Measurement of heat transfer coefficients for polymer processing simulation Polymeric Materials IAG

Wednesday 12 March 2008

Angela Dawson, Martin Rides and Crispin Allen

2

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 orderto investigate the significance of different interfaces to commercial processing

3

Heat transfer apparatus (HTC)

Adjustable screws to raise or lower upper (cold) plate

Loading (pressure) platform

Cold plate

Specimen

Hot plate

Adjustable screws to raise or lower upper (cold) plate

Loading (pressure) platform

Cold plate

Specimen

Hot plate

4

Heat transfer coefficient calculation

21 TTqh

=

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)

5

Thermal resistance calculation

+===l l

l

i ii

xh

rQTR

1

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

Total thermal resistance R (m.K.W-1) = sum of thermal resistances of the individual layers rl

Where: hi is heat transfer coefficient at interfacesxl is thickness of layerl is thermal conductivity of layer

6

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

0

0.01

0.02

0.03

0.04

0.05

0.06

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40Thickness of air gap, mm

Ther

mal

resi

stan

ce, (

m^2

.K)/W Hot plate

Polymer specimen (2 mm)Air gapCold plate

7

Comparison of measured HTC coefficient across air gap with HTC predicted by air model

y = 28.812x-1

R2 = 10

100

200

300

400

500

600

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

Thickness of air gap, mm

Heat

tran

sfer c

oeffic

ient,

W/(m

^2.K

)

8

Effect of errors on derived heat transfer coefficients

0

4000

8000

12000

16000

20000

0 1 2 3 4 5 6 7 8Measured thermal resistance differences, arbitrary units

Hea

t tra

nsfe

r coe

ffici

ent,

W/(m

2 K)

Measured data

HTC calculated using Equation 17

9

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

0

0.01

0.02

0.03

0.04

0.05

0.06

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4Thickness of air gap, mm

Ther

mal

resi

stan

ce, (

m2 .K

)/W

R interface

Hot platePolymer specimen (2 mm)Air gapCold plate

10

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

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

12

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

13

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?

14

Plastics thermal conductivity standards -intercomparison

Intercomparison of thermal conductivity methods

Carried out in support of standardisation activityRepeatability / reproducibility of methods was unknownTo cover transient methods

- but not excluding steady state methodsResults to help prepare precision statement for ISO 22007 series

Led by NPL/Japan

15

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 methodTransient plane source hot-disc method (Hot Disk)Laser flash methodTransient line source probe Guarded Hot plate / heat flow meter

16

Summary of thermal conductivity and diffusivity methods

Method Thermal

conductivity / diffusivity

Nominal specimen

thickness, mm

Specimen size, mm

Pre-treatment

Uncertainty estimate (95% confidence level)

Hot Disk , , (Cp) 2, 3 5; 10

: 2% - 5% : 5% - 10 %

(repeatability 1% - 2%) Temperature wave analysis 0.01 3 x 5

5% (repeatability < 1%)

Laser flash (cast PMMA)

only) 2 Disk

silver paint

(30 m) 8%

Laser flash 1.14 cast, 1.49 extrude Disk sputtered graphite

3% - 5% (repeatability < 1%)

Transient line-source probe

moulded in-situ

moulded in-situ (repeatability 3% - 6%)

Heat flow meter 2, 3 5% Heat flow meter 2, 3 80 (repeatability 3%)

17

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

0.14

0.15

0.16

0.17

0.18

0.19

0.2

0.21

0.22

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

Ther

mal

con

duct

ivity

, W/(m

.K)

HFmeter_Sumipex_Lobo_conductivity

LS_Sumipex_Lobo_cooling, TC

LS_Sumi_Lobo_heating, TC

Hotdisk_Sumipex_conductivity

HFmeter_NPL_Sumipex

Cast PMMA

18

Thermal diffusivity of the cast PMMA measured by Hot Disk, laser flash and temperature wave analysis methods

6.0E-08

7.0E-08

8.0E-08

9.0E-08

1.0E-07

1.1E-07

1.2E-07

1.3E-07

1.4E-07

0 20 40 60 80 100 120 140 160 180 200

Temperature, C

Ther

mal

diff

usiv

ity, m

2 /s

TWA_measLF_LNE_Sumipex_diffusivity1LF_LNE_Sumipex_diffusivity2LF_Lobo_Sumipex_diffusivityHotdisk_Sumipex_diffusivity

Cast PMMA

19

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

0

0.05

0.1

0.15

0.2

0.25

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

Ther

mal

con

duct

ivity

, W/(m

.K)

Hotdisk_AAJHF_conductivity

HFmeter_NPL_AAJHF_conductivity

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

Extruded PMMA

20

Thermal diffusivity of extruded PMMA measured by Hot Disk, laser flash and temperature wave analysis methods

0.0E+00

2.0E-08

4.0E-08

6.0E-08

8.0E-08

1.0E-07

1.2E-07

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

Ther

mal

diff

usiv

ity, m

2 /s

TWA_AAJHF_diffusivity

LF_Lobo_AAJHF_diffusivity

Hotdisk_AAJHF_diffusivity

Extruded PMMA

21

Thermal conductivity thermal diffusivity conversion

Thermal conductivity can be calculated from thermal diffusivity , and vice-versa, given the specific heat capacity Cp and density of the sample at the same temperature using:

pC=

22

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

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

0 20 40 60 80 100 120 140 160 180 200

Temperature, C

Spe

cific

hea

t cap

acity

, J/(g

.K)

AAJH M001 Sample 5 - 035 AAJH M001 sample 6 - 036 AAJH M001 sample 7 - 037NPL Average specific heat capacity, J/(g.K)LoboHay / SUMIPEX 000 lot 6621114meanCp (HD calc)

Cast PMMA7% tolerance bars on mean values

23

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

y = -1.439E-03x2 - 1.509E-01x + 1.188E+03

1150

1160

1170

1180

1190

1200

10 20 30 40 50 60 70 80 90 100

Temperature, C

Den

sity

, kg/

m3

Hay / SUMIPEX 000 lot 6621114Hay 23C / SUMIPEX 000 lot 6621114Lobo Sumipex 000 Lot 6621114 22.3CAAJH M001 NPLAAJH M001, NPLNPL dimensionsmean (+/- 1% for 95% confidence level)

Cast PMMA

24

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

0

0.5

1

1.5

2

2.5

0 20 40 60 80 100 120 140 160 180 200

Temperature, C

Spe

cific

hea

t cap

acity

, J/(g

.K)

LoboNPL ref 22-42 Average specific heat capacity, J/(g.K)NPL ref 14-17, Cp, AAJHF002MeanCp (HD calc)

Extruded PMMA

6% tolerance bars on mean values

25

Thermal conductivity of cast PMMA:measured - heat flux meter, line-source probe, Hot Disk;

calculated from - laser flash, temperature wave analysis, Hot Disk

0.14

0.15

0.16

0.17

0.18

0.19

0.2

0.21

0.22

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

Ther

mal

con

duct

ivity

, W/(m

.K)

HFmeter_Sumipex_Lobo_conductivityLS_Sumipex_Lobo_cooling, TCLS_Sumi_Lobo_heating, TCHotdisk_Sumipex_conductivityHFmeter_NPL_SumipexTWA cond_calcLF_LNE_Sumipex_ cond_1 _calcLF_LNE_Sumipex_ cond2_calcLF_Lobo_Sumipex_ conductivity_calcHotdisk_Sumipex_diffusivity calc condHD Axial Therm cond _calc_prev

Cast PMMA

26

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

6.0E-08

7.0E-08

8.0E-08

9.0E-08

1.0E-07

1.1E-07

1.2E-07

1.3E-07

1.4E-07

1.5E-07

0 20 40 60 80 100 120 140 160 180 200

Temperature, C

Ther

mal

diff

usiv

ity, m

2 /s

TWA_measLF_LNE_Sumipex_diffusivity1LF_LNE_Sumipex_diffusivity2LF_Lobo_Sumipex_diffusivityHotdisk_Sumipex_diffusivityHotdisk_Sumipex_conductivity calc diffLS_Sumipex_HL_cooling, TC diffusivity_calcLS_Sumi_HL_heating TC diffusivity_calcHFmeter_NPL_Sumipex____thermal diffusivity_calcHFmeter_Sumi_HL_conductivity diffusivity_calcHD_Sumipex_axial _diffusivity_prev.HD_Sumipex_radial_diffusivity_prev.HD axial Diff_calc_prev.HD radial Diff_calc_prev.

Cast PMMA

27

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

0.05

0.1

0.15

0.2

0.25

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

Ther

mal

con

duct

ivity

, W/(m

.K)

Hotdisk_AAJHF_conductivityHFmeter_NPL_AAJHF_conductivityLinesource_Lobo_AAJHF_conductivity_heating-sheetLinesource_Lobo_AAJHF_conductivity_cooling-sheet'PMMA-AAJHF001 (line source - cooling scan) pelletsPMMA-AAJHF001 (line source - heating) pelletsTWA_AAJHF_cond_calcLF_Lobo_AAJHF_cond_calcHotdisk_AAJHF_cond_calc

Extruded PMMA

28

Thermal diffusivity of extruded PMMA:measured - Hot Disk, laser flash, temperature wave analysis;

calculated from - Hot Disk, heat flow meter, line-source probe

0.0E+00

2.0E-08

4.0E-08

6.0E-08

8.0E-08

1.0E-07

1.2E-07

1.4E-07

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

Ther

mal

diff

usiv

ity, m

2 /s

TWA_AAJHF_diffusivityLF_Lobo_AAJHF_diffusivityHotdisk_AAJHF_diffusivityHotdisk_AAJHF_diffusivity_calcLinesource_Lobo_AAJHF_cooling_diff calc-sheetLinesource_Lobo_AAJHF_heating_diff calc-sheetLinesource_Lobo_AAJHF_cooling_diff calc-pelletsLinesource_Lobo_AAJHF_heating_diff calc-pelletsHFmeter_NPL_AAJHF_diffusivity_calc

Extruded PMMA

29

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.

30

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

31

PPS 2008 Conference and NPL ReportTHE MEASUREMENT OF THERMAL CONDUCTIVITY OF AMORPHOUS POLYMERS

ABOVE GLASS TRANSITION TEMPERATUREA. 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.

32

PPS 2008 Conference

INTERCOMPARISON OF THERMAL CONDUCTIVITY AND THERMAL DIFFUSIVITY MEASUREMENTS OF POLYMERS

Martin Rides, Junko Morikawa, Lars Hlldahl, 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%.

33

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.

34

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.

35

Thermal Analysis and Calorimetry 20081 - 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/

http://conferences.npl.co.uk/tac2008/http://conferences.npl.co.uk/tac2008/

36

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

http://www.npl.co.uk/server.php?show=nav.600

Measurement of heat transfer coefficients for polymer processing simulationHeat transfer coefficientHeat transfer coefficient calculationThermal resistance calculationThermal resistance of PMMA specimen (2 mm) without and with air gaps of varying thicknessComparison of measured HTC coefficient across air gap with HTC predicted by ? air modelEffect of errors on derived heat transfer coefficientsThermal resistance of PMMA specimen (2 mm) without and with air gaps of varying thicknessEffect of an air gap on HTC measurements and repeatability of HTC measurement across asteel/air InterfaceThermal conductivity and diffusivity intercomparison in support of the development of ISO 22007 Parts 1 to 4 Plastics - DetPlastics thermal conductivity standardsPlastics thermal conductivity standardsPlastics thermal conductivity standards - intercomparisonThermal conductivity and diffusivity intercomparison outlineSummary of thermal conductivity and diffusivity methodsThermal conductivity of the cast PMMA measured by line-source probe, Hot Disk and heat flux meter methodsThermal diffusivity of the cast PMMA measured by Hot Disk, laser flash and temperature wave analysis methodsThermal conductivity of extruded PMMA measured by line-source probe, Hot Disk and heat flux meter methodsThermal diffusivity of extruded PMMA measured by Hot Disk, laser flash and temperature wave analysis methodsThermal conductivity thermal diffusivity conversionSpecific heat capacity, Cp, of the cast PMMA measured by DSCDensity of the cast PMMA:Archimedes and dimensions & weight methodsSpecific heat capacity, Cp, of extruded PMMA measured by DSCThermal conductivity of cast PMMA:measured - heat flux meter, line-source probe, Hot Disk;calculated from - laser flash, temThermal diffusivity of cast PMMA: measured - Hot Disk, laser flash, temperature wave analysis;calculated from - Hot Disk, heThermal conductivity of the extruded PMMA: measured - line-source probe, Hot Disk and heat flux meter;calculated from - laseThermal diffusivity of extruded PMMA: measured - Hot Disk, laser flash, temperature wave analysis;calculated from - Hot DiskIntercomparison summaryDifferential scanning calorimetry standardsPPS 2008 Conference and NPL ReportPPS 2008 ConferenceScientific journal accepted for publicationScientific journal & ISO Technical ReportThermal Analysis and Calorimetry 20081 - 2 April 2008, Teddington, UKAcknowledgements