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 R2 = 1 0 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 Thickness of air gap, mm 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 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) 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 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) 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 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) 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 1 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) 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) 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.