Thermal conductivity of polymer melts and implications of uncertainties in data for process simulation

A Dawson, M Rides, J Urquhart and C S Brown

Division of Engineering and Process Control National Physical Laboratory

Teddington Middlesex, TW11 0LW

United Kingdom

ABSTRACT

The polymer industry needs to continue to develop innovative high value products, reduce costs and improve productivity. One key aspect of enhancing productivity is improving equipment utilisation through reduced cycle times. Modelling can be used to predict and thus minimise cycle times in injection moulding through, for example, improved mould design. A reliable model with accurate data is needed to achieve this goal. In polymer processing, heat transfer is crucial in determining cycle times due to the low thermal conductivity of polymers. Thermal conductivity measurements on a range of crystalline and semi-crystalline polymers have been made, investigating the effects of temperature and pressure on values. A line-source probe method was used at pressures from 20 MPa to 120 MPa and temperatures, in cooling, from 250 °C to 50 °C. The results clearly illustrate that pressure and temperature have a significant effect on thermal conductivity values. The polyethylene and polypropylene materials exhibited a significant step in thermal conductivity values at the crystallisation transition. A study has been conducted using Moldflow Plastics Insight simulation software to investigate the effect of uncertainties in thermal conductivity data on predictions of injection moulding. Polymer thermal conductivity shows an inverse correlation with time-to-freeze of the moulding. The time to freeze can be used as a measure of when the moulding can be ejected from the mould cavity, and is usually a significant component of the cycle time. A typical value for the uncertainty in measured thermal conductivity data of 15% for a high-density polyethylene [1] leads to an uncertainty in the time to freeze of the moulding of +18% to –13%. This clearly illustrates the importance for reliable predictions of accurately modelling the thermal conductivity data as functions of temperature and pressure and minimising the uncertainties in thermal conductivity data. 1. Introduction Plastics processing, such as injection moulding, is a rapid, high pressure process where pressure plays a critical role, for example, in the final component dimensions. Improved measurement, prediction and understanding of heat transfer in production processes can lead, for example, to improved processing equipment and materials design and increases in productivity by reducing cycle times so speeding up production. Scrap rates could also be reduced as a result of these improvements in prediction and understanding of heat transfer processes by the elimination of hot spots causing degradation, cold spots resulting in poor

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mechanical strength, e.g. at weld-lines, or excessive temperature gradients leading to internal stresses and unacceptable warpage of products. Due to the low thermal conductivity of polymers and their relatively high specific heat capacities, heat transfer is critical in determining processing cycle times. Previous studies [2] have reported that thermal conductivity is the least accurately measured property of polymers, and yet it is one of the most important material properties for polymer processing. Until recently [3] most of the experimental thermal conductivity data in the literature were obtained at atmospheric pressure conditions that are far from the actual conditions experienced during polymer processing. The measurement of thermal conductivity at high pressures and melt temperatures as reported herein brings the thermal conductivity testing close to industrial polymer processing conditions. There is increasing demand for accurate and relevant data for the behaviour of polymers at elevated pressure from designers, engineers and software manufacturers and users. The effect of uncertainty in measurement of thermal conductivity on simulation predictions of injection moulding has also to be taken into account in order to obtain the most accurate data. The study, utilising Moldflow Plastics Insight, of the effect of uncertainty of thermal conductivity measurements on the time to freeze for an injection moulded part demonstrates the need for accurate measurement data for the simulation of heat transfer within polymer processing. 2. Experimental 2.1 Method for thermal conductivity testing of polymer melts Thermal conductivity measurements were made using a commercial apparatus, the pvT 100 (SWO Polymertechnik Gmbh) with a thermal conductivity cell attached. A diagram of the instrument is shown in Figure 1. The sample (diameter 9.8 mm, length approximately 50 mm) is contained within a heated chamber, sealed at the top and bottom by PTFE seals. Pressures in the range of 15 MPa to 160 MPa can be applied to the material at temperatures from 21 °C to 280 °C. A probe containing a heating element and a thermocouple is inserted into the test sample held at constant temperature. A known voltage is then applied to the heater element in the probe for 30 seconds. The thermocouple within the probe records the temperature during this process. The heating element and the thermocouple are at horizontal distance of 0.5 mm apart and are vertically parallel to each other within the probe. The thermal conductivity of the material for each 30 seconds heating can be obtained from a plot of temperature versus ln(time) as schematically shown in Figure 2.

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T h e r m a l c o n d u c t iv it y p ro b e

P T F E se a ls

P is t o n G u id in g b a r

M e a su re m e n t C y lin d e r

H e a t e r B a n d s

S a m p le

Figure 1. Schematic of the thermal conductivity apparatus.

Tempera

ln(ti)

Dominated by initial heating ofthe probe

Linear portion of curve

determines λ

Temperature

ln (time)

Dominated by axial losses Dominated by radial losses

Figure 2. A schematic temperature-time profile for thermal conductivity measurements.

Figure 2 shows three distinct regions. At short times the temperature rise is dominated by the initial heating of the probe. At long times the rate at which the probe temperature increases decreases due to radial heat losses from the sample (heat loss out through wall of the sample chamber begins to dominate as heat has had time to reach the wall at long times). Between these two extremes there is a linear region that is characteristic of the sample’s properties.

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It can be shown [4] that the temperature rise ∆T from temperature T1 to T2 produced within the probe, over the time interval from t1 to t2 is given by

Btt

πQTTT .ln

4 2

121

=−=∆

λ (1)

where Q is the heat energy supplied to the probe, λ is the thermal conductivity of the sample, and B is a correction factor that accounts for deviations from the theoretical model. The correction factor B is determined by calibration of the instrument with a glycerol sample of known thermal conductivity. The gradient of the linear portion of the curve corresponds to QB/4πλ. Hence a value for thermal conductivity can be obtained for the material providing the applied energy is known. 2.2 Moldflow simulations Two components were selected for this study; a pipe ‘T’ piece and a simple circular disc 80 mm in diameter with variable thickness in the range 0.5 mm to 25 mm. The pipe ‘T’ piece is a substantial injection moulded component, varying in thickness with position from 4.9 mm to 7.5 mm. By contrast, the disc offers a simple geometric shape more suitable for investigating the effect of variables on predictions, including that of thickness. Figure 3 shows the model of the pipe ‘T’ piece. The mesh was created using the Moldflow modeller, and is a mid-plane shell mesh composed of two dimensional triangular elements, where the thickness of the part is an attribute of the elements. The thickness attributed to the standard pipe ‘T’ piece model is that of the real component. In addition, analyses were also performed on a half-thickness model. A cooling circuit was created in MPI using the ‘cooling circuit wizard’ using information from the mould’s engineering drawings. The coolant employed was water at 20 °C. Figure 4 shows the model of the disc, also modelled as a mid-plane mesh. The injection point is at the centre of the disc with injection normal to the mid-plane. To simulate cooling a cooling circuit was produced for this model in MPI, using water at 20 °C as the coolant.

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Figure 3. Pipe ‘T’ piece model, showing the injection location and two of the locations from which results were obtained.

Figure 4. 80 mm diameter disc model with a central injection location. The Moldflow simulations were carried out with a fill-cool-flow analysis sequence. The process settings were specified in the ‘process settings wizard’. The default automatic filling control and automatic velocity/pressure switch over were used for the simulations. A packing pressure verses time pack/holding profile was chosen, and a packing profile was described for each of the simulations. The profile for the pipe ‘T’ piece simulations was a constant packing pressure of 50 MPa for 137 s, based upon pressure information supplied by industry and the results of previous analysis to establish an appropriate holding time. The profile for the disc simulations was a constant packing pressure of 50 MPa for the default time of 10 s. Adequate

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cooling time was allowed in the simulations to ensure that the mouldings would be fully frozen by the end of the analysis. For the analyses of the disc the default values of 35 °C for mould surface temperature, 255 °C for melt temperature and 5 s clamp open time were used. The analyses of the pipe ‘T’ piece differed from this by having a melt temperature of 240 °C as used in the actual production of the pipes. ‘Time to freeze’ (Tf) is defined by Moldflow as ‘the amount of time taken for all the elements in the part to freeze to ejection temperature, measured from the start of the cycle’. During their manufacture the pipe ‘T’ pieces were ejected at 55 °C; this value has been used for ejection temperature in the pipe ‘T’ piece simulations. The disc analyses use either 55 °C or the Moldflow recommended ejection temperature for this polymer of 90 °C. 3. Results and discussion 3.1 Thermal conductivity of polymer melts Thermal conductivity measurements were made at pressures of 20 MPa, 80 MPa and 120 MPa over the temperature range, in cooling, of 250 °C to 50 °C. For each material tested, five separate thermal conductivity readings were taken for each temperature and pressure and the reported value is the average of the five thermal conductivity results. 3.1.1 Semi-crystalline polymers The thermal conductivity values obtained for PP and HDPE at 20 MPa, 80 MPa and 120 MPa over a temperature range of 250 °C to 50 °C are shown in Figure 5 and Figure 6. Percentage changes in thermal conductivity values with pressure derived from these data are presented in Table 1. The isobaric cooling plots for polypropylene and high density polyethylene show a typical “Z” shape for each of the pressures indicating a phase transition, apparent form the sharp increase in thermal conductivity on cooling due to the crystallisation process. Such semi-crystalline polymers have percentage crystallinity values typically greater than 60 % [5, 6]. Increasing the pressure from 20 MPa to 120 MPa increases the onset temperature of crystallisation by approximately 40 °C. Furthermore, the effect of pressure increases the thermal conductivity values by approximately 0.7 W/mK, or 20%.

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0.35

0 50 100 150 200 250 300

Temperature,°C

120 MPa80 MPa20 MPa

Ther

mal

Con

duct

ivity

, W/m

K

Cooling

Figure 5. Thermal conductivity of polypropylene on cooling from 250 °C to 50 °C at pressures of 20 MPa, 80 MPa and 120 MPa

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0.20

0.25

0.30

0.35

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0.45

0 50 100 150 200 250 300

Temperature,°C

120 MPa80 MPa20 MPa

Ther

mal

con

duct

ivity

, W/m

K

Cooling

Figure 6. Thermal conductivity of high density polyethylene on cooling from 250 °C to 50 °C at pressures of 20 MPa, 80 MPa and 120 MPa The thermal conductivity behaviour for polyethylene (terephthalate) and glass filled nylon at pressures of 20 MPa to 120 MPa and temperatures from 250 °C to 50 °C is shown in Figures 7 and 8. The isobaric cooling plots for polyethylene (terephthalate) and glass filled nylon show a decrease in thermal conductivity with decreasing temperature at all pressures. For these semi-crystalline materials, which typically have percentage crystallinity values lower than 60 % [7, 8], there was not the distinct “Z” shaped step increase in thermal conductivity as observed for

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PP and HDPE due to crystallisation. The effect of pressure on thermal conductivity is indicated in Table 1.

0.25

0.30

0.35

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0.45

0.50

0.55

0 50 100 150 200 250 300Temperature, °C

120 MPa80 MPa20 MPa

Ther

mal

Con

duct

ivity

, W/m

KCooling

Figure 7. Thermal conductivity of polyethylene (terephthalate) on cooling from 250 °C to 50 °C at pressures of 20 MPa, 80 MPa and 120 MPa

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0.40

0.45

0.50

0.55

0.60

0 50 100 150 200 250 300

Temperature, °C

120 MPa

80 MPa

20 MPa

Ther

mal

Con

duct

ivity

W/m

K

Cooling

Figure 8. Thermal conductivity of glass filled nylon on cooling from 250 °C to 50 °C at pressures of 20 MPa, 80 MPa and 120 MPa 3.1.2. Amorphous polymers

The thermal conductivity behaviour of acrylonitrile-butadiene-styrene, polystyrene, and polycarbonate pressures of 20 MPa, 80 MPa and 120 MPa over a temperature range of 250 °C

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to 50 °C are shown in Figures 9 - 11. These plots show a decrease in thermal conductivity with decreasing temperature at all pressures. The effect of pressure on thermal conductivity is indicated in Table 1.

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0.22

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0.32

0 50 100 150 200 250 300

Temperature, °C

120 MPa80 MPa20 MPa

Ther

mal

Con

duct

ivity

, W/m

K

Cooling

Figure 9. Thermal conductivity of acrylonitrile-butadiene-styrene on cooling from 250 °C to 50 °C at pressures of 20 MPa, 80 MPa and 120 MPa

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0 50 100 150 200 250 300

Temperature,°C

120 MPa80 MPa20 MPa

Ther

mal

con

duct

ivity

, W/m

K

Cooling

Figure 10. Thermal conductivity of polystyrene on cooling from 250 °C to 50 °C at pressures of 20 MPa, 80 MPa and 120 MPa

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0.20

0.25

0.30

0.35

0.40

0.45

0 50 100 150 200 250 300Temperature,°C

200 bar800 bar1200 bar

Ther

mal

Con

duct

ivity

, W/m

KCooling

Figure 11. Thermal conductivity of polycarbonate on cooling from 250 °C to 50 °C at pressures of 20 MPa, 80 MPa and 120 MPa Table 1: Percentage increase in thermal conductivity with increase in pressure at 250 °C

of semi-crystalline and amorphous polymers

Approximate % increase in thermal conductivity Material Pressure increase from

20 MPa to 80 MPa Pressure increase from

20 MPa to 120 MPa Polypropylene 8 23 High Density Polyethylene 7 17 Polyethylene (terephthalate) 10 16 Glass filled nylon 2 4 Polystyrene 11 17 Acrylonitrile-butadiene-styrene 4 6 Polycarbonate 5 10

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3.2 Moldflow Simulations Tables 2 and 3 provide details of the injection moulding simulations carried out for the ‘T’ piece and disc mouldings showing the values of the variable input parameters used, and give the predicted time to freeze Tf values.

Table 2: Details of the pipe ‘T’ piece analyses showing the variable input parameters and Tf results.

Analysis reference number

Model thickness

Polymer thermal conductivity,

W/(m K)

Time to freeze, Tf,

s T1 Standard 0.234 132 T2 Standard 0.117 268 T3 Standard 0.199 156 T4 Standard 0.230 134 T5 Standard 0.238 130 T6 Standard 0.269 114 T7 Standard 0.351 86.4 T8 Half 0.234 29.7 T9 Half 0.117 60.0 T10 Half 0.199 35.0 T11 Half 0.230 30.1 T12 Half 0.238 29.2 T13 Half 0.269 25.6 T14 Half 0.351 19.5

Additional simulation conditions:

Mould-melt heat transfer coefficient = 25000 W/(m2 K) Mould thermal conductivity = 29 W/(m K)

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Table 3: Details of the disc analyses showing the variable input parameters and Tf results.

Analysis reference number

Disc thickness,

mm

Polymer thermal

conductivity,W/(m K)

Ejection temperature,

°C

Time to freeze, Tf, s

D1 2 0.234 55 8.36 D2 2 0.117 55 16.8 D3 2 0.351 55 5.54 D4 2 0.247 90 5.12 D5 2 0.124 90 10.2 D6 2 0.210 90 6.03 D7 2 0.243 90 5.20 D8 2 0.251 90 5.04 D9 2 0.284 90 4.45 D10 2 0.371 90 3.40 D11 0.5 0.234 55 0.48 D12 0.5 0.117 55 1.00 D13 5 0.234 55 52.6 D14 5 0.117 55 105 D15 5 0.351 55 35.1 D16 25 0.234 55 1320 D17 25 0.117 55 2630 D18 25 0.351 55 877

Additional simulation conditions:

Mould-melt heat transfer coefficient = 25000 W/(m2 K) Mould thermal conductivity = 29 W/(m K)

3.2.1 The effect of variations in polymer thermal conductivity on the pipe ‘T’ piece The effect of variations in polymer melt thermal conductivity λ on the temperature change during the analysis of the pipe ‘T’ piece is illustrated in figure 12. The simulations predict that increasing the melt thermal conductivity causes faster cooling, and the ejection temperature is reached sooner. Figure 13 shows the effect of varying the melt thermal conductivity upon the time to freeze Tf. It is clear that Tf may be described with a simple power law where:

Tf =A λ b (2) Excellent fits to the data were found with a value for the index b of approximately -1 for both thicknesses and values of A of 29.5 and 6.71 for standard and half thickness components respectively.

3.2.2 The effect of variations in polymer thermal conductivity on the disc The effect of melt thermal conductivity on Tf predictions for the disc analyses (shown in figure 14) are similar to those from the pipe ‘T’ piece analyses. Again the exponent b values

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were approximately –1. Figure 15 shows the effect of different polymer thermal conductivity values over a range of disc thickness from 0.5 mm to 25 mm: the Tf predictions have been normalised to the time to freeze value obtained using a thermal conductivity value of 0.234 W/(m K) (standard processing conditions). The predictions suggest halving the polymer thermal conductivity value doubles the Tf value, whilst a 50% increase to the polymer thermal conductivity value reduces Tf by a third. The effect of thickness is more significant, but still small, at small thicknesses. The effect of disk thickness greater than 2 mm on Tf is less than 0.5%, and is less than 2.1% over the full range studied, Figure 15. As with the pipe ‘T’ piece simulations, Tf may be calculated using equation 2 with an index b of -1. Furthermore the value of A can be approximated for a given disc thickness, d, using equation 3, as indicated by figure 16 (for ejection temperature 55 °C). of -1. Furthermore the value of A can be approximated for a given disc thickness, d, using equation 3, as indicated by figure 16 (for ejection temperature 55 °C). A = 0.46d2 (3) A = 0.46d2 (3) Combining equations 1 and 2 and assuming b = -1 gives equation 4: Combining equations 1 and 2 and assuming b = -1 gives equation 4:

λ

2

f 46.0 dT = (4)

Figure 17 shows a compilation of all Tf values scaled by A from individual fits of equation 1 for each disc thickness in the range 0.5 to 25 mm. All the data exhibits the same general behaviour and shows good correlation with equation 4.

igure 12. The effect of different polymer thermal conductivity values on cooling at

0

50

100

150

200

250

0 100 200 300 400 500 600Time, s

Tem

pera

ture

, °C

Thermal conductivity = 0.234 W/(m K)+ 15% (0.269 W/(m K))+ 50% (0.351 W/(m K))Ejection Temperature

Flocation T1717 on the pipe ‘T’ piece model.

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y = 29.535x-1.0294

y = 6.7013x-1.0228

1

10

100

1000

0.1 1Thermal conductivity, W/(m K)

Tim

e to

free

ze, T

f, s

Standard thicknessHalf-thickness

Figure 13. The effect of different polymer thermal conductivity and wall thickness values on Tf for the pipe ‘T’ piece model.

y = 308.03x-0.9996

y = 1.2601x-1.0023

y = 1.9269x-1.0095

y = 12.354x-0.9974

y = 0.1011x-1.0679

0.1

1

10

100

1000

10000

0.1 1Polymer thermal conductivity, W/(m K)

Tim

e to

free

ze, T

f, s

25 mm, 55 °C5 mm, 55 °C2 mm, 55 °C2 mm, 90 °C0.5 mm, 55 °C

Figure 14. The effect of different polymer thermal conductivity values upon Tf for the 2 mm thickness disc model with 90 °C ejection temperature, and the 25 mm, 5 mm, 2 mm and 0.5 mm thickness disc models with 55 °C ejection temperature. .

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0

0.5

1

1.5

2

2.5

0 5 10 15 20 25 30Disc thickness, mm

Rat

io o

f Tim

e to

free

ze fo

r mou

ldin

gs,

T f(λ

)/T f

(λ =

0.2

34 W

/(m K

))

50% decrease in thermal conductivity (λ = 0.117 W/(m K))

50% increase in thermal conductivity (λ = 0.351 W/(m K))

Figure 15. Normalised Tf predictions for disc model, for thickness from 0.5 mm to 25 mm and with 55 °C ejection temperature showing the effects of different polymer melt thermal conductivity value. (The predictions for each disc thickness have been normalised to the prediction from the analysis with polymer thermal conductivity 0.234 W/(m K)).

mm to 25 mm and with 55 °C ejection temperature showing the effects of different polymer melt thermal conductivity value. (The predictions for each disc thickness have been normalised to the prediction from the analysis with polymer thermal conductivity 0.234 W/(m K)).

igure 16. The relationship between the pre-exponent A and the disc thickness for

igure 16. The relationship between the pre-exponent A and the disc thickness for

y = 0.457x2.031

R2 = 1.000

0.1

1

10

100

1000

0.1 1 10 100Disc thickness, mm

Pre

-exp

onen

t A

FFsimulations with an ejection temperature of 55 °C. simulations with an ejection temperature of 55 °C.

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y = 0.9874x-1.0153

1

10

0.1 1Polymer thermal conductivity, W/(m K)

T f/A

0.5 mm, 55 °C

2 mm, 55 °C

5 mm, 55 °C

25 mm, 55 °C

2 mm, 90 °C

Figure 17. A plot showing the correlation of Tf/A values with thermal conductivity for results from disc analyses of different thickness and ejection temperature (55 °C or 90 °C). 4. Discussion and conclusions The thermal conductivity of the polymer melt is a dominant heat transfer parameter in the injection moulding process. Measurements of thermal conductivity values under conditions approaching those of industrial polymer processing have been reported. For the semi-crystalline materials PP and HDPE, the crystallisation temperature was indicated by a step increase in measured thermal conductivity. This measurement technique therefore might be used to determine the crystallisation temperature under pressure. For the semi-crystalline PET and glass filled nylon no such sharp transition was observed. For PP and HDPE the effect of an increase in pressure resulted in an increase in the temperature at which the onset of crystallisation was observed. For the amorphous polymers, ABS, PS and PC, there was a steady decrease in thermal conductivity values with decreasing temperature. For all materials increasing the pressure increased the thermal conductivity values. These results have significant implications for process simulation where a single value for thermal conductivity is normally used, and often determined at or near room temperature and ambient pressure. For the amorphous polymers, and as shown by this work also for PET and glass filled nylon, this will result in a value used in modelling that is a lower limit to that occurring at the higher temperatures and pressures experienced in processing. In comparison, the use of a single value obtained for PP or HDPE at or near room temperature and ambient pressure will be a better approximation to the values occurring in processing. However, in

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both cases the discrepancy of the single value determined at or near room temperature and ambient pressure from that measured as a function of both pressure and temperature can be significant. The effect of uncertainties in thermal conductivity data on predictions has been quantified. If published data from the open literature is used, melt thermal conductivity could have an uncertainty as high as 50% [9]. The simulations of the injection moulding of the disc predict that a 50% reduction in the melt thermal conductivity value results in a doubling of the Tf, and that a 50% increase in melt thermal conductivity leads to a one third reduction in Tf. It has been shown that the time to freeze has an inverse correlation with thermal conductivity for both geometries investigated. For the disc model investigated, it has also been shown that the time to freeze is proportional to the square of the disc thickness. If this can be extended to other geometries, materials and processing conditions these correlations will provide a simple means for predicting processing behaviour. It is clear that the use of a single thermal conductivity value in modelling will have a significant affect on the accuracy of predictions of time to freeze, and therefore cycle times. Through the use of improved data in simulation packages, and also models to describe thermal conductivity as a function of pressure and temperature, the accuracy of predictions will be improved. 5. References [1] J. M. Urquhart and C. S. Brown, The Effect of Uncertainty in Heat Transfer Data on Simulation of Polymer Processing, NPL Report DEPC-MPR 001, National Physical Laboratory, Teddington, Middlesex, TW11 0LW, April 2004 [2] S. Chakravorty, C.S. Brown, “Significance of thermal material parameters in polymer processing”, NPL Report DMM(A) 167, National Physical Laboratory, Teddington, Middlesex, TW11 0LW, (1995) [3] F. Oemke, T. Wiegmann, “Measuring Thermal Conductivity Under High Pressures”, 2240/ ANTEC ’94 [4] R.P. Tye, “Thermal Conductivity, Volume 1”, Academic Press, London, 1969. [5] F.J. Balta Calleja, D. R. Rueda, Polymer J. 6 (3), 216, 1974 [6] G. Crespi, L. Luciana, “Olefin Polymers; Polypropylene,” Encyclopedia of Chemical Technology, Editor Kirk-Othmer, 3rd Edition, Wiley, Vol. 16, 453, 1981 [7] H.F. Mark, N.M. Bikales, C.G. Overburger, G. Menges, “Polyesters”, Encyclopedia of Polymer Science and Engineering, J. Wiley and Sons, Vol. 12, p5, 1988 [8] H.F. Mark, N.M. Bikales, C.G. Overburger, G. Menges, “Polyamides”, Encyclopedia of Polymer Science and Engineering, J. Wiley and Sons, Vol. 11, p350, 1988 [9] S. Chakravorty, “A Review of Requirements For Improved Methods Of Measuring Thermal Properties Of Polymers.” CMMT(A)246, 1999