Measurement of Heat Transfer Coefficients for Polymer Processing Simulation

Measurement of heat transfer coefficients for polymer processing simulation

Polymeric Materials IAG Wednesday 12 March 2008

Angela Dawson, Martin Rides and Crispin Allen Heat transfer coefficient

• Heat transfer coefficient is boundary condition for process simulation

• In injection moulding & compression moulding – Polymer to metal – Polymer-air-metal (GASM, shrinkage)

• In extrusion & film blowing – Polymer to fluid (eg air or water)

• Apparatus built to measure heat transfer coefficient at mould/polymer interface and mould polymer/air interface in order to investigate the significance of different interfaces to commercial processing

2 Heat transfer apparatus (HTC) Loading (pressure) platform

Adjustable screws to raise or lower upper (cold) plate

Col d pl ate

Specimen

Hot plate

3 Heat transfer coefficient calculation

q h = T 1 − T 2

Heat transfer coefficient (h) across an interface is the heat flux per unit area

(q) across an interface from one material of temperature T1 to another material of temperature T2:

h = heat transfer coefficient (Wm-2K-1) q = heat flux at ‘hot’ surface (W.m-2)

T1 = temperature on ‘hot’ side of interface (K) T2 = temperature on ‘cold’ side of interface (K)

4 Thermal resistance calculation

δT 1 xl R= =∑∑ri =∑ + Q i hi l λl

For a multi-layer system with heat flow in the through-thickness direction:

Total thermal resistance R (m².K.W-1) = sum of thermal resistances of

the individual layers rl

Where: hi is heat transfer coefficient at interfaces xl is thickness of layer λl is thermal conductivity of layer

5 Thermal resistance of PMMA specimen (2 mm) without and with air gaps of varying thickness

0.06 ‘Cold’ plate Air gap 0.05 Polymer specimen (2 mm) Hot plate 0.04

0.03

0.02

0.01

Thermal resistance, (m^2.K)/W 0 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 Thickness of air gap, mm 6 Comparison of measured HTC coefficient across air gap with HTC predicted by λ air model

600

) 500 .K 2 ^ (m / 400 t, W n

ficie 300 f e o c r 200 sfe n tra t a

e 100 H y = 28. 812x -1 R 2 = 1 0 0. 00 0. 20 0. 40 0. 60 0. 80 1. 00 1. 20 1. 40 T h ic k n es s of ai r g ap , m m 7 Effect of errors on derived heat transfer coefficients

20000 Measured data

HTC calculated using Equation 17

K) 16000 2

12000

8000

4000 Heat transfer coefficient, W/(m Heat transfer coefficient,

0 012345678 Measured thermal resistance differences, arbitrary units

8 Thermal resistance of PMMA specimen (2 mm) without and with air gaps of varying thickness

0.06 ‘Cold’ plate Air gap 0.05 Polymer specimen (2 mm) Hot plate /W )

.K 0.04 2 m (

, 0.03

0.02

0.01 R interface Thermal resistance 0 0.00.20.40.60.81.01.21.4 Thickness of air gap, mm

9 Effect of an air gap on HTC measurements and repeatability of HTC measurement across a steel/air Interface

• Effect of air gap on thermal resistance quantified: air gap equivalent to polymer of 6.6 x thickness

• Experimental data shows a rapid decrease in heat transfer coefficient across the air gap is observed as thickness of the air gap increases.

• Good correlation with heat transfer coefficient values obtained from calculations based on the thermal conductivity of air.

• Heat transfer coefficient data could be used to provide more accurate modelling data for polymer processing and product design

10 Thermal conductivity and diffusivity intercomparison in support of the development of ISO 22007 Parts 1 to 4 Plastics - Determination of thermal conductivity and thermal diffusivity Plastics thermal conductivity standards

ISO TC61 SC5 WG8 Thermal Properties

ISO 22007 Plastics – Determination of thermal conductivity and thermal diffusivity

ISO/CD 22007-1 Part 1: General principles

ISO/DIS 22007-2 Part 2: Transient plane source hot-disc method (Gustafsson method)

ISO/DIS 22007-3 Part 3: Temperature wave analysis method

ISO/DIS 22007-4 Part 4: Laser flash method

12 Plastics thermal conductivity standards

Potential proposal to develop Line Source Method for Thermal Conductivity as part of ISO 22007 series

Method currently standardized as: • ASTM D 5930-01, Test Method for Thermal Conductivity of Plastics by Means of a Transient Line-Source Technique

However this does not make provision for: • effect of applying pressure to minimize measurement scatter, and • effect of pressure on thermal conductivity • inadequate calibration procedure • over-simplified analysis of data

Your support?. Other methods?

13 Plastics thermal conductivity standards - intercomparison

Intercomparison of thermal conductivity methods

Carried out in support of standardisation activity Repeatability / reproducibility of methods was unknown To cover transient methods - but not excluding steady state methods Results to help prepare precision statement for ISO 22007 series

Led by NPL/Japan

14 Thermal conductivity and diffusivity intercomparison outline

• Thermal diffusivity and thermal conductivity • Initial study involved project leaders • Two grades of PMMA studied: one supplied through NPL and the other from Sumitomo Chemical (Sumipex) • Various measurement techniques used in round robin study: Temperature wave analysis method Transient plane source hot-disc method (Hot Disk) Laser flash method Transient line source probe Guarded Hot plate / heat flow meter

15 Summary of thermal conductivity and diffusivity methods

Speci Thermal Nominal men Pre- Uncertainty estimate Method conductivity specimen size, treatment (95% confidence level) / diffusivity thickness, mm mm λ: 2% - 5% φ 5; Hot Disk λ, α, (Cp) 2, 3 α: 5% - 10 % φ 10 (repeatability 1% - 2%) Temperature 5% α 0.01 3 x 5 wave analysis (repeatability < 1%) Laser flash silver (cast PMMA) α 2 Disk paint 8% only) (30 µm) 1.14 – cast, sputtered 3% - 5% Laser flash α Disk 1.49 – extrude graphite (repeatability < 1%) Transient line- moulded in- moulded λ (repeatability 3% - 6%) source probe situ in-situ Heat flow meter λ 2, 3 5% Heat flow meter λ 2, 3 φ 80 (repeatability 3%)

16 Thermal conductivity of the cast PMMA measured by line-source probe, Hot Disk and heat flux meter methods

0.22 Cast PMMA 0.21

0.2

0.19

0.18

0.17 HFmeter_Sumipex_Lobo_conductivity

LS_Sumipex_Lobo_cooling, TC 0.16 LS_Sumi_Lobo_heating, TC Thermal conductivity, W/(m.K) Thermal conductivity, Hotdisk_Sumipex_conductivity 0.15 HFmeter_NPL_Sumipex

0.14 0 20 40 60 80 100 120 140 160 180 200 Temperature, °C 17 Thermal diffusivity of the cast PMMA measured by Hot Disk, laser flash and temperature wave analysis methods

1.4E-07 Cast PMMA TWA_meas 1.3E-07 LF_LNE_Sumipex_diffusivity1 LF_LNE_Sumipex_diffusivity2 LF_Lobo_Sumipex_diffusivity 1.2E-07 Hotdisk_Sumipex_diffusivity /s 2

1.1E-07

1.0E-07

9.0E-08

Thermal diffusivity, m Thermal diffusivity, 8.0E-08

7.0E-08

6.0E-08 0 20 40 60 80 100 120 140 160 180 200 Temperature, °C 18 Thermal conductivity of extruded PMMA measured by line-source probe, Hot Disk and heat flux meter methods

0.25

Extruded PMMA

0.2

0.15

Hotdisk_AAJHF_conductivity 0.1 HFmeter_NPL_AAJHF_conductivity Linesource_Lobo_AAJHF_conductivity_heating-sheet Linesource_Lobo_AAJHF_conductivity_cooling-sheet 'PMMA-AAJHF001 (line source - cooling scan) – pellets 0.05 Thermal conductivity, W/(m.K) Thermal conductivity, PMMA-AAJHF001 (line source - heating) – pellets

0 0 20 40 60 80 100 120 140 160 180 200 Temperature, °C 19 Thermal diffusivity of extruded PMMA measured by Hot Disk, laser flash and temperature wave analysis methods

1.2E-07 Extruded PMMA

1.0E-07 /s 2 8.0E-08

6.0E-08

4.0E-08

TWA_AAJHF_diffusivity Thermal diffusivity, m Thermal diffusivity,

2.0E-08 LF_Lobo_AAJHF_diffusivity Hotdisk_AAJHF_diffusivity

0.0E+00 0 20 40 60 80 100 120 140 160 180 200 Temperature, °C

20 Thermal conductivity – thermal diffusivity conversion

Thermal conductivity λ can be calculated from thermal diffusivity α, and vice-versa, given the

specific heat capacity Cp and density ρ of the sample at the same temperature using:

λ = ρ C pα

21 Specific heat capacity, Cp, of the cast PMMA measured by DSC

2.8 Cast PMMA 2.6 7% tolerance bars on mean values

2.4

2.2

2.0

1.8 AAJH M001 Sample 5 - 035 AAJH M001 sample 6 - 036 1.6 AAJH M001 sample 7 - 037 NPL Average specific heat capacity, J/(g.K) Lobo 1.4 Hay / SUMIPEX 000 lot 6621114

Specific heat capacity, J/(g.K) Specific heat capacity, mean Cp (HD calc) 1.2

1.0 0 20 40 60 80 100 120 140 160 180 200 Temperature, °C

22 Density of the cast PMMA: Archimedes and dimensions & weight methods 1200 Cast PMMA

1190 3 1180

1170 Hay / SUMIPEX 000 lot 6621114

Density, kg/m Hay 23C / SUMIPEX 000 lot 6621114 Lobo Sumipex 000 Lot 6621114 22.3°C AAJH M001 NPL 1160 AAJH M001, NPL 2 NPL dimensions y = -1.439E-03x - 1.509E-01x + 1.188E+03 mean (+/- 1% for 95% confidence level)

1150 10 20 30 40 50 60 70 80 90 100 Temperature, °C

23 Specific heat capacity, Cp, of extruded PMMA measured by DSC

2.5 Extruded PMMA

6% tolerance bars on mean values 2

1.5

Lobo NPL ref 22-42 Average specific heat capacity, J/(g.K) 0.5 NPL ref 14-17, Cp, AAJHF002 Specific heat capacity, J/(g.K) Specific heat capacity, Mean Cp (HD calc)

0 0 20 40 60 80 100 120 140 160 180 200 Temperature, °C

24 Thermal conductivity of cast PMMA: measured - heat flux meter, line-source probe, Hot Disk; calculated from - laser flash, temperature wave analysis, Hot Disk

0.22 Cast PMMA 0.21

0.2

0.19

0.18 HFmeter_Sumipex_Lobo_conductivity LS_Sumipex_Lobo_cooling, TC 0.17 LS_Sumi_Lobo_heating, TC Hotdisk_Sumipex_conductivity HFmeter_NPL_Sumipex 0.16 TWA cond_calc LF_LNE_Sumipex_ cond_1 _calc Thermal conductivity, W/(m.K) Thermal conductivity, LF_LNE_Sumipex_ cond2_calc 0.15 LF_Lobo_Sumipex_ conductivity_calc Hotdisk_Sumipex_diffusivity calc cond HD Axial Therm cond _calc_prev 0.14 0 20 40 60 80 100 120 140 160 180 200 Temperature, °C 25 Thermal diffusivity of cast PMMA: measured - Hot Disk, laser flash, temperature wave analysis; calculated from - Hot Disk, heat flux meter line-source probe 1.5E-07 TWA_meas Cast PMMA LF_LNE_Sumipex_diffusivity1 1.4E-07 LF_LNE_Sumipex_diffusivity2 LF_Lobo_Sumipex_diffusivity Hotdisk_Sumipex_diffusivity Hotdisk_Sumipex_conductivity calc diff 1.3E-07 LS_Sumipex_HL_cooling, TC diffusivity_calc LS_Sumi_HL_heating TC diffusivity_calc /s

2 HFmeter_NPL_Sumipex____thermal diffusivity_calc 1.2E-07 HFmeter_Sumi_HL_conductivity diffusivity_calc HD_Sumipex_axial _diffusivity_prev. HD_Sumipex_radial_diffusivity_prev. HD axial Diff_calc_prev. 1.1E-07 HD radial Diff_calc_prev.

1.0E-07

9.0E-08 Thermal diffusivity, m Thermal diffusivity, 8.0E-08

7.0E-08

6.0E-08 0 20 40 60 80 100 120 140 160 180 200 Temperature, °C 26 Thermal conductivity of the extruded PMMA: measured - line-source probe, Hot Disk and heat flux meter; calculated from - laser flash, temperature wave analysis, Hot Disk 0.25

Extruded PMMA

0.2

0.15

Hotdisk_AAJHF_conductivity HFmeter_NPL_AAJHF_conductivity 0.1 Linesource_Lobo_AAJHF_conductivity_heating-sheet Linesource_Lobo_AAJHF_conductivity_cooling-sheet 'PMMA-AAJHF001 (line source - cooling scan) – pellets PMMA-AAJHF001 (line source - heating) – pellets TWA_AAJHF_cond_calc LF_Lobo_AAJHF_cond_calc

Thermal conductivity, W/(m.K) Thermal conductivity, 0.05 Hotdisk_AAJHF_cond_calc

0 0 20 40 60 80 100 120 140 160 180 200 Temperature, °C 27 Thermal diffusivity of extruded PMMA: measured - Hot Disk, laser flash, temperature wave analysis; calculated from - Hot Disk, heat flow meter, line-source probe

1.4E-07 Extruded PMMA

1.2E-07 /s

2 1.0E-07

8.0E-08

6.0E-08 TWA_AAJHF_diffusivity LF_Lobo_AAJHF_diffusivity Hotdisk_AAJHF_diffusivity 4.0E-08 Hotdisk_AAJHF_diffusivity_calc

Thermal diffusivity, m Thermal diffusivity, Linesource_Lobo_AAJHF_cooling_diff calc-sheet Linesource_Lobo_AAJHF_heating_diff calc-sheet Linesource_Lobo_AAJHF_cooling_diff calc-pellets 2.0E-08 Linesource_Lobo_AAJHF_heating_diff calc-pellets HFmeter_NPL_AAJHF_diffusivity_calc 0.0E+00 0 20406080100120140160180200 Temperature, °C 28 Intercomparison summary

Good agreement obtained between methods and between thermal conductivity and diffusivity values.

The reproducibility of Cp estimated at ± 10% (95% confidence level).

The reproducibility of density estimated at ± 1% (95% confidence level).

Thermal conductivity and diffusivity values estimated to be within approximately ± 10% of mean value.

29 Differential scanning calorimetry standards

ISO TC61 SC5 WG8 Thermal Properties

ISO 11357 Plastics - Differential scanning calorimetry (DSC)

ISO 11357-1: 1997 Part 1: General principles (being revised)

ISO 11357-2: 1999 Part 2: Determination of glass transition temperature

ISO 11357-3: 1999 Part 3: Determination of temperature and enthalpy of melting and crystallization

ISO 11357-4: 2005 Part 4: Determination of specific heat capacity

ISO 11357-5: 1999 Part 5: Determination of characteristic reaction-curve temperatures and times, enthalpy of reaction and degree of conversion

ISO 11357-6: 2002 Part 6: Determination of oxidation induction time

ISO 11357-7: 2002 Part 7: Determination of crystallization kinetics

30 PPS 2008 Conference and NPL Report THE MEASUREMENT OF THERMAL CONDUCTIVITY OF AMORPHOUS POLYMERS ABOVE GLASS TRANSITION TEMPERATURE A. Dawson, M. Rides and C.R.G. Allen Modelling is used to predict cooling times during the injection moulding cycle and to reduce them through improvements in mould design leading to shorter cycle times. For these models to be reliable the data input into the model have to be accurate. Polymers have low thermal conductivities and because of this, heat transfer data are key to predicting accurate cycle times. The thermal conductivity behaviour of amorphous polymers at temperatures above the glass transition temperature (Tg) is not well described. In the literature, different experimental techniques produce data, nominally for the same polymer, describing conflicting trends in thermal conductivity behaviour above the Tg. A novel measurement instrument, the heat transfer coefficient (HTC) apparatus, has been designed and built in order to attempt to resolve the measurement issues for thermal conductivity of amorphous polymers above Tg. The repeatability of thermal conductivity for poly(methyl methacrylate) (PMMA) tested at a set temperature of 60 °C was determined as 3.0 % (2 standard deviations). The value compares with a repeatability of 8 % (2 standard deviations) for the line-source probe technique. For PMMA at 60 °C, the mean thermal conductivity value of 0.189 W/(m.K) compares with an accepted standard value for the specimen of 0.192 W/(m.K) differing from the known specimen value by 1.6 %. Therefore, the HTC instrument could be used to establish reliable thermal conductivity data for modelling predictions of cooling time during the injection moulding of amorphous polymers. The thermal conductivities for both polycarbonate (PC) and polystyrene (PS) were measured from 53 °C to 180 °C and showed an increase in thermal conductivity with temperature above the Tg. This trend is in agreement with line source probe technique data. A model predicting increasing thermal conductivity with increasing temperature above Tg was reviewed.

31 PPS 2008 Conference

INTERCOMPARISON OF THERMAL CONDUCTIVITY AND THERMAL DIFFUSIVITY MEASUREMENTS OF POLYMERS Martin Rides, Junko Morikawa, Lars Hälldahl, Bruno Hay, Hubert Lobo, Angela Dawson

Abstract Heat transport properties data on plastics are essential for the design of many plastics products. Such data are essential for process design where reliable data are required, for example, to minimise warpage and internal stresses in injection moulding. Transient methods are particularly suited for measuring heat transport properties of polymers at elevated temperatures due to their relatively short test duration, compared with steady-state methods, thereby reducing problems associated with specimen degradation. An intercomparison on the measurement of thermal conductivity and thermal diffusivity of polymethyl methacrylate (PMMA) samples using both transient and steady-state techniques has been carried out to quantify the precision of such data. The methods used in the intercomparison include the transient plane heat source (Hot Disk ®), temperature wave analysis, laser flash, line source probe and heat flow meter. Results indicate a variation in measured values of approximately ± 10%.

32 Scientific journal – accepted for publication

POLYMER – MOULD INTERFACE HEAT TRANSFER COEFFICIENT MEASUREMENTS FOR POLYMER PROCESSING A. Dawson, M. Rides, C.R.G. Allen and J.M. Urquhart

ABSTRACT Reliable process and product design for plastics through simulation requires reliable heat transfer properties data. The thermal contact resistance of interfaces can have a significant influence in simulation predictions, in particular for micro-moulding, yet the availability of data is limited. Furthermore, the formation of air gaps forming at the polymer-wall interface due to shrinkage of the polymer on cooling are not adequately modelled in process simulations. To address these issues an instrument has been developed for measuring the thermal contact resistance of interfaces relevant to polymer processing, in particular for injection moulding. It has been used to quantify the thermal resistance of the polymer-mould interface and also that of air gaps introduced between the mould surface and the polymer, thereby representing the interfaces occurring in injection moulding. Heat transfer coefficients (HTC) across a polymer-steel interface were measured to be of the order of 7000 W/(m2 K). The thermal contact resistance of the polymer-air-steel interface were in reasonable agreement with predictions assuming heat transfer across an air gap based on thermal conduction through air.

33 Scientific journal & ISO Technical Report

INTERCOMPARISON OF THERMAL CONDUCTIVITY AND THERMAL DIFFUSIVITY METHODS FOR PLASTICS Martin Rides, Junko Morikawa, Lars Halldahl, Bruno Hay, Hubert Lobo, Angela Dawson and Crispin Allen

Abstract An intercomparison of measurements of the thermal conductivity and thermal diffusivity of two poly(methyl methacrylates) is reported. A wide variety of methods were used: temperature wave analysis, laser flash, transient plane source (Hot Disk), transient line-source probe, and heat flux meter methods. Very good agreement of thermal conductivity results, and separately of thermal diffusivity results, were obtained. Similarly, good agreement between thermal conductivity and thermal diffusivity results, when converted using specific heat capacity and density values, was also obtained. Typically, the values were within approximately ± 10% of the mean value, or better. Considering the significant differences between methods and the requirements on specimen thicknesses, the level of agreement was considered to be good.

34 Thermal Analysis and Calorimetry 2008 1 - 2 April 2008, Teddington, UK Ensuring Accuracy and Relevance • The TAC series of conferences are a specialist annual event on Thermal Analysis and Calorimetry. The Conference brings together scientists, technologists, metrologists and industry specialists to discuss issues and developments in measurements related to thermal analytical techniques. • Thermal analysis and calorimetry are being applied across a wide range of industries from aerospace and petroleum engineering to medicine and packaging. The increasing role of thermal analytical techniques not only provides opportunities, but also measurement challenges, which need to be solved. • The 2008 meeting will consist of invited and contributed papers and will focus on the metrology aspects while including the techniques and latest applications to ensure data are correct, traceable and fit for purpose. Contributions are sought on all experimental and theoretical aspects of measurements in thermal analysis and calorimetry. http://conferences.npl.co.uk/tac2008/ 35 Acknowledgements

This research was carried out as part of a programme of underpinning research funded by the Department of Innovation, Universities and Science (DIUS), United Kingdom ISO TC61 SC5 WG9 members

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