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 DOI: 10.1177/0734904112459264

published online 21 November 2012Journal of Fire SciencesAndreas Häggkvist, Johan Sjöström and Ulf Wickström

Using plate thermometer measurements to calculate incident heat radiation  

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DOI: 10.1177/0734904112459264

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Using plate thermometermeasurements to calculateincident heat radiation

Andreas Haggkvist1, Johan Sjostrom1

and Ulf Wickstrom1,2

Date received: 28 May 2012; accepted: 5 August 2012

AbstractThe plate thermometer is a device used mainly to measure temperatures in fire resistance testsaccording to ISO 834-1 and EN 1363-1 and to measure the so-called adiabatic surface tempera-ture. However, it can also be used to measure incident radiant heat flux ( _q0inc) as a simpler, morerobust and less-expensive alternative to water-cooled heat flux meters. The accuracy of the mea-sured _q0inc is subject to simplifications in the heat transfer analysis model and uncertainties of para-meters such as convective heat transfer coefficients, emissivities and ambient gas temperatures.This study investigates the accuracy of the model itself, isolated from the uncertainties of the phys-ical surrounding, by comparing a simple one-dimensional model to the results of finite elementmodelling. The so-obtained model includes a heat transfer coefficient due to heat losses of theplate thermometer, found to be KPT = 8 W/m2 K and a heat storage lumped heat capacity CPT =4200 J/m2 K for an ISO/EN standard plate thermometer. The model is also compared to real fieldexperiments.

KeywordsFire, plate thermometer, incident heat radiation, irradiance, heat flux meters, measuring instru-ment, thermal exposure

Introduction

The plate thermometer (PT), developed by Wickstrom1 for measuring high temperatures infire resistance furnaces, is a very simple and robust instrument. It has replaced traditional

1SP Technical Research Institute of Sweden, Boras, Sweden2Dept. of Civil, Environmental and Natural Resources Engineering, Lulea Technical University, Lulea, Sweden

Corresponding author:

Johan Sjostrom, SP Technical Research Institute of Sweden, Box 857, 501 15 Boras, Sweden.

Email: johan.sjostrom@sp.se

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thermocouples for the purpose of harmonising the thermal exposure when testing accordingto the European standard EN 1363-1 as well as the international standard ISO 834.According to the standards, the exposed surface of the PT consists of a 0.7-mm-thick, 100 3

100-mm nickel alloy sheet folded around a 100 3 100-mm and 10-mm-thick inorganic insu-lation material with a density of 280 (630) kg/m3 (see Figure 1). The temperature of the PTis measured by a type K thermocouple fixed to the geometrical centre of the sheet.

During recent years, the PT has also been used to measure the so-called adiabatic surfacetemperature (AST), which is defined as the temperature of a perfectly insulated surface.2,3

Even though the analysis of extracting AST is related to the study presented here, this studydoes not consider AST. Instead, it focuses on using the PT to measure incident radiant heatflux ( _q0inc), which enables a simpler, more robust and less-expensive instrument compared toconventional water-cooled heat flux meters (HFMs).4,5 Thus, it offers the possibility to mea-sure heat flux in very tough environments and in field tests where HFMs are unpractical touse. The PT has successfully measured _q0inc in various configurations, such as the cone calori-meter,4 pool fires,6 burning goods7 and model scale fire scenarios,8 by using correction termsfor different heat losses in/from the PT. When the incident radiation heat flux _q99inc shall bederived from PT temperatures, two parameters depending on the thermal properties of thePT have to be determined. This study presents a way of determining these parameters. Oneof the parameters considers the heat losses by conduction and the other the heat capacity ofthe PT. The magnitudes of the parameters have been obtained by comparisons against atwo-dimensional finite element model (FEM) where thermal conditions are well defined andagainst experimental heat exposures. The results enable us to analyse the errors induced bythe model separately and thereafter test its performance in real fires. The accuracy of _q0inc

measurements using PTs is not only subject to the use of suitable correction terms but alsoresponds to uncertainties in emissivity, convective heat transfer, gas temperatures and so on.

Figure 1. Sketch of the PT. The exposed area consists of a 100 3 100-mm metal sheet. Behind, it is a 10-mm-thick insulation pad. Additional metal is folded over the insulation.PT: plate thermometer.

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One-dimensional model of the PT

The total net heat transfer _q99tot to a surface from the gas phase is characterised by the fol-lowing three physically independent terms: (a) absorbed radiation, (b) emitted radiation and(c) convective heat transfer. These are balanced by the heat transferred by conduction intothe material. The absorbed radiation is a portion, defined by the emissivity, e, of the _q99inc.The emitted radiation is proportional to the surface temperature (to the fourth power) ande. The magnitude of the convective heat transfer is usually simplified to being directly pro-portional to the temperature difference between the surface and the adjacent gas, TN, wherethe proportionality constant is the convective heat transfer coefficient, h.

In the simplified model presented here, a lumped heat is assumed, that is, the PT isassumed to have a uniform temperature (lumped heat capacity) as indicated by the thermo-couple attached to its metal surface. Heat is then transferred to the surface from the environ-ment by radiation and convection. In addition, however, two correction terms areintroduced. One is due to heat losses to the rear side of the PT and the other is due to ther-mal inertia, that is, heat is stored in the PT.

For the loss term, the effects of conduction through the insulation as well as the in-planeconduction in the metal that overlaps the insulation, including the corresponding convectivecooling, are linearised to be proportional to the temperature difference between the plate sur-face and the ambient gas temperature. Thus, it is assumed that the combined effects of conduc-tion in insulation and the folded metal with its associated convective cooling can be treated viaa temperature-independent parameter,KPT. The correction for the losses is thus given as

_q0loss = KPT TPT � T‘ð Þ ð1Þ

where TPT is the temperature of the metal sheet of the PT. In addition, during transient con-ditions, heat is absorbed when increasing the temperature of the metal and the insulationpad. The lumped heat capacity of the metal of the PT is then added to a portion of the heatcapacity of the insulation. Thus, the temperature distribution through the PT is assumed uni-form in the metal and part of the insulation as shown in Figure 2. The storage correctionterm for the heat flux associated with this lumped specific heat is therefore

_q0stor = cmetrmetdmet + bcinsrinsdinsð Þ dTPT

dt= CPT

dTPT

dtð2Þ

where c is specific heat capacity, r is the density and d is the thickness of the materials. Thesubscripts met and ins refer to metal and insulation, respectively, and b is the portion of theinsulation that is considered for the lumped heat capacity.

Given these two parameters, KPT and CPT, the heat balance at the PT surface can be writ-ten as

ePT _q0inc � sT4PT

� �+ h T‘ � TPTð Þ+ KPT T‘ � TPTð Þ= CPT

dTPT

dtð3Þ

The incident radiant heat flux can then be calculated on the basis of temperature measure-ments of PT and the adjacent gas

_q0inc = sT4PT +

h + KPTð Þ TPT � T‘ð Þ+ CPTdTPT

dt

ePT

ð4Þ

Haggkvist et al. 3

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As KPT is added to the heat transfer coefficient h, the accuracy of the model depends on theprecision of the sum of the two. For steady-state conditions, only the loss correction term deter-mines _q0inc, while the storage correction term dominates when the temperature of the PT changesrapidly. The combined importance of the correction terms is indicated in Figure 7.

Under transient conditions, _q0inc can be obtained by approximating the time derivative ofthe measured TPT. For this study, central difference is used in order to obtain the incidentflux, given the time–temperature output from the PT

_q0inc½ �i = s T4PT

� �i+

(h + KPT ) TPT½ �i � T‘½ �i� �

+ CPTTPT½ �i + 1� TPT½ �i�1

t½ �i + 1� t½ �i�1

ePT

ð5Þ

where i represents the ith time step for which a new TPT and T‘ are probed. Note that whenthe ambient gas temperature is close to the PT temperature as in a furnace, the influence ofthe conduction losses is negligible, and only the influence of the inertia needs to be consid-ered. It is important to probe the gas temperature close to the PT. However, for measure-ments beyond the flames or any hot smoke layer, the gas temperatures are often very closeto ambient air; h can be calculated from standard textbooks. It is estimated to be approxi-mately 10 W/m2 K for natural convection.4 For other flow cases, it depends on gas velocitiesand may be difficult to estimate. This causes uncertainties, which increase with the differencebetween the gas temperature and the PT temperature. Similar uncertainties occur for water-cooled HFM. Then, the uncertainty increases with the difference between the gas tempera-ture and the temperature of the sensor, which is normally just over the cooling watertemperature. Therefore, a HFM is expected to yield accurate temperature when placed ingases of ambient temperature while the uncertainties are much greater when placed in, forexample, hot flames. In such cases, the PT is likely to yield more accurate results.

Validation to FEM

The parameters KPT and CPT of the one-dimensional model are obtained by comparing atwo-dimensional FEM of the PT, using the FEM software Temperature Analysis ofStructures Exposed to Fire (TASEF)9. In the first step, KPT is obtained by a steady-state

Figure 2. Assumed temperature distribution through the PT to calculate (a) loss correction and (b)storage correction, consisting of the exposed metal surface (white) and the insulation (shaded). (a) Thetemperature is assumed uniform in the metal and linear in the insulation. (b) Lumped heat capacity isassumed in the metal and in a part of the insulation pad.PT: plate thermometer.

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analysis, and CPT is obtained by transient analyses. Half the PT is modelled with a line ofsymmetry in the middle. The insulation pad and metal sheet are divided into 35 and 17square cells, respectively, as shown in Figure 3.

In the modelling, the exposed left surface of the PT (between nodes 1 and 9) is subject touniform incident radiant heat fluxes of 6.12, 33.0, 107 and 267 kW/m2. These represent theemitted radiation flux from a black surface with temperatures of 300�C, 600�C, 900�C and1200�C, respectively. The surfaces of the PT are exposed to convective cooling to the ambi-ent atmosphere with temperature TN = 20�C using a heat transfer coefficient of 10 W/m2 Kand emitted radiation using an emissivity e = 0.8. The material properties are chosen to rep-resent two common materials for PTs. Inconel 600 is most commonly used as a metal sheet.Its thermal properties (conductivity, density and specific heat) as a function of temperatureare given by Special Metals Corporation.10 A common material for the insulation pad isCarbowool, Unifrax. Its properties were measured at SP using the transient plane source(TPS) method,11 according to the ISO 22007-212 for determining thermal conductivity anddiffusivity.5 The temperature-dependent properties used in the FEM is given by the expres-sion k = 0.0002T + 0.0057 and rc = 2324T + 586,100, where k is given in Watt per metreKelvin, T in Kelvin and rc in Joule per cubic metre Kelvin.

Steady-state conditions

The heating of the PT exposed to the four different radiation levels is modelled with the two-dimensional FEM until steady state was reached. The steady-state temperatures of the PT(node 10 in Figure 5) are 463, 784, 1107 and 1423 K for the radiation levels of 6.12, 33, 107and 267 kW/m2, respectively. Using equation (5), _q99inc can then be calculated for differentvalues of KPT. These calculated values, compared to the actual radiation used in the FEMsimulation, are shown in Figure 4.

The optimum values of KPT are different depending on the incident radiation level andthereby the temperature level of the PT. Optimisation for low radiation levels yields KPT val-ues around 7 W/m2 K, while the highest radiation level used in this study yields an optimalKPT of 15 W/m2 K. For high radiation levels, the relative error is, however, small, within6% for any correction term between 5 and 15 W/m2 K. For the lowest radiation level, therelative error is large for high correction terms, but the absolute error is still less than 2 kW/m2 for any correction term below 15 W/m2 K. Optimising the combined relative error for allradiation levels used here, one finds an optimum value just over 8 W/m2 K (see Figure 5).This value yields calculated _q99inc within 5% of the radiation used as input in the FEM forall radiation levels.

Transient conditions

To estimate the effective value of the inertia (specific heat), the transient part of the simula-tions is investigated. Using different portions (b) of the insulation contributing to the lumpedheat capacity, the errors develop differently over the transient condition. A large value yieldslarge error at short exposure times since the model then greatly overestimates the heat storedby the insulation. A low value, on the other hand, underestimates this contribution at timeswhen the heat penetrates further into the insulation. At steady state, the heat capacity is irre-levant. Figure 6 shows the relative error of calculated radiation according to equation (5)using different values of CPT.

Haggkvist et al. 5

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According to Eurocode 3, when analysing fire resistance of heavily insulated steel struc-tures, the best fit is achieved when using a lumped heat capacity considering a third of theactual insulation heat capacity (see also Ref. 13). Also in this study, using b = 1/3 gives

Figure 3. Symmetric model of the PTused in the TASEF FEM analysis (illustration is not in scale).PT: plate thermometer; TASEF: Temperature Analysis of Structures Exposed to Fire; FEM: finite element model.

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acceptable results with errors around 20% at the very start of the transient period but within12% after 20 s for an incident radiation of 33 kW/m2 as shown in Figure 6. A third of theinsulation thickness yields a total lumped heat capacity for the PT of CPT = 4200 J/m2 K.

Validation against experiments

To investigate the effect of the two correction terms, a PT is exposed to a radiant panel witha constant temperature. The incident radiant heat flux is measured using a HFM (indicating

Figure 4. Calculated _q0inc (solid lines) according to equation (5), given the steady-state TPT from the FEMsimulation for different values of KPT. The radiation levels used in the FEM are indicated by dashed lines.FEM: finite element model.

Figure 5. Relative errors of calculated _q0inc according to equation (5), given the steady-state TPT from theFEM simulation for different values of KPT.FEM: finite element model.

Haggkvist et al. 7

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15 kW/m2) but also using a PT. The radiation is introduced as a step function by removingan insulation board shielding the panel. Figure 7 shows the results. Calculating _q99inc, with-out the correction terms, only considering radiation from the exposed surface and convectivecooling, yields a response of several minutes and a final level well below the result of theHFM. Introduction of the correction for the loss, using KPT = 8 W/m2 K, yields a corre-spondence between PT and HFM within 1 kW/m2 for the steady state, but still there is a sig-nificantly slower response of the PT at almost 5 min. However, by also introducing thestorage correction term, using CPT = 4200 J/m2 K, the agreement between PT and HFM isvery good over both transient and steady-state period.

Ingason and Wickstrom4 describe several experiments where different sets of parametersare used. Good agreement between HFM and PTs has been demonstrated using KPT

between 5 and 22 W/m2 K and CPT = 2610 J/m2 K. However, the outcome is not onlydependent on the choice of KPT and CPT but also on the assumed values of h, e and TN.

Using the model described here and the set of parameters that are optimised against theFEM (KPT = 8.4 W/m2 K; CPT = 4200 J/m2 K), Lonnermark and Ingason8 comparedHFM and PTs measuring incident radiation 0.5 and 2 m from a 1:10 model scale fire in anindustrial building. The agreement between the two methods was mostly within 10% asshown in Figure 8. Several experiments were conducted with different fuels and differentopenings of the building, and all showed good agreement between HFM and PTs.8

Furthermore, _q0inc has been measured in the room/corner test configuration as defined byISO 9705. Details of the test can be found in Ref. 5. Figure 9 shows comparison of HFMand PTs situated on the floor level of 0.9 and 1.2 m from the short wall on which a gas bur-ner with a constant output of 450 kW was situated. At first, the PTs and HFM agree verywell, but the difference grows during the 10-min long exposure to a maximum difference of;2.5 kW/m2. However, it should be noted that the gas temperature in the experiment, mea-sured close to the PT, increased to between 100�C and 150�C during the exposure. The effectof the convective heat transfer to the PT for this situation is corrected for according to equa-tion (5) using continuously probed gas temperatures and h= 10W/m2 K for natural convec-tion as discussed in Ref. 4. For the HFM, the convective heat transfer is harder to estimateand not corrected for in the data of the HFM when plotting the heat fluxes measured withHFMs and PTs, respectively, as shown in Figure 9. This effect, which was estimated by

Figure 6. Relative error of calculated _q0inc using the simple one-dimensional model during the transientheating for various values of b. For all curve, the correction term uses KPT = 8 W/m2 K.

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Haggkvist5 to be a few kilowatt per square metre, clearly influences the HFM to overesti-mate the incident radiation and is therefore a contribution to the differences between theHFM and PT results in Figure 9. This situation highlights that the PT can be used to mea-sure heat flux also in situations of hot surrounding gas with a high convective heat transferwhere the HFM is inappropriate to use.5 The PT results take the increasing surrounding gastemperature into account according to equation (5), but the HFM is used without anycorrections.

Discussion

This study has focused on the accuracy of a simplified method of calculating incident radi-ant heat flux based on PT measurements. The first correction term used is an effective heat

Figure 7. _q0inc from a radiant panel measured by HFM and PTusing no correction term (thin dashed), onlycorrection for the loss term (dotted) and both loss and storage correction (solid line).HFM: heat flux meter; PT: plate thermometer.

Figure 8. Calculated radiation from PT measurements using equation (13) with KPT = 8.4 W/m2 K and CPT

= 4200 J/m2 K together with HFM data: (a) 0.5 m distance and (b) 2 m distance.Source: From Ref. 7.

HFM: heat flux meter; PT: plate thermometer.

Haggkvist et al. 9

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transfer coefficient that accounts for the losses by conduction through the insulation padand in the plane of metal folded over the insulation. This term is added to the convectiveheat transfer coefficient, and since these are rarely known within accuracy of 1 W/m2 K, amore detailed optimisation of the correction term is not motivated in an experimental situa-tion. The total error due to convection and conduction uncertainties can be studied fromFigure 5. For high radiation levels, �33 kW/m2 in the example presented here, the errorfrom the conduction is below 4% compared to the numerical model, and adding an uncer-tainty of the convective heat transfer coefficient of 64 W/m2 K still yields accuracy wellwithin 10%. The better accuracy of the higher thermal exposure is due to the relative impor-tance of radiation, which increases dramatically compared to the losses from convection andconduction at high temperatures. For radiation levels up to about 6 kW/m2 K, usually wellbelow levels relevant to fire spread scenarios, the combined relative error can become quitelarge, but in absolute values, this error is very small. In general, a best fit is obtained forKPT = 8 W/m2 K.

The second correction term is the lumped heat capacity of the PT, which is relevant fortransient conditions. This term is deemed to yield optimum corrections when incorporatingthe metal plate facing the heat source plus a third of the insulation behind it, which yieldsCPT = 4200 J/m2 K.

The present and previous studies show that the PT can be used to measure incident radia-tion with accuracy within 5%. This can be compared to the accuracy of a newly calibratedHFM (according to ISO 14934), which under ideal conditions has a relative error of about3% at low radiation levels and 1%–2% for the highest radiation levels. The robustness ofthe PT, together with its correction for convective heat losses as an integral part of its calcu-lation routine, makes it well suited to measurements in situations with elevated ambient gastemperatures where convective heating is substantial. In such applications, the robustness ofthe PT is a great advantage.

However, the standard PT was developed to measure temperature in fire resistance fur-naces, and to really improve the measurements of heat flux in ambient air, some modifica-tions of the PT are suggested. First, using a thicker insulation and by cutting off most of themetal folded around the insulation, only keeping enough to maintain mechanical stability,the conduction (in-plane metal and through insulation) could be considerably reduced. In

Figure 9. _q0inc measured by HFM and PTon the floor in the room corner configuration. The indices 4 and5 correspond to 0.9 and 1.2 m from the gas burner, respectively.HFM: heat flux meter; PT: plate thermometer.

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addition, the heat capacity of the PT could be reduced by using an insulation pad with alower density and a thinner metal sheet.

Conclusions

The PT is able to measure incident heat radiation from fires. This study presents a modelsuitable for a wide range of radiation levels correcting for the convective heat transfer, thelosses to the rear side and the heating of the material. This model is analysed against a FEMwhere external conditions and material properties are known. The correction terms of KPT

= 8 W/m2 K and CPT = 4200 J/m2 K are suggested for accurate calculations of the incidentradiation. For steady state, the errors induced solely by the assumptions of the one-dimensional model itself are limited to within 4% for high radiation levels. For levels belowthose usually considered when studying flame spread and ignition, the errors from the modelare expected to be limited to 10% under steady-state conditions. When placed in gases atthe same temperature as the corresponding black-body radiation temperature, only correc-tions due to inertia need be considered. The momentary incident radiation can be obtainedfrom PT measurements using equation (5).

The corresponding accuracy of water-cooled HFMs is relatively high when placed in airof ambient temperature (temperature of cooling water), while the accuracy when placed inhot fire gases or flames is likely to be very poor. For such applications, more research isneeded to be able to present quantitative values.

Funding

This project was internally funded by SP and Lulea Technical University.

Acknowledgement

The authors are grateful to Dr A. Lonnermark and Prof. H. Ingason for providing them with experi-mental data.

References

1. Wickstrom U. The plate thermometer – a simpleinstrument for reaching harmonized resistance tests. FireTechnol 1994; 30: 195–208.

2. Duthinh D, McGrattan K and Khaskia A. Recentadvances in fire-structure analysis. Fire Safety J 2008; 43:161–167.

3. Wickstrom U. The adiabatic surface temperature and theplate thermometer. Fire Safety Sci 2011; 10: 1001–1011.

4. Ingason H and Wickstrom U. Measuring incident radiantheat flux using the plate thermometer. Fire Safety J 2007;42: 161–166.

5. Haggkvist A. The plate thermometer as a mean ofcalculating incident heat radiation – a practical andtheoretical study. NR 2009:183, 2009. Sweden: LuleaUniversity of Technology, ISSN: 1402-1617.

6. Arvidsson M and Ingason H. Measurement of theefficiency of a water spray system against diesel oil pool andspray fires. SP report 2005:33, 2005. Sweden: SP TechnicalResearch Institute of Sweden.

7. Lonnermark A and Ingason H. Fire spread in largeindustrial premise and warehouses. SP report 2005:21,

2005. Sweden: SP Technical Research Institute ofSweden.

8. Lonnermark A and Ingason H. Fire spread betweenindustry premises. SP report 2010:18, 2010. Sweden:Technical Research Institute of Sweden.

9. Sterner E and Wickstrom U. TASEF – TemperatureAnalysis of Structures Exposed to Fire – user’s manual. SPreport 1990:05, 1990. Sweden: Technical Research Instituteof Sweden, ISBN: 91-7848-210-0.

10. Special Metals Corporation. Technical Bulletin – Inconelalloy 600, http://www.specialmetals.com/products/inconelalloy600.php (accessed 11 March 2012).

11. Gustafsson SE. Transient plane source techniques forthermal conductivity and thermal diffusivity measurementsof solid materials. Review of Scientific Instruments 1991;62: 797–804.

12. ISO 22007-2:2008. Plastics – determination of thermalconductivity and thermal diffusivity – Part 2: transientplane heat source (hot disc) method.

13. Wickstrom U. Temperature analysis of heavily insulatedsteel structures. Fire Safety J 1985; 9: 281–285.

Haggkvist et al. 11

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Appendix 1

Nomenclature

Roman capital letters

CPT Lumped heat capacity of platethermometer (PT) (J/m2 K)

KPT Effective heat transfer coefficient due toconduction (W/m2 K)

TPT Temperature measured by PT (K)TN Ambient temperature (K)

Roman lower-case letters

cA Specific heat capacity for material A (J/kgK)

dA Thickness of material A (m)h Convective heat transfer coefficient (W/

m2 K)_q0inc Incident radiation heat flux to a surface

(W/m2)_q0loss Heat flux lost at the non-exposed surfaces

of the PT (W/m2)_q0stor Heat stored per unit area and time (W/m2)

Greek lower-case letters

ePT Emissivity of PT surface (–)rA Density of material A (kg/m3)s Stefan–Boltzmann’s constant (= 5.67 3

1028) (W/m2 K4)

Author Biographies

Andreas Hoggkvist is presently working as a fire protection engineer at Halmstad’s Fire and RescueService. His Master thesis, conducted at SP, concerned measurements of incident heat radiation usingPT.

Johan Sjostrom is a senior scientist at SP Technical Research Institute of Sweden. His work focuses onthermal properties of materials exposed to fire and measurement techniques in fire sciences.

Ulf Wickstrom is part time professor at Lulea Technical University, Lulea, and part time seniorscientist at SP, Boras.

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