cal aodel aentioned above, we require the nuaerical values of several foaa paraaeters.

Part of this study has been devoted to the aeasureaent of these paraaeters. Radiative heat transfer requires data on optical properties, this has been given special attention in this investigation. The effect of radiation shields in the foaa has also been studied.

Iaportant aodel paraaeters are: bulk density, cell size, cell elongation and orientation, gas filling and foaa thickness.

A second topic of this project was the developaent of a heat flow aeter apparatus, not as a goal in itself, but aerely because this apparatus is an essential instruaent for quick aeasureaents of the theraal conductivity (A ) of insulating aaterials. Although for aany years theraal conductivi ties of insulating foaas have been accurately aeasured, there is still no apparatus for reasonably quick aeasureaents with an accuracy of ± 2 %. There is a need for such a device, because accurate aeasureaents using the guarded hot plate aethod, which is an absolute aethod, take about one day per aeasureaent. So when theraal conductivities of a series of slabs are aeasured at several different teaperatures it takes a aonth or longer to do so.

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This is reduced considerably by the use of a relative heat fIon meter aethod, in which heat fluxes are aeasured by heat floH aeters. The flux through a slab with a sell known theraal conductivity is coapared with the flux through the unknonn sanple. In this study these calibration slabs sere supplied by the Commission of European Communities.

In this way several measurements per day are possible, Rith an acceptable accuracy of about ± 3 % in the absolute value of A.

For aeasureaents on one single apparatus the repeatability of the aeasured values for tRO speciaens is higher, the differences being ± 1 %.

k third topic of investigation has been the ageing process in foams. Re especially investigated the ageing in foaas that are protected against the infusion of air. In these foaas the gas coaposition Rill change due to absorption in the solid polyaer. This absorption process was studied.

1.3 Outline of the investigations.

Chapter 2 deals Rith theraal insulation aaterials in general and explains the benefits of closed cells insulators such as polyurethane foaa.

The production process of polyurethane foaa and its cheaistry is briefly described, as are the aain heat transfer mechanisms.

The physical aodels for heat transfer are presented in chapters 3 and 4. In chapter 3 the pure conduction in foaas is modelled. This aodelling is necessary because of the irregular distribution of gas and solid in foaa slabs. For this purpose the foaa is quite often modelled by a structure of regularly arranged (soaetiaes staggered) cubical or elongated cells, in which the solid aaterial is uniforaly distributed over the cell Rails. Other authors use regularly arranged dodecahedrons as a cell aodel.

Foaa aodels in which aost of the solid aaterial (about 80 %) is concen trated at the intersections of the cell walls have recently been seen aore often in literature. This concentration of solid is called a ' strut' , and the aodel will be called the 'strut aodel'.

Soae analytical equations are presented in chapter 3 for the coabined heat transfer by solid and gas conduction. Most of these equations are based on the saae cell aodel, regularly arranged gas filled rectangular (or cubical) cells, where the solid is uniforaly distributed over the cell

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■alls. Based on this aodel there are two different approaches for calcu lating the heat fluxes and both are presented here.

Recent research at the Massachusetts Institute of Technology (621 indicates that the 'strut nodel" Rill be a better cell aodel. Equations for the purely conductive heat fluxes according to this nodel are also presented in chapter 3.

In chapter 4 the radiative heat transfer is modelled. For calculations of radiative fluxes several aodels can be used, Rhich can be divided into tRO groups.

In the first group the foam is seen as a continuum, Rith empirical averaged radiation properties for thin layers (tRO-f lux-model [6,24,38,631: approxi mate analytical solution (711).

The other approach aodels conductive and radiative fluxes in every cell in a physical Ray, using real optical properties of the aaterial (lamellae aodel, 1361).

One of the intentions of this research prograaae Has the reduction of radiative transfer by influencing aaterial properties. The lamellae aodel is very suitable for this and has been chosen for coaputing heat transfer in foams.

In chapter S several types of apparatus for theraal conductivity measure ments of foam slabs are described.

In this chapter Re also presented our relative heat floR aeter apparatus. Attempts at absolute calibration of this apparatus and the probleas that occurred are presented in appendix 4.

Foam characterization is done in chapter 6, where the parameters are presented that affect the thermal conductivity of a foaa slab. Special attention is given to the gas coaposition in the cells. This is iaportant for the conductive heat transfer. Special attention is also given to the infrared properties Rhich are important for the radiative part of the heat flux through the foam. Each section of this chapter describes the Ray that such a parameter is measured, or calculated froa the measured foaa proper ties.

Chapter 7 deals Rith coaputer siaulations, using the physical aodels of the foregoing chapters. The results of the siaulations based on these aodels

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are presented in this chapter, ichere the theraal conductivity of the foam slabs is plotted as a function of foaa parameters such as density, foam thickness, cell size and so on. Fro» these siaulations Re can deduce the essential properties of a good insulating foaa.

In chapter 8 the measured theraal conductivity of several foam slabs is presented. Aaongst these there are soae special samples aith pigments, and some Hith radiation shields. These are supplied by the industries partici pating in the S. 0. K. Iaportant results of aeasureaents by other authors are also presented.

Chapter 9 concerns the ageing of foaas. Soae basic information about gas diffusion (air, CO. , and trichlorofluoroaethane (Refrigerant 11) ) and absorption of gases in the solid aaterial is presented. The absorption of Refrigerant 11 (R11) in solid polyurethane is investigated more closely, in theory and practice.

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CHAPTER 2 THERMAL INSULATION

2.1 Thermal insulation in general.

The great variety of types of . thermal insulations and their applications have one thing in common: the intention to reduce the heat fluxes from the insulated space to the surroundings, or vice versa.

For aost applications energy saving is the ultimate goal for which the insulation is used. Another reason can for example be the protection of human operators from extreme temperatures.

Basically several types of insulators can be distinguished, by their structure, but they all consist of a solid and a gas phase, with the excep tion of vacuum insulations.

These vacuum insulations are used in very low temperature techniques: super insulations. For refrigerated lorries, or cold stores, such a vacuum insu lation is not suitable, because it demands a strong (and heavy) mechanical construction to withstand the atmospheric pressure on these large surfaces. Quite recently a new type of vacuum insulation has been produced (Nippon Sanso K. K. , Japan), based on a granular calcium silicate, encased in stain less steel sheet faces. This volume is evacuated. It provides good insula tion ( A = 0.012 H/m. K) with sufficient mechanical strength. This kind of technique in principle can be used for the insulation of lorries, but the insulation is vulnerable. Once the vacuum is destroyed, the insulation effectiveness decreases drastically, as does its mechanical strength. For this reason vacuum insulations are not included in this study, and we only consider gas filled insulations.

In one such type of insulation gas is enclosed in the solid material. Bxamples of this closed cell structure are polystyrene, polyurethane and fenolaldehyde foam and expanded glass and cork.

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In a second type the gas is not enclosed, it forms the continuous phase and the particles of the solid material are discontinuously arranged in the insulation material. Examples of this are granular and ponder insulations or fibre insulations such as glass- and rock-Rool, kapok, cotton and nool.

Rhen the gas and the solid both form a continuous phase Re have an intermediate situation, an open cell structure, of union ureumformaldehyde foam is an example.

A combination of open and closed cells is found in foam rubber and in some polyurethane foams.

All of these insulations are described in more detail by Timmermans (71). Considering the aims of the investigation, the closed cell foams are the most promising, because the gas occluded in the cellular voids can be one Rith good insulating properties e.g. refrigerant 11 ( CFC1, ) instead of air. The bulk of current thermal insulations consists of closed cell foams. So improvements on this type of foam Rill be the most interesting commercially.

Closed cell foams have several important features.

For instance, du Prez 155) reported the follORing as typical properties of a polyurethane foam:

-very good thermal insulation

-very good Rater diffusion resistance -great mechanical stiffness

-usable from -100 to +100 °C 3 -IOR density (about 30 kg/m ) -good ageing properties

Polystyrene foam, another closed cell structure, is also suitable for insulating purposes, but due to the fact that polystyrene is permeable to all normally used fill gases the air-filled equilibrium state Rill be reached in a very short time, unless the foam is properly sealed. This is a disadvantage, because air is not a good insulator.

Fenolaldehyde foam is a slightly better insulator than polyurethane foam, but mechanically it is not as strong, Rhich reduces the number of possible applications.

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In this research project efforts concentrate on polyurethane foans, from Hhich heat fluxes by conduction and radiation are calculated, using a phys ical model. The heat fluxes are also measured, using a heat floR meter apparatus.

2. 2 Rigid polyurethane foam.

The first rigid polyurethane foam Has made by I. Q. Farben during 1940-1945, using toluene diisocyanate ( TDI), but there Rere technical defi ciencies and toxicity troubles Rith this type of system. In the early 1950's, I.C.I. Ltd. developed the low toxicity system based on diisocyana-to-diphenyl methane compositions ( H D D and the first systems using this isocyanate and polyester resins Here marketed in 1957. Later in 1959 polyether resins Rere employed Rith this isocyanate.

The first large-scale applications of the I.C.I, systems Rere the insula tion of portable refrigerated containers, the insulation of the holds and domestic chambers of ships, and the insulation of chemioal plants (taken from Buist, Hurd and Stafford 191).

The basic chemistry for polyurethane foam production is the exothermic reaction of a polyisocyanate with a polyalcohol, forming polyurethane.

OCM-B-MCO ♦ HO-B' -OH — — R - HH-C-0 - R' - O-C-HH - R — + heat

I I

0 0 diisocyanate dialcohol urethane urethane

The use of an isocyanate or alcohol Rith more than tRO functional groups leads to a 3-dimensional, cross-linked structure (thermo-setting).

Thus the polymerisation starts Rith a mixture of two liquid components (isocyanate and alcohol), and finally forms a rigid polymer, Rith a viscous gel as an intermediate fase.

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-R-HCO + H20 — - -R-HH2 + COjT

isocyanate Hater amine carbon dioxide

folloned by:

-R-HH, + OCH-R ■ R - HH-C-HH - R —

2

I

0

amine isocyanate urea

Here carbon dioxide is formed. This gas blons up the reacting mass and changes it into a cellular foam. This is called the bloning reaction, or chemical blowing. The resulting amine reacts Hith isocyanate and becomes a part of the molecular chain.

For the production of insulating foams another bloHing principle is important; physical bloning. A Ion boiling solvent is used as bloHing agent. The heat produced by the exothermic reaction of the isocyanate and the alcohol makes it boil and the resulting gas bloHs up the foam.

The use of trichlorofluoromethane (refrigerant 11 or R11) and dichlorodi-fluoromethane (refrigerant 12 or R12) are of special interest because of their Ion thermal conductivity coefficient. Of these R11 is the most com mon, because of the convenient boiling temperature (23'C), nhich makes it easy to process.

In real foam manufacturing both bloaing mechanisms are used at the same time.

Several additives and catalysts are added to the bulk cheaicals to iaprove the foam quality and the reaction procedure, exaaples: surfactants (essen tial for the cell forming process), flame retardants and pigments.

The tRO mixtures of cheaicals, Hith the basic components isocyanate and alcohol, are mixed together at the last moment Hhen the foaming process has to start. In one type of foaming, called block foaming, the reacting mix ture of components is spread over a conveyor Hith a moving sheet of paper

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ALCOHOL SIDE CONVEYOR

-MOVING SPRAY GUN

CUT-OFF

SAW

Figure .( 2. 1).

The polyurethane block foam production line.

in a 0 shape, about tuo meters Ride and one meter high (at both edges), see figure (2.1). The reaction starts immediately and the mixture rises, until viscosity becomes too high to bloR the foam any further (free rising, up to t 1 m. high). At the end of the production line the foam is cut into length of about 30 meters.

The cells in the foam are elongated parallel to the foam rise, in a verti cal plane, and the insulating plates are usually cut from this block in a horizontal plane. This causes the heat flui direction to be parallel to the cell elongation.

The cell gas pressure is originally more or less atmospheric, Rhile the foam temperature during production rises to about 160*C, due to the exot hermic reaction. After some time this reaction stops and the foam tempera ture decreases to that of the environment (curing process), Rhile the gas

5

pressure decreases to approximately 0.7x10 Pa., Rhich is in agreement Rith the ideal gas laR, Rhen assuming constant cell volume.

The curing process takes about a Reek. During this time the foam block Rill be stored in a Rell ventilated environment.

Rhen the foam has been cured some mechanical processing Rill folios, during Rhich the foam block is cut to the desired dimensions, for example panels or pipe insulations. Dote that this type of insulation is not fully homo geneous. The cell size and density at the top differs from that in the middle, which affects the effectiveness of the insulation.

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alcohol isocyanate

cover sheet

Figure ( 2. 2).

The polyurethane laminator foam production line.

In another type of foaming, laminator foaming, the foam rises until it is suppressed by a second conveyor at the top, Rhich compresses the foam to a certain thickness, usually 20 to 60 mm., see figure (2.2). Both conveyors are covered with paper or a coating layer such as bitumen. Sometimes solid plates or metal layers are used for this (double metal facing). The foam adheres to these layers, forming a sandwich panel,

By this technique cell size, cell elongation and gas pressure are influ enced by the outside mechanical forces, Rhich can be advantageous as Rill be seen further on in this thesis. The heat flux direction in this type of foam Rill be parallel to the foam rise.

The foams produced on the laminator are thinner and cool down much faster. Their properties are more uniform throughout the foam.

The laminator foams are directly cut to the desired length and are prepared for transport to the customer.

The foregoing tRo processes are 'horizontal foaming' systems. A third foaming process is ' vertical foaming' . To the author' s knoRledge it is rarely used and then only as a batch procedure.

The chemicals are released in a mould (open at the top), consisting of tRo vertical boundary surfaces, set at a distance equal to the desired foam thickness. Quite often these boundary surfaces are a part of the construc tion, the foam adheres to them, forming sandwich panels. In this process

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ISOCYANATE

Figure (2. 3).

The vertical foaming systea, a batch procedure.

the foaa is allotted to rise freely. Usually several layers are foamed, one after another, to fill the mould completely. (See figure 2.3).

This technique produces cells that are elongated in the foam rise direc tion, perpendicular to the heat flux direction. The foaa produced in this »ay is not uniform, the top of each foaa layer has smaller cells and a higher density than the bulk of the foaa.

For insulating purposes the best type of foaas are, at the moment, prod uced on the laainator described above.

2. 3 Beat transfer Mechanisms.

It is important to understand the heat transfer in foams. In general three modes of heat transfer are distinguished:

- conduction. - radiation. - convection.

They «ill be described in short.

-Conduction: A heat flux occurs through a material along the temper ature gradient, from the hot to the cold side, proportional to the temper ature gradient.

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-Radiation : Energy is transferred via electromagnetic naves. In contrast to conduction there is also radiative transfer from cold to hot surfaces, although the net fluxes Kill be in the opposite direction. The emitted energy of a radiating surface is proportional to the fourth poner of the absolute temperature.

This mode of heat transfer also exists in vacuum, so without intermediate materials. If there is a medium, radiation can interfere Kith it, in the form of absorption and scattering.

-Convection: Energy is transferred by way of material transport. At hot surfaces molecules take up energy which is released again when they reach colder surfaces. So, for convective heat fluxes a moving medium is indispensable.

Even when convection is not created deliberately (forced convection), one should be aware of free convection in gases or liquids in the presence of temperature differences. This is caused by gravity and by the dependence of the density on temperature; hot gases or liquids have a lower density than cold ones, resulting in an upward force that produces (undesired) convection.

Heat transfer in foams in particular is governed by the first two mecha nisms. This is shown for example by Timmermans (71} and Sparks [651. They proved from theoretical and experimental research that convection is of no importance in insulating foams at cell sizes of 3 mm. or less. Schuetz (62J proved this to be 1.5 mm. for B11 (CC13F) blown foams.

So for normal polyurethane insulations, having an average cell size of no more than 0. 5 mm. , convection is negligible, which leaves conduction and radiation as the transport mechanisms.

From these the combined effect of gas and solid conduction originally was far more important than radiation, so in the past efforts concentrated on reducing conduction. This has been achieved by using high molecular fill gases like refrigerant 11 (CCI3F), or refrigerant 12 (CC12F2). As a result the ratio of radiative and conductive heat transfer increased, because the radiative flux was hardly influenced. According to Timmermans (701, for example, radiation may cause 30 % of the total heat flux (through expanded polystyrene-foam). So today radiation cannot be neglected any longer when searching for better insulations.

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Using the physical models of the foam presented further on the heat flux through the foam is calculated from the foam properties and the temperature gradient. From this heat flux the apparent thermal conductivity coeffi cient (A ) is derived.

Quite often in literature Re find the equation:

A = Ac + AR (2. 1)

«here Ac = thermal conductivity caused by conduction (H/m. K)

AV. = thermal conductivity caused by radiation ( H/m. K)

Because radiation and conduction are interacting in foams, there is not a simple conductive, nor a radiative part of the thermal conductivity, Rhich makes (2.1) a bit artificial. This is sometimes solved by defining A'R as

the difference of the apparent thermal conductivity ( including the conduc tion/radiation interaction) and the calculated purely conductive part of heat transfer, A. , in the absence of radiation:

c

A'p = A - Ac ( 2. 2)

Rhere A . folloRS from the thermal conductivities of the solid material ( A ) and the void gas ( A ) , as Hell as their volume fractions. _s

g

As >ill be seen in chapter 3, A depends (strongly) on the foam model used, so this has an effect on AR , Rhen it is defined in this Ray.

Rhen the dependence on temperature of the gas thermal conductivity ( A ) is included, A_ is no longer constant over the foam (nhatever cell model is used), because of the temperature gradient over the foam. Of course, it is possible to use an average value of A . over the foam, but the defini

te

tion of A'R , using <2.2), becomes even more artificial.

For practical purposes the interaction of radiation and conduction is important, especially for thin foam layers, or reflecting boundary sur faces.

Because of that, in this thesis the apparent foam thermal conductivity coefficient of the combined and interacting effects Rill be presented throughout.

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He Rill split this apparent thermal conductivity into a conductive ( Ac) , a radiative (*R) and an interactive part ( Aj).

So:

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CHAPTER 3 GAS AND SOLID CONDUCTION

3. 1 Cell model, g a s - f r a c t i o n and thermal conductivity.

In general, c o n d u c t i v e heat transfer in an isotropic medium is described by Fourier' s Ian:

q = -A • grad T ( 3. 1)

2 «here q = areal density of heat f loir rate ( H/m )

A = thermal c o n d u c t i v i t y ( H/ra. K) T = thermodynamic t e m p e r a t u r e ( K)

which is t h e defining e q u a t i o n of thermal conductivity, A. This is a m a t e  rial property; f o r a g i v e n A heat fluxes can be c a l c u l a t e d f o r any tempera ture gradient.

Onfortunately A i s in g e n e r a l dependent on temperature, so f o r large temp erature d i f f e r e n c e s c a l c u l a t i o n s become more complex.

In the case of insulating foams, thermal conduction r e s u l t s from c o n d u c  tivity in the solid and t h e gas phase. C a l c u l a t i n g t h e combined thermal conductivity of such an a n i s o t r o p i c c e l l u l a r structure r e q u i r e s for m o d e l l  ing the foam, because of t h e cell size d i f f e r e n c e s and the irregular arrangement of p o r e s in the foam.

Hhen a s s u m i n g all c e l l s t o be cubical, of t h e same size and regularly arranged, t h e cubical cell model c a n be obtained ( S t e p h e n a o n [803, Koglin ( 3 6 ) , Timmermans ( 7 1 3 ) .

Hore generally a n elongated cell model c a n be used to describe anisotropy in the d i r e c t i o n t h e foam r i s e s , s e e figure ( 3 . 1 ) .

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Thermal c o n d u c t i v i t y of such m o d e l l e d c e l l u l a r s t r u c t u r e s h a s been c a l  c u l a t e d by s e v e r a l authors. T h e f o r m u l a e obtained h a v e b e e n g a t h e r e d a n d p r e s e n t e d by T i m m e r m a n s C 7 1 ] a s Rell a s f o r m u l a e f o r e l o n g a t e d .cells a n d open cell s t r u c t u r e s . In s e c t i o n 3. 3. 4 these m o d e l s Hill b e compared. T h e c u b i c a l cell model Rill b e compared Kith a n u m e r i c a l model i n s e c t i o n 3. 4. 2.

FOAM

SLAB

HOT

COLD

CELL

MODEL

F i g u r e ( 3. 1 ) . The e l o n g a t e d cell model.

A c h a r a c t e r i s t i c property of the foam ( o r cell) is t h e p o r o s i t y ( t h e f r a c  tion by volume of gas) R h i c h i s d e f i n e d by:

( h-g) • ( b-g) • ( s-g) g g = = ( 1 - - ) - ( 1 - -

)-(1-9 h.b-s h b

(3. 2)

Rhere g = cell Rail thickness (m) h = cell dimension perpendicular to the

direction the heat floRS ( m) b = cell d i m e n s i o n p e r p e n d i c u l a r to t h e

d i r e c t i o n t h e heat f l o R S ( m ) s = cell d i m e n s i o n p a r a l l e l t o t h e

d i r e c t i o n t h e heat f l o w s ( m )

For h = b and s = a - b ( a n i s o t r o p i c i n o n e d i r e c t i o n caused by foam rise; 'a' the cell a s p e c t r a t i o ) , t h i s r e d u c e s to:

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/ - - 1 \ / g \ 3 r 2 ■> /- g \ 2 r 1 \ g

I — I • - I + 1+ - • I - I + I-2- - I • - + (1-va) = 0 (3.3)

On a macroscopic scale v can be found from density measurements, real-izing that:

cell mass = pore gas mass + solid mass

Hhen Re divide this by the cell volume Re find, after rearranging:

cell mass pore volume pore gas mass solid volume solid mass

= . + •

cell volume cell volume pore volume cell volume solid volume

This becomes: Pi = vg . P g + (1-vg) . PS (3.4) PT = insulation density (kg/m ) p - gas density (kg/m ) 9 p = solid density (kg/m )

Rhich results in:

ps " pI

Vg = (3.S) Ps - Pg

So from density measurements (see chapter 6, section 6) and aspect ratio measurements (see chapter 6, section 4) the ratio of g/h can be derived, using (3.3) and a standard computer program for finding the root. ( Only the real root Rill be physically acceptable. )

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3.2 The thermal conductivity coefficient of the foam cell.

3.2.1 The thermal conductivity coefficient of the pore gas.

One of the most important factors that determine the thermal conductiv ity coefficient of an insulating foam is the pore gas conductivity. Usu ally the gas will be a mixture of air, carbon dioxide, R11 and/or R12. For insulation purposes R11 and R12 are used as blowing agents because of their low thermal conductivity coefficients.

Air, which is an inferior insulator, will be in the foam too, for two rea sons.

- it is used in the foam production, in which it acts as a nucleus for the chemical reaction.

- it diffuses into the foam when no proper measures are taken to avoid gas diffusion either in to or out of the foam.

Carbon dioxide, with a thermal conductivity between that of air and R12, is formed in the chemical reaction of isocyanate with water (see section 2.2). It diffuses rather quickly out of the foam when there is no vapour-tight protection.

Our attempt to compare results of measurements with those of calculations demands a suitable equation to calculate the thermal conductivity coeffi cient of the gas mixture in the voids, at different temperatures. For ideal gases we know from kinetic gas theory that the thermal conductivity is proportional to the square root of the absolute temperature. On the other hand real gases do not fit into this pattern accurately, and another temperature dependence, such as a linear one, would suit as well for a small temperature region.

First of all the thermal conductivity of the separate components will be needed. A linear regression of tabulated values (Touloukian (731) in the temperature range 250-300 K results in:

-5 f o r a i r f o r CO f o r R11 A = 0 . 0 0 2 7 3 + 7 . 8 1 • 10 . T ( ± 1 %) (U/m. K) A = - 0 . 0 0 5 6 + 7 . 4 • 1 0 ~5 • T ( ± 5 % ( H/m. K) - 5 A = - 0 . 0 0 4 1 + 4 . 0 • 10 • T ( a c c u r a c y unknown) (H/m. K) A = - 0 . 0 0 5 3 + 5 . 0 • 1 0 "5 • T ( ± 2. 5 %) ( H/m. K) f o r R12

Hext an equation will be needed to calculate the thermal conductivity coefficient of gas mixtures, A ._

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For t h i s p u r p o s e t h e L i n d s a y and Bromley formula i s a d v i s e d by T s e d e r b e r g C74J. A + £ + m i x x x x x x x 1+B • +B • +B • 1+B • +B • +B • -12 X 13 X 14 X 21 X 23 X 24 X ( 3 . 6) _*3 + *4_ X X X X X X 1 9 A 1 2 ^ 1+B • +B • +B • 1+B • +B • +B • -31 X, 3 2 X, 3 4 X , 41 X. 4 2 X. 4 3 X. 3 J 3 4 4 4

where x. = mole f r a c t i o n o f t h e i component ( - ) and: r \2 1 ! l' „ . , M. S 3 / 4 ( 1 + 3i/ T ) V'2 ! ( 1 + Si j/ T ) B = - . M + | -X • I -3 I • -1 . *• M, ' ( -1 i j 4 I i U . K H. ' ( 1 + S . / T ) I i ( 1 + S . / T ) I ^ 3 v. 3 , I 1 Kith : u = viscosity ( kg/m. s) H - molecular Height ( kg/kaole)

s

ij= V

S

i-

3

J

where T. is the boiling temperature of component i at a pressure of 1

b» l

atm. S. is called the Sutherland constant.

Viscosity is dependent on temperature too. Here tabulated values from the ' Encyclopedie des Oaz' 184] are used.

After linear regression we get:

for air : u = 3. 38 • 1 0- 5 + 5 . 0 3 • 10~7 • T (1 bar, 250-300 K) for CO : u = 0.33 ■ 10~5 +4.91 . 10~7 • T (1 bar, 250-300 K)

Heat transfer reduction in closed cell polyurethane foams