Effects of Convective Heat Transfer Coefficient in Prediction of Materials Properties from Cone Calorimeter Testing

Effects of Convective Heat Transfer Coefficient in Prediction of Materials Properties from Cone Calorimeter Testing Noah Ryder a,b*, Elizabeth Weckman a a Department of Mechanical and Mechatronics Engineering, University of Waterloo 200 University Avenue West, Waterloo ON N2L 3G1, Canada b Delta Q Consultants, Inc 5457 Twin Knolls Rd, Suite 100, Columbia, Maryland, USA 21045 ABSTRACT It is increasingly important to develop appropriate models for material behavior under fire, particularly as structures and products use increasingly complex materials and computer simulations of fire become more prevalent. Both large and small-scale fire test methods are used; however, largescale testing under realistic fire conditions is costly and often does not allow for examination of material properties across the full parameter space. Thus, full-scale work is being replaced by testing at reduced scales, combined with correlations and modeling of results to larger scales. A key to proper characterization of material properties in fire lies in understanding the key parameters in the scaled tests and appropriately interpreting the data. The cone calorimeter is a small-scale test used extensively to characterize ignition and flammability parameters of materials. Results are incorporated into physical models to extract values of thermal inertia, kρc, and critical flux levels as a function of imposed heat flux. The method is based upon the assumption that the convective heat-transfer coefficient, h c, within the cone-sampling region is a known, and typically constant, parameter that describes heat transfer between the material and surrounding air under the prescribed radiative heat flux of the cone. In reality, the degree of scatter in values of h c reported in the literature is remarkable. For comparable test situations reported values span between 7 and 34 W m -2 K -1 ; most are between 10 and 20 W m -2 K -1. This study examines the current methods used to determine h c in cone calorimeter tests, and presents results on the impact of h c values in the derivation of materials properties for even a well-known material such as PMMA. INTRODUCTION Material properties related to ignition have been the subject of extensive study such that over the years understanding of material behavior when exposed to elevated heat exposures has increased. Part of this increased knowledge is due to the development of new technologies for the measurement of material performance in fire. Whereas fire performance was at one time primarily ranked on a qualitative basis, typically via an indexing method, today materials are being examined with the intent of extracting quantitative performance data. This data is being used for a variety of purposes; however, one major function is to provide the scientific community with basic information required to predict how the material would respond under various heat exposures. As structures and products use increasingly complex materials, and as computer programming of thermal and fire exposure becomes more prominent, extracting the correct properties and pairing them with appropriate models of material behavior are important. Indeed without properly characterizing the materials, model advancement will be inherently limited. During the past 30 years, there have been significant advances in the quantitative evaluation of materials within the fire science community, namely through the development of the Cone

Calorimeter, Lateral Ignition and Flame Spread, and Fire Propagation test systems. These devices allow relatively small samples of material to be tested with the expectation that the quantitative data obtained can then be used to predict the fire performance of the material under large-scale conditions. These devices are frequently used to evaluate the time to ignition of the material under a variety of heat fluxes and through use of mathematical manipulation and the underlying theory of the operation of the device, a value for thermal inertia of the material is developed. The thermal inertia is oft cited within the fire science community as a quantitative means of predicting material behavior under thermal exposure. It is an important measure since it can be used to determine material performance regardless of scale of the test sample. Another area in which values of thermal inertia are important is as input for determination of ignition and flame spread of materials in computer models of fire. Recent work 1 has shown that varying thermal inertia in the Fire Dynamics simulator can result in significant changes (40%) in the calculated surface temperature of the solid, thus altering predictions of the time to ignition and subsequent flame spread rate. As modeling of all types continues to increase in use within the fire safety community, it is important that the basic material properties are well characterized to ensure that the potential variability of inputs used by practitioners is understood and that the values applied are reasonable for the scenario under study. Since thermal inertia kρc is represented by the product of thermal conductivity, density, and specific heat of the material, it would seem relatively simple to obtain. Literature shows, however, that across a wide range of tests by numerous investigators, significantly different values for kρc can be derived for identical materials using the above-mentioned experimental apparatus. In addition, there are also discrepancies seen when comparing the experimentally derived values for kρc against values calculated based on data in standard tables of thermophysical properties for a material. Therefore, this study aims to examine the variability that has been observed in the methodologies used to determine the value of the convective heat transfer coefficient, h c, and its impact on the derivation of thermal inertia as derived using the cone calorimeter. CONE CALORIMETER THEORY There are ample references that detail the theory and operation of the cone calorimeter so this section will focus on only those aspects important to the present work. The cone calorimeter test method is based on the concept of oxygen consumption calorimetry, which is founded on the principle that a specific amount of heat is generated from a burning material per unit of oxygen consumed. During a typical test, a 100cm x 100cm sample of material is exposed to a constant uniform heat flux across its surface. The time to ignition is measured and the amount of energy released from a material during combustion is deduced based on the measured reduction in oxygen concentration below ambient in the exhaust gases. In other situations, the response of a material to heat flux levels that might be typical in the early stages of a fire can be determined by exposing samples of a given material to different values of applied heat flux and measuring the times to ignition for each heat exposure. This information is then used with a theoretical model for ignition in order to estimate the value of kρc for the material of interest. It is this latter test procedure that is of interest to the present work. The theoretical model is based on an ignition model for a liquid, adapted to apply to a solid combustible fuel. It is assumed that decomposition chemical reactions do not cause any significant variation of the surface temperature of the solid, an approximation considered reasonable for most materials 2. For a thermally thin solid, once the surface temperature is high enough, it is expected that sufficient vapors are generated to reach the lower flammable limit local to the surface of the sample. At this point if it is also assumed that the surface temperature is equal to the auto-ignition temperature of the vapor mixture at the surface, the sample will ignite. The concept may also be applied to thermally thick materials more representative of those encountered in practice 2. In this case, the surface temperature can be expressed as:

q Ts T0 = (T0 T ) i F ( t ) ht where τ n τ < τ * * 1 τ τ F (t ) = For thermally thick materials, n is equal to 1/2, while the non-dimensional time τ* is defined as τ* = 4ht2t/πkρc. If one assumes that T0=T and since ignition is occurring that Ts=Tig, the critical heat flux may be related to ignition temperature through the following: ( = ht Tig T q0,ig ) Combining Eq. (1) and (2), the time to ignition is given by: t ig = π k ρc T T 2 ( ig 0 ) 4 q 2 It should be noted that in this model the time to ignition, tig, is approximately equal to the characteristic equilibrium time, t*, for the imposed heat flux to reach the critical value for ignition. Based on the development above, the ASTM E 1321 standard 3 provides the following formula to determine thermal inertia, kρc, of the material under test: k ρc = 4 ht π b 2 from which the total heat transfer coefficient can be obtained by substituting Eq. (3) into Eq. (4) and finding the parameter b as the slope of the function F(t) in Eq. (1). This can be approximated as the / q, t 0.5 ) obtained from cone calorimeter experiments. best-fit linear approximation to the pairs ( q 0,ig In Figure 1 is plotted a set of typical experimental measurements of incident heat flux versus time to ignition, from which the critical heat flux for ignition can be obtained. This is then used to plot / q versus t 0.5 shown in Figure 2. The data points collapse onto a line, which leads to a q 0,ig straightforward evaluation of b, from Eq. (5), as its slope. As can be observed from Figure 2 a change in the heat transfer coefficient has a squared impact on thermal inertia. At this stage, all the parameters required to evaluate the square of the thermal inertia through Eq. (5) are known. THERMAL INERTIA As shown above, and detailed in Quintiere 2 and elsewhere, thermal inertia is a key parameter in determining the time to ignition for a thermally thick solid. After a long enough exposure to a surface heat flux, even a thermally thick solid may be treated as thermally thin so that for fuels of all thicknesses thermal inertia remains important. Extensive testing has been done using fire tests such as the Cone Calorimeter, Lateral Ignition and Flame Spread, and Fire Propagation tests to determine values of kρc for a wide range of materials and has been well summarized 4,5. When reviewing the existing literature however there are definite discrepancies in the listed values of thermal inertia for identical materials. Some portion of this discrepancy can perhaps be accounted for through normal variation of material properties and

experimental test uncertainty, however the very wide range of values reported in the literature indicates that additional factors must also be impacting the experimentally determined values. It is the source of these discrepancies that is of primary interest here. Figure 1 Figure 2 Time to Ignition There is relative consistency in the literature with respect to values of ignition time as functions of applied heat flux for a given material. A cross-section of such data from cone calorimeter tests on Black PMMA calibration samples is summarized in Figure 3 below. The range of uncertainty across the referenced experiments is approximately ±3.5% of the slope of best-fit line, which indicates fairly good agreement, especially when the various definitions of ignition are taken into account. Since these data form the basis for estimation of the thermal inertia for this material, one would expect the agreement amongst the thermal inertia values to follow suit, however this is not the case. Based on a review of the existing work it is evident that much of this difference arises from the uncertainty associated with modeling convective heat transfer at the surface of the sample and thus determining an appropriate value for the convective heat transfer coefficient. Figure 3: Summary of Time to Ignition Data for Black PMMA

DETERMINATION OF h c The procedure for extracting thermal inertia, as described above, necessarily relies on knowing or being able to determine h c. Further the procedure is based upon the assumption that the convective heat-transfer coefficient h c within the cone-sampling region is a known (and typically constant) parameter. In particular, the coefficient refers to the condition in which heat is transferred from the surrounding air to a (usually horizontal) material sample under the prescribed radiative heat flux from the cone heater. Though typically assumed to be constant, the degree of uncertainty in estimates of the convective heat transfer coefficient appears to be quite remarkable. Quantitative values span between 7 and 34 W m -2 K -1 in the literature with most references reporting values between 10 and 20 W m -2 K -1 as detailed below. In early work, the most common method used to evaluate h c was to assume the physical configuration to be represented as a horizontal hot plate in initially quiescent air. Classic correlations, as expressed in recognized heat transfer textbooks, were applied: Nu = 0.54Ra 1/4, 10 4 < Ra < 10 7 As an example, the large body of research conducted under the guidance of Quintiere 1,6,7 to determine material properties of thermoplastics follows the approach as shown in Eq. 6, quantitatively resulting in a value of h c = 10 W m -2 K -1. Shields et al. 2,8 and Moghtaderi et al. 2,9 utilized almost the same value in research conducted in the same period. An implicit acknowledgment to this method to evaluate h c is also given by Spearpoint and Quintiere 3,10,11 throughout their analysis of ignitability of wood. This research does not appear to account for variations of this coefficient with respect to heat flux, which in effect ignores temperature changes at the sample surface over the range of tested conditions. Dietenberger was one of the earliest to propose analysis of the potential dependence the convective heat transfer coefficient on the exposure heat flux 2,12,13. He argued that the convective coefficient and the air temperature were the only parameters within the overall heat balance on the surface of the sample that were functions of the experimental apparatus. His methodology was primarily experimental and was carried out for both the cone calorimeter and the LIFT apparatus 3-5. Notably, he used wood samples where insulating plugs (LIFT) or slabs (cone) were inserted. Thermocouples were introduced within the plugs and the slabs at various distances from the exposed surface, thus allowing the measurement of the temperature gradient through the sample. The surface temperature of the sample was then determined through interpolation. Based on the results, it was also shown that conduction heat transfer through the samples became negligible long before a steady temperature was reached at the sample surface. The radiative heat transfer from the cone was calculated from the panel irradiance profiles, while the sample surface emissivity was measured by an emissometer. As soon as conduction became negligible, h c could be considered constant and be calculated as the radiative heat flux divided by the surface temperature rise, ΔT. As a validation to the process, the derived value of h c was applied to predict the temperature profiles radially and in-depth of the material. Then, Dietenberger correlated the results with imposed irradiance for both the apparatus: 1/4 h lift = ( 0.0139 0.0138x)I 50 h cone = 0.01433 + 1.33 10 4 q e where x is the distance from the hot end, I 50 is the irradiance at 50 cm distance (expressed in kw/m 2 ) and q e is the exposure heat flux. As the irradiance ranges between 20 and 65 kw/m 2, estimated values of h c vary between 20 and 34 W m -2 K -1. Some criticism to this approach relates to its empirical

nature, but its value lies in the ability to account for temperature variation at the sample surface, even though via a non-explicit expression. In using the cone calorimeter to determine h or kρc, it was noted by de Ris and Khan 14 that the sample holder may also affect the evaluation, with relation to both its geometric shape and its material. They aimed to develop an optimized holder 14 by sealing the unexposed sample surfaces with thick fiberglass aluminum tape; then wrapping the assembly in an insulating shell of Cotronics ceramic paper, and externally protecting everything with another layer of fiberglass aluminum tape. The low conductivity of the ceramic paper and low emissivity of the tape represent a de facto insulating holder for the sample, where interior radiation from the sample to the holder is also minimized. Thick black-painted brass plates were chosen for the tests; however, specific influences of the sample holder on convective heat transfer were not clearly discriminated from the other involved phenomena. Recent efforts by Staggs and co-workers have attempted to establish a better evaluation of h c as a function of the various experimental conditions in the cone calorimeter. Staggs and Phylaktou 15 performed a range of tests over a restricted heat-flux range (25-45 kw/m 2 ) using a steel plate with coatings of a priori known emissivity as the test samples. Three different coatings were tested (candle soot, low-emissivity and high-emissivity coating) on 100 100 4 mm steel backing plates mounted on mineral wool and placed into a standard holder. Three thermocouples were embedded in the exposed surface, thus measuring steady-state temperature. From this data h c was derived, with the resulting values being higher than in previous studies and equal to approximately 28 W m -2 K -1. Their evaluation did not seem to take into account heat losses from the sample to the holder and from the latter to the surroundings, as recommended in 14. Zhang and Delichatsios 16 developed an experimental approach based on a customized steel sample (24 24 3 mm), insulated everywhere except on the exposed surface with a Fiberfrax LD Duraboard slab (80 80 20 mm). The exposed surface was painted black and thermocouples were inserted at various depths within the steel sample and the insulation. Given the high conductivity of the surface, the temperature gradient was nominal over the measurement locations in the sample. Heat flux from the cone heater to the sample was also measured using a Gardon gauge and an inverse heat conduction method was applied to extrapolate h c. By minimizing the standard error between the measured and estimated temperatures they determined h c. This was found to be about 7 W m -2 K -1 for a horizontal orientation of the sample and between 11 and 15 W m -2 K -1 for the vertical orientation. The values for h c found in this work are significantly smaller than those determined in other studies (e.g. 15 ), but the authors claim that a small sampling probe yields a more realistic evaluation than the standard samples, because of a glancing angle effect which reduces the effective emissivity of the exposed surface. There is no quantitative evidence of the effect of this, whereas higher heat losses expected due to the dependence of h c on the details of the sample holder 14 may explain at least part of this discrepancy. Other recent work by Janssens 17 reports measurements of h c obtained using a directional flame thermometer placed under the heater of the cone calorimeter. This study suggests some temperaturerelated variations, in h c with values ranging between 9.3 and 13.8 W m -2 K -1 for surface temperatures between 435 and 1086 K respectively. These lower values seem to support the model proposed by Zhang and Delichatsios 16. Staggs performed additional studies 18,19 on convective heat transfer effects in the cone calorimeter using steel plates of standard dimensions (100 100 4 mm) insulated with 25 mm thick Rockwool mineral fiber in all locations that would be in contact with a standard sample holder in a real test. Most samples were coated on their exposed surface with candle soot, with a few coated with a low-emissivity (0.5) paint, consisting of aluminum flakes in a siloxane binder. Test conditions were kept as similar to the ISO 5660 standard procedure as possible and as in 15, K-type thermocouples were embedded in the sample surface. Tests were then conducted across a wide range of incident heat flux, from 5 to 65 kw/m 2. The experimental dataset was used to develop a dimensionless correlation for Nu as a function of Ra:

Nu = 0.222Ra 0.348, 4.8 10 6 Ra 7.1 10 6 which translates into a relation between h c and the exposed surface temperature T: h c = 8.91+ 0.50( T 293) 0.54, 400K T 930K Values for h c ranging between 14 and 30 W m -2 K -1 were obtained over the temperature range of applicability. Although these values initially appear to be close to those determined by Dietenberger, when the correlation developed by Dietenberger (Eq. (8)) is applied to this data, distinctly lower values of h c are obtained. It appears from the results that neglecting heat losses through the back of the sample results in overestimates of h c of 2-4 W m -2 K -1 which also partially addresses the issue raised earlier by de Ris and Khan 14. This may still not be the entire explanation, however, since another source of error that may lead to overestimates of h c could relate to variations in airflow across the exposed surface of the test sample, possibly caused by the cone heater. Together, these explanations could address generally high values of h c obtained from certain studies. To further investigate these effects, some refinement of the model presented in 19 was proposed to reevaluate potential heat losses through the sample holder and the impact of insulating the back of the sample. The experimental data collected in 14 was used as a reference and measured incident heat flux from the experiments by Staggs 18 were compared to calculated values, accounting for the view factor between the cone walls and the sample. Taking an average value over the sampling surface resulted in minor error with respect to calculations. Conduction through the insulation and sample holder appeared to be high enough to explain high measured values of h c since insulation thicknesses of at least 80 mm appeared to be necessary to avoid heat losses through the bottom of the sample. Incorporating these results, a revised correlation was developed: Nu = (1.03 ± 0.04)Ra 0.26 This new correlation yields values of h c that are reduced by about 10% over those in 18, and appear to better support the correlation of Dietenberger 12. Equation (11) results from a one-dimensional heattransfer model, which appears to be physically representative. If heat losses through the bottom of the holder are considered, a one-dimensional heat-transfer model such as that in Eq. (11) appears to be somewhat representative, but it does not appear to hold when heat losses through the vertical sides of the sample are included. Overall, however, changes in local surface airflow due to the cone heater appear to be better modeled through a more complex correlation, a generic form of which is proposed in 19 and equation 11 above. Nelson 20 developed a non-linear model for ignition of thermally thin thermoplastics in the cone calorimeter that includes two heat transfer coefficients: one between the solid sample and the reacting gases, and another between the gaseous bulk and the surrounding air, although Nelson applies the same value (30 W m -2 K -1 ) for both of them. A summary of the values presented throughout the discussed studies is presented in Table 1. Table 1 Summary of the reported values of h in the cone calorimeter Study h (W m -2 K -1 ) Rhodes and Quintiere 6, Hopkins Jr. and 10 Quintiere 7 Moghtaderi et al. 9 11 Dietenberger 12,13 20-34 Staggs and Phylaktou 15 28 Zhang and Delichatsios 16 7 (horizontal orientation of the sample) 11-15 (vertical orientation of the sample)

INFLUENCE OF h c ON DERIVED VALUES Janssens 21 9.3-13.8 Staggs 18 14-30 Staggs 19 12.6-27 (extrapolated) Nelson 13,20 30 (dual coefficient) From equations 1 through 5, it is clear that convective heat transfer plays a significant role with respect to determination and interpretation of values of both critical heat flux for ignition and derived thermophysical properties, kρc, of a material exposed to an incident radiant heat flux. Yet, it is also clear that the convective heat transfer coefficient is dependent on the experimental test configuration or scenario. Therefore it is important to understand the convective heat transfer process for a given situation in order to assess the accuracy of thermophysical property and critical heat flux values deduced from even standard fire test apparatus. Given the focus that exists regarding determination of h c from cone calorimeter data, it is remarkable that so much uncertainty still remains with regards to the correct approach. Influence of h c on Critical Heat Flux for Ignition The critical heat flux for ignition of a given material is defined as the minimum quantity of energy that, when applied to the surface of a sample of that material, will result in ignition of the material after an infinitely long exposure time, t. The critical heat flux for ignition is often cited as a material property; however, measured values of this parameter are highly dependent on convective heat losses from the surface of the material. The impact of the convective heat transfer coefficient on measured values of critical heat flux in different test apparatus and for different orientations has been observed experimentally. For example, measured values of critical heat flux determined from vertical wall test configurations are approximately half those derived for the same material using the cone calorimeter and LIFT test methods 12. At the low levels of heat flux characteristic of the critical value, the convective losses, and thus the flow field and heat transfer coefficient local to the sample surface, are significant. Therefore, the size and orientation of the sample under test, and the configuration of the test apparatus, will have a significant effect on a measured value of critical heat flux. While the thermophysical properties of the material itself can be expected to remain constant (though are potentially unknown) across small ranges of sample temperature, the convective heat flux at the surface of the sample will change as a function of both temperature and velocity and thus the variability in value of h c is of significance in the determination of a value of critical heat flux. The connection between the value of h c and measured values of critical heat flux becomes more important when one considers that measured values of critical heat flux are used as the basis for determination of other critical parameters that describe material performance in a fire. In cone calorimeter tests, determination of the critical heat flux is often used as a precursor for the determination of T ig. In other applications, the critical flux for ignition is typically taken to be a fixed value and is used for modeling and risk assessment purposes. In all cases, a factor of 2 difference in measured values might easily overcome any inherent safety factor that was incorporated into a design, with the result that a real fire may develop in significantly different ways than are expected from modeled results. Therefore, in order to make scaled tests useful for models and general engineering use, the linkage between h c in the test and in the fire scenario must be understood and values of critical heat flux measured in small-scale experiments must be correlated to those appropriate for a realistic fire scenario. If this is taken one step further and methods were developed to accurately calculate or measure h c as a function of time for particular situations, more appropriate values of critical heat flux for ignition could be obtained and even time dependent aspects of ignition might be better understood. Influence of h c on Derived Values of Effective Thermal Inertia As shown earlier in Equation 5, the effective thermal inertia of a material, kρc, is proportional to the

square of the heat transfer coefficient. From the discussions above, it is clear that the derived values of thermal inertia are dependent on the apparatus used in their determination as well as value of h c chosen for the analysis. Based on the range of values of h c documented in the literature and summarized in Table 1, estimated values of effective thermal inertia for a given material could differ by up to a factor of 25. Rarely do values derived from fire tests correlate well with those obtained independently by taking the product of the three material properties. In practice, values of kρc derived using a cone calorimeter are most often shown to vary by a factor of 2.7 22 from those derived based on other data. These differences are significant as they translate into differences in estimated times to ignition of approximately the same order. In models that rely on the use of kρc (or thermal diffusivity, k/ρc) for determining ignition and flame spread, inaccuracies in thermal inertia have also been shown to have significant effects. As highlighted in 1, a change of 50% of the specified thermal inertia for a material resulted in a 40% change in the predicted surface temperature of the solid in FDS. Since kρc is critical in determining material performance in fires, in particular related to time to ignition and surface temperatures, it is important that it be correctly determined. For this, better estimates of the values of h c appropriate to each test are required and values of kρc measured in small-scale experiments must be better correlated to those appropriate for a realistic fire scenario. SUMMARY A review of the literature indicates that there is broad consistency between laboratories when evaluating the time to ignition versus incident heat flux for typical black PMMA samples tested in the cone calorimeter. The interlaboratory data implies that differences in methodologies, equipment, and other factors have a minimal influence on values such as time to ignition when using the same basic apparatus. This is a positive indicator since consistency amongst laboratories is key in progressing the use of data from reduced scale experiments as input into full-scale fire models. There appears to be no general consensus on how to determine appropriate values of convective heat transfer coefficient for use in interpreting results from a fire test system. In fact, the values that have been used vary significantly between different researchers even for a single test method. This has resulted in a very large range of values for properties derived from the test results, such as the thermophysical property, kρc. Such discrepancies further complicate the use of any of the smaller scale test data for other purposes, such as scaling of fire performance information or for input into fire models. Using test results from the cone calorimeter, LIFT or FPA in order to derive effective thermophysical properties and critical heat flux values for a material can be problematic. There is currently no consistency in results obtained from different test methods and even the methodologies used to obtain the basic information needed to estimate thermophysical properties from test data differ widely amongst practitioners. As such, there is currently no methodology by which to link results from one experimental design to another or, in turn, to a real world condition. At the same time, it must be recognized that materials, surfaces, and objects may not have well characterized thermophysical properties or that these properties may be unknown, even at an engineering level. In these cases, the sensitivity of models to such input parameters must be recognized since predicted times to ignition, rate of flame spread, and flashover will vary greatly based on the values of the parameters specified. The difficulty in determining appropriate values of fire performance parameters for a given test situation is exacerbated by many conditions (in-depth radiation, sample holder design, etc.); however, at a fundamental level it can be traced to uncertainty in the value of the convective heat transfer coefficient. This makes it extremely difficult to determine how to appropriately use data obtained from fire performance tests as input to fire models and risk assessment. Based on the current state of uncertainty, the use of ignition delay data with derived properties for fire safety calculations should be assessed more thoroughly. The ignition delay times themselves may be useful, but until a better understanding of the convective heat transfer coefficient for different situations can be established and can, in turn, be matched to real world values of h c, it is clear that any derived property values must be used with the utmost scrutiny.

Further, while the derived values oft cited in the literature may be useful for ranking or indexing materials, their use in any model that directly simulates heat transfer, and may have different boundary conditions than those found in the test apparatus, will inevitably result in poor model results. In conclusion, then, there is a need to improve our understanding of the convective heat transfer problem in the cone calorimeter and other fire test devices and find new ways to estimate critical fire performance parameters and to derive appropriate thermophysical properties for use in scaling fire performance test results and for input into next generation fire models. REFERENCES 1. Jahn, W. & al, E. The effect of model parameters on the simulation of fire dynamics. era.lib.ed.ac.uk (2008). 2. Quintiere, J. G. A theoretical basis for flammability properties. Fire and Materials 30, 175 214 (2006). 3. ASTM ASTM 1321 Standard Test Method for Determining Material Ignition and Flame Spread Properties. 4. DiNenno, P. J. SFPE Handbook of Fire Protection Engineering. (National Fire Protection Association Quincy, MA, 2002). 5. Babrauskas, V. Ignition Handbook. (Fire Science Publishers, 2003). 6. Rhodes, B. T. & Quintiere, J. G. Burning rate and flame heat flux for PMMA in a cone calorimeter. Fire Safety Journal 26, 221 240 (1996). 7. Hopkins, D. & Quintiere, J. G. Material fire properties and predictions for thermoplastics. Fire Safety Journal 26, 241 268 (1996). 8. Shields, T. J., Silcock, G. W. & Murray, J. J. Evaluating ignition data using the flux time product. Fire and Materials 18, 243 254 (1994). 9. Moghtaderi, B., Dlugogorski, B. & Kennedy, E. Effects of the structural properties of solid fuels on their re-ignition characteristics. Fire and Materials (1998). 10. Spearpoint, M. J. & Quintiere, J. G. Predicting the burning of wood using an integral model. Combustion and Flame 123, 308 325 (2000). 11. Spearpoint, M. J. & Quintiere, J. G. Predicting the piloted ignition of wood in the cone calorimeter using an integral model effect of species, grain orientation and heat flux. Fire Safety Journal 36, 391 415 (2001). 12. Dietenberger, M. A. Ignitability analysis using the cone calorimeter and LIFT apparatus. in Proceedings of the International Conference on Fire Safety 22, 189 (1996). 13. Dietenberger, M. A. Ignitability analysis of siding materials using modified protocol for LIFT apparatus. Fire and Materials 20, 115 121 (1996). 14. de Ris, J. L. & Khan, M. M. A sample holder for determining material properties. Fire and Materials 24, 219 226 (2000). 15. Staggs, J. & Phylaktou, H. The effects of emissivity on the performance of steel in furnace tests. Fire Safety Journal 43, 1 10 (2008). 16. Zhang, J. & Delichatsios, M. A. Determination of the convective heat transfer coefficient in three-dimensional inverse heat conduction problems. Fire Safety Journal 44, 681 690 (2009). 17. Janssens, M. & Gomez, C. CONVECTIVE HEAT TRANSFER IN THE CONE CALORIMETER. in BCC Conference on Flame Retardancy 1 11 (2009). 18. Staggs, J. Convection heat transfer in the cone calorimeter. Fire Safety Journal 44, 469 474 (2009). 19. Staggs, J. A reappraisal of convection heat transfer in the cone calorimeter. Fire Safety Journal 46, 125 131 (2011). 20. Nelson, M. I. Ignition mechanisms of thermally thin thermoplastics in the cone calorimeter. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 454, 789 814 (1998). 21. Janssens, M. L. Measuring rate of heat release by oxygen consumption. Fire Technology 27,

234 249 (1991). 22. Mowrer, F. W. An analysis of effective thermal properties of thermally thick materials. Fire Safety Journal 40, 395 410 (2005).