Nicholas Dembsey - Academia.edu (original) (raw)
Papers by Nicholas Dembsey
A widely accepted consensus on entrainment models for large jives in compartments does not yet ex... more A widely accepted consensus on entrainment models for large jives in compartments does not yet exist. To obtain further information on such entrainment rates, 20 full-scale, near-field experiments were condticted. Near-field entrainment occurs when hot layer interface heights are beneath the burner mean flame height so that cold layer entrainment occurs only near the burner surface. A durable compartment, similar
Fire Safety Science, 2008
This work assesses the effect of decomposition kinetics on overall pyrolysis behavior using exper... more This work assesses the effect of decomposition kinetics on overall pyrolysis behavior using experimental data from thermogravimetric analysis (TGA) and Fire Propagation Apparatus (FPA) experiments. TGA data are presented for an unsaturated brominated polyester resin (reinforcement free), and the FPA is used to investigate the pyrolysis behavior of a fiber reinforced polymer (FRP) composite slab with matrix comprised of the same resin tested via TGA. Three different kinetic models are fit to the TGA data: singlestep n th order, 3-step n th order, and 3-step n th order with one autocatalytic step. These kinetics models are then used to simulate the pyrolysis of a composite slab in the FPA, with thermophysical properties estimated by genetic algorithm optimization. It is shown that the two 3-step mechanisms provide nearly identical calculations of total mass loss rate (MLR) in the FPA, while the single-step mechanism provides similar, but quantitatively different, MLR predictions. Although no broad conclusions regarding the importance of multi-step thermal decomposition kinetics can be drawn on the basis of a single study, detailed reaction mechanisms may be superfluous unless TGA curves show multiple distinct reaction peaks and/or all thermophysical properties/model input parameters are precisely known.
Fire Safety Science, 2008
Fire Safety Science, 2003
Fire and Materials, 2008
... up to 200 kW/m 2 Patricia A. Beaulieu1,∗,† and Nicholas A. Dembsey2 1FM Global, Fire Hazards ... more ... up to 200 kW/m 2 Patricia A. Beaulieu1,∗,† and Nicholas A. Dembsey2 1FM Global, Fire Hazards and Protection Research, Norwood, MA, USA 2Worcester Polytechnic Institute, Fire Protection Engineering Department, Worcester, MA, USA SUMMARY ...
This study provides the composites industry and the. re engineering industry with baseline data f... more This study provides the composites industry and the. re engineering industry with baseline data for pyrolysis modelling of common FRP systems. All of the resins used are listed by the manufacturers as Class 1 or Class A per ASTM E 84. The composites are being evaluated in bench scale modern. re test apparatuses (FPA, ASTM E 2058 and Cone, ASTM
This study is designed to provide the compos- ites industry as well as the fire engineering indus... more This study is designed to provide the compos- ites industry as well as the fire engineering industry base- line data and engineering "properties" of common fiber reinforced polymer (FRP) systems. Four resin systems and three glass contents will be considered. This matrix of FRP systems has been carefully fabricated and docu- mented so as to provide "transparency" as to the
Fire Safety Journal, 1995
Twenty full-scale compartment fire experiments suitable for model comparison were conducted. Ceil... more Twenty full-scale compartment fire experiments suitable for model comparison were conducted. Ceiling jet temperatures, surface heat fluxes and heat transfer coefficients which have not been previously reported are discussed. The ceiling jet temperatures 0·10 m below the ceiling show the effects of compartment ventilation, near-field entrainment conditions and burner location on the ceiling jet. Net and radiant incident heat fluxes
Fire Safety Journal, 1995
A widely accepted consensus on entrainment models for large fires in compartments does not yet ex... more A widely accepted consensus on entrainment models for large fires in compartments does not yet exist. To obtain further information on such entrainment rates, 20 full-scale, near-field experiments were conducted. Near-field entrainment occurs when hot layer interface heights are beneath the burner mean flame height so that cold layer entrainment occurs only near the burner surface. A durable compartment, similar
Composites Research …, 2008
... Chris Lautenberger, Post Doctoral Researcher at University of California, Berkeley, with inte... more ... Chris Lautenberger, Post Doctoral Researcher at University of California, Berkeley, with interests in pyrol-ysis modeling of materials and the related spread of fire. Charles Dore is President and founder of Abate Fire Technologies. ... Gobain plain cloth (332g/m2). ...
Journal of Hazardous Materials, 2009
A method to estimate thermal and kinetic parameters of Pittsburgh seam coal subject to thermal ru... more A method to estimate thermal and kinetic parameters of Pittsburgh seam coal subject to thermal runaway is presented using the standard ASTM E 2021 hot surface ignition test apparatus. Parameters include thermal conductivity (k), activation energy (E), coupled term (QA) of heat of reaction (Q) and pre-exponential factor (A) which are required, but rarely known input values to determine the thermal runaway propensity of a dust material. Four different dust layer thicknesses: 6.4, 12.7, 19.1 and 25.4 mm, are tested, and among them, a single steady state dust layer temperature profile of 12.7 mm thick dust layer is used to estimate k, E and QA. k is calculated by equating heat flux from the hot surface layer and heat loss rate on the boundary assuming negligible heat generation in the coal dust layer at a low hot surface temperature. E and QA are calculated by optimizing a numerically estimated steady state dust layer temperature distribution to the experimentally obtained temperature profile of a 12.7 mm thick dust layer. Two unknowns, E and QA, are reduced to one from the correlation of E and QA obtained at criticality of thermal runaway. The estimated k is 0.1 W/m K matching the previously reported value. E ranges from 61.7 to 83.1 kJ/mol, and the corresponding QA ranges from 1.7 × 10 9 to 4.8 × 10 11 J/kg s. The mean values of E (72.4 kJ/mol) and QA (2.8 × 10 10 J/kg s) are used to predict the critical hot surface temperatures for other thicknesses, and good agreement is observed between measured and experimental values. Also, the estimated E and QA ranges match the corresponding ranges calculated from the multiple tests method and values reported in previous research.
Journal of Fire Protection Engineering, 1996
The role of combustible interior finish materials (CIFMS) in fire growth is often termed &quo... more The role of combustible interior finish materials (CIFMS) in fire growth is often termed "flame spread" or "reaction to fire.".This phenomenon is inextricably tied to the heat release rate of the ignition source. Performance fire codes need to have a means of limiting the fire growth contribution of CIFMs and at the same time accounting for the expected role performed
Journal of Fire Protection Engineering, 2012
Few robust engineering approaches currently exist to assess flame spread performance of interior ... more Few robust engineering approaches currently exist to assess flame spread performance of interior finish materials for a range of source fires, in support of compartment fire hazard analysis. As a step toward closing this gap, a simplified approach for assessing (a) the propensity for a material to support self-propagating flame spread and (b) the extent of flame spread for a range of source fire conditions has been developed. In addition, a general approach for integrating the output of the simplified flame spread analysis into a computational fluid dynamics (CFD) model has been developed to predict the overall fire growth and spread hazard for a passenger rail vehicle compartment.
Fire Technology, 2007
NIST's Fire Dynamics Simulator (FDS) is a powerful tool for simulating the gas phase fire environ... more NIST's Fire Dynamics Simulator (FDS) is a powerful tool for simulating the gas phase fire environment of scenarios involving realistic geometries. If the fire engineer is interested in simulating fire spread processes, FDS provides possible tools involving simulation of the decomposition of the condensed phase: gas burners and simplified pyrolysis models. Continuing to develop understanding of the capability and proper use of FDS related to fire spread will provide the practicing fire engineer with valuable information. In this work three simulations are conducted to evaluate FDS V.4's capabilities for predicting upward flame spread. The FDS predictions are compared with empirical correlations and experimental data for upward flame spread on a 5 m PMMA panel. A simplified flame spread model is also applied to assess the FDS simulation results. Capabilities and limitations of FDS V.4 for upward flame spread predictions are addressed, and recommendations for improvements of FDS and practical use of FDS for fire spread are presented. iii ACKNOWLEDGEMENTS
Fire Technology, 2008
Abstract In this study, a series of sensitivity analyses were conducted to evaluate a computation... more Abstract In this study, a series of sensitivity analyses were conducted to evaluate a computational fluid dynamic (CFD) model, Fire Dynamics Simulator (FDS) version 4.0, for tunnel fire simulations. A tunnel fire test with a fire size on the order of a 100 MW with ...
Fire Technology, 2010
Performance based methodologies are becoming increasingly common in fire safety due to the inabil... more Performance based methodologies are becoming increasingly common in fire safety due to the inability of prescriptive codes to account for every architectural feature. Fire Sprinkler suppression systems have long been used to provide property protection and enhance life safety.
Fire Safety Journal, 2000
Di!ering perceptions of risk by various stakeholders have long played a role in in#uencing the de... more Di!ering perceptions of risk by various stakeholders have long played a role in in#uencing the development of prescriptive-based building "re safety codes. As performance-based building "re safety codes are developed, di!ering perceptions of risk will continue to be a signi"cant in#uence. In this paper, the concepts of revealed preference, risk factors, risk adjustment factors and risk conversion factors are discussed, and two methods to address risk perceptions in a performance-based building "re safety code are introduced. The "rst method proposes the use of risk factors to classify buildings in terms such as low, medium, and high risk. Each class of building would be assigned a risk adjustment factor. Similar to safety factors, risk adjustment factors would be applied during deterministic building "re safety design to provide an increased level of safety in buildings where the risk perceptions would mandate greater safety. The second method would be used with a probabilistic-based building "re safety design approach, and uses risk factors to develop risk conversion factors (RCFs). In the probabilistic approach, a maximum expected-risk-to-life (ERL) value would be established by the code, with appropriate RCFs being applied to adjust maximum ERL values depending on how the building's "re safety risk is perceived.
Fire Safety Journal, 2008
... View Within Article. Fig. 3 shows the historical Tewarson data for free burn conditions (no a... more ... View Within Article. Fig. 3 shows the historical Tewarson data for free burn conditions (no applied heat flux) of thermally thick behaving samples with a physical thickness of 2.5 cm. ... Fig. 3. Mass loss flux for free burn black PMMA as a function of oxygen concentration. ...
Fire Safety Journal, 2005
A new approach to modeling soot formation and oxidation in non-premixed hydrocarbon flames has be... more A new approach to modeling soot formation and oxidation in non-premixed hydrocarbon flames has been developed and subjected to an initial calibration. The model considers only the phenomena essential for obtaining sufficiently accurate predictions of soot concentrations to make CFD calculations of fire radiation feasible in an engineering context. It is generalized to multiple fuels by relating the peak soot formation rate to a fuel's laminar smoke point height, an empirical measure of relative sooting propensity, and applying simple scaling relationships to account for differences in fuel stoichiometry. Soot oxidation is modeled as a surface area independent process because it is controlled by the diffusion of molecular oxygen into the zone of active soot oxidation rather than being limited by reaction of OH Á radicals with the available soot surface area. The soot model is embedded within a modified version of NIST's Fire Dynamics Simulator and used for a comparison of predicted and measured temperatures, soot volume fractions, and velocities in laminar ethylene, propylene, and propane flames. The
Fire Safety Journal, 1998
ABS¹RAC¹ ¹his paper presents results from Cone Calorimeter testing of two types of cored composit... more ABS¹RAC¹ ¹his paper presents results from Cone Calorimeter testing of two types of cored composite materials used in shipbuilding: a GRP/Balsa-cored sandwich and a GRP/P»C foam-cored sandwich. ¹he observed phenomena of delamination, melting and charring of the core materials, and edge effects are discussed in the context of how they affect test results. ¹he ''standard'' ignition data analysis method specified in AS¹M E 1321 and Janssens' ''improved'' method of analysis were both used to derive effective material ignition properties such as ignition temperature and k c. ¹he findings of the study indicate that Janssens' method is well suited for analyzing the ignition data of cored composite materials. Derived material properties are used as input to Quintiere's fire growth model in order to evaluate their influence on time to flashover predictions in the ISO 9705 Room-Corner test scenario. 1998 Elsevier Science¸td. All rights reserved. NOTATION Bi Biot number c Specific heat (J/kg K) C Constant, eqn (2) h Convective heat transfer coefficient (W/m K) h Total heat transfer coefficient at ignition (kW/m K) k Thermal conductivity (W/m K) k c Effective thermal property [(kW/m K) s] l Characteristic length (m) Effective heat of gasification (kJ/g) n Exponent, eqn (2) 137 q Critical irradiance for ignition (curve-fitting parameter) (kW/m) qR Measured incident irradiance (kW/m) q Critical irradiance for ignition (kW/m) q Minimum irradiance for ignition (kW/m) t Time (s) ¹ Ignition temperature (K or°C) ¹ Minimum temperature for flame spread (K or°C) ¹ Ambient temperature (K or°C) Greek letters Thermal diffusivity (m/s) Thickness (m) H Effective heat of combustion (MJ/kg) Surface emissivity Flame heating parameter (kW/m) Density (kg/m) Stefan-Boltzmann constant (5.67;10\ kW/m K)
A widely accepted consensus on entrainment models for large jives in compartments does not yet ex... more A widely accepted consensus on entrainment models for large jives in compartments does not yet exist. To obtain further information on such entrainment rates, 20 full-scale, near-field experiments were condticted. Near-field entrainment occurs when hot layer interface heights are beneath the burner mean flame height so that cold layer entrainment occurs only near the burner surface. A durable compartment, similar
Fire Safety Science, 2008
This work assesses the effect of decomposition kinetics on overall pyrolysis behavior using exper... more This work assesses the effect of decomposition kinetics on overall pyrolysis behavior using experimental data from thermogravimetric analysis (TGA) and Fire Propagation Apparatus (FPA) experiments. TGA data are presented for an unsaturated brominated polyester resin (reinforcement free), and the FPA is used to investigate the pyrolysis behavior of a fiber reinforced polymer (FRP) composite slab with matrix comprised of the same resin tested via TGA. Three different kinetic models are fit to the TGA data: singlestep n th order, 3-step n th order, and 3-step n th order with one autocatalytic step. These kinetics models are then used to simulate the pyrolysis of a composite slab in the FPA, with thermophysical properties estimated by genetic algorithm optimization. It is shown that the two 3-step mechanisms provide nearly identical calculations of total mass loss rate (MLR) in the FPA, while the single-step mechanism provides similar, but quantitatively different, MLR predictions. Although no broad conclusions regarding the importance of multi-step thermal decomposition kinetics can be drawn on the basis of a single study, detailed reaction mechanisms may be superfluous unless TGA curves show multiple distinct reaction peaks and/or all thermophysical properties/model input parameters are precisely known.
Fire Safety Science, 2008
Fire Safety Science, 2003
Fire and Materials, 2008
... up to 200 kW/m 2 Patricia A. Beaulieu1,∗,† and Nicholas A. Dembsey2 1FM Global, Fire Hazards ... more ... up to 200 kW/m 2 Patricia A. Beaulieu1,∗,† and Nicholas A. Dembsey2 1FM Global, Fire Hazards and Protection Research, Norwood, MA, USA 2Worcester Polytechnic Institute, Fire Protection Engineering Department, Worcester, MA, USA SUMMARY ...
This study provides the composites industry and the. re engineering industry with baseline data f... more This study provides the composites industry and the. re engineering industry with baseline data for pyrolysis modelling of common FRP systems. All of the resins used are listed by the manufacturers as Class 1 or Class A per ASTM E 84. The composites are being evaluated in bench scale modern. re test apparatuses (FPA, ASTM E 2058 and Cone, ASTM
This study is designed to provide the compos- ites industry as well as the fire engineering indus... more This study is designed to provide the compos- ites industry as well as the fire engineering industry base- line data and engineering "properties" of common fiber reinforced polymer (FRP) systems. Four resin systems and three glass contents will be considered. This matrix of FRP systems has been carefully fabricated and docu- mented so as to provide "transparency" as to the
Fire Safety Journal, 1995
Twenty full-scale compartment fire experiments suitable for model comparison were conducted. Ceil... more Twenty full-scale compartment fire experiments suitable for model comparison were conducted. Ceiling jet temperatures, surface heat fluxes and heat transfer coefficients which have not been previously reported are discussed. The ceiling jet temperatures 0·10 m below the ceiling show the effects of compartment ventilation, near-field entrainment conditions and burner location on the ceiling jet. Net and radiant incident heat fluxes
Fire Safety Journal, 1995
A widely accepted consensus on entrainment models for large fires in compartments does not yet ex... more A widely accepted consensus on entrainment models for large fires in compartments does not yet exist. To obtain further information on such entrainment rates, 20 full-scale, near-field experiments were conducted. Near-field entrainment occurs when hot layer interface heights are beneath the burner mean flame height so that cold layer entrainment occurs only near the burner surface. A durable compartment, similar
Composites Research …, 2008
... Chris Lautenberger, Post Doctoral Researcher at University of California, Berkeley, with inte... more ... Chris Lautenberger, Post Doctoral Researcher at University of California, Berkeley, with interests in pyrol-ysis modeling of materials and the related spread of fire. Charles Dore is President and founder of Abate Fire Technologies. ... Gobain plain cloth (332g/m2). ...
Journal of Hazardous Materials, 2009
A method to estimate thermal and kinetic parameters of Pittsburgh seam coal subject to thermal ru... more A method to estimate thermal and kinetic parameters of Pittsburgh seam coal subject to thermal runaway is presented using the standard ASTM E 2021 hot surface ignition test apparatus. Parameters include thermal conductivity (k), activation energy (E), coupled term (QA) of heat of reaction (Q) and pre-exponential factor (A) which are required, but rarely known input values to determine the thermal runaway propensity of a dust material. Four different dust layer thicknesses: 6.4, 12.7, 19.1 and 25.4 mm, are tested, and among them, a single steady state dust layer temperature profile of 12.7 mm thick dust layer is used to estimate k, E and QA. k is calculated by equating heat flux from the hot surface layer and heat loss rate on the boundary assuming negligible heat generation in the coal dust layer at a low hot surface temperature. E and QA are calculated by optimizing a numerically estimated steady state dust layer temperature distribution to the experimentally obtained temperature profile of a 12.7 mm thick dust layer. Two unknowns, E and QA, are reduced to one from the correlation of E and QA obtained at criticality of thermal runaway. The estimated k is 0.1 W/m K matching the previously reported value. E ranges from 61.7 to 83.1 kJ/mol, and the corresponding QA ranges from 1.7 × 10 9 to 4.8 × 10 11 J/kg s. The mean values of E (72.4 kJ/mol) and QA (2.8 × 10 10 J/kg s) are used to predict the critical hot surface temperatures for other thicknesses, and good agreement is observed between measured and experimental values. Also, the estimated E and QA ranges match the corresponding ranges calculated from the multiple tests method and values reported in previous research.
Journal of Fire Protection Engineering, 1996
The role of combustible interior finish materials (CIFMS) in fire growth is often termed &quo... more The role of combustible interior finish materials (CIFMS) in fire growth is often termed "flame spread" or "reaction to fire.".This phenomenon is inextricably tied to the heat release rate of the ignition source. Performance fire codes need to have a means of limiting the fire growth contribution of CIFMs and at the same time accounting for the expected role performed
Journal of Fire Protection Engineering, 2012
Few robust engineering approaches currently exist to assess flame spread performance of interior ... more Few robust engineering approaches currently exist to assess flame spread performance of interior finish materials for a range of source fires, in support of compartment fire hazard analysis. As a step toward closing this gap, a simplified approach for assessing (a) the propensity for a material to support self-propagating flame spread and (b) the extent of flame spread for a range of source fire conditions has been developed. In addition, a general approach for integrating the output of the simplified flame spread analysis into a computational fluid dynamics (CFD) model has been developed to predict the overall fire growth and spread hazard for a passenger rail vehicle compartment.
Fire Technology, 2007
NIST's Fire Dynamics Simulator (FDS) is a powerful tool for simulating the gas phase fire environ... more NIST's Fire Dynamics Simulator (FDS) is a powerful tool for simulating the gas phase fire environment of scenarios involving realistic geometries. If the fire engineer is interested in simulating fire spread processes, FDS provides possible tools involving simulation of the decomposition of the condensed phase: gas burners and simplified pyrolysis models. Continuing to develop understanding of the capability and proper use of FDS related to fire spread will provide the practicing fire engineer with valuable information. In this work three simulations are conducted to evaluate FDS V.4's capabilities for predicting upward flame spread. The FDS predictions are compared with empirical correlations and experimental data for upward flame spread on a 5 m PMMA panel. A simplified flame spread model is also applied to assess the FDS simulation results. Capabilities and limitations of FDS V.4 for upward flame spread predictions are addressed, and recommendations for improvements of FDS and practical use of FDS for fire spread are presented. iii ACKNOWLEDGEMENTS
Fire Technology, 2008
Abstract In this study, a series of sensitivity analyses were conducted to evaluate a computation... more Abstract In this study, a series of sensitivity analyses were conducted to evaluate a computational fluid dynamic (CFD) model, Fire Dynamics Simulator (FDS) version 4.0, for tunnel fire simulations. A tunnel fire test with a fire size on the order of a 100 MW with ...
Fire Technology, 2010
Performance based methodologies are becoming increasingly common in fire safety due to the inabil... more Performance based methodologies are becoming increasingly common in fire safety due to the inability of prescriptive codes to account for every architectural feature. Fire Sprinkler suppression systems have long been used to provide property protection and enhance life safety.
Fire Safety Journal, 2000
Di!ering perceptions of risk by various stakeholders have long played a role in in#uencing the de... more Di!ering perceptions of risk by various stakeholders have long played a role in in#uencing the development of prescriptive-based building "re safety codes. As performance-based building "re safety codes are developed, di!ering perceptions of risk will continue to be a signi"cant in#uence. In this paper, the concepts of revealed preference, risk factors, risk adjustment factors and risk conversion factors are discussed, and two methods to address risk perceptions in a performance-based building "re safety code are introduced. The "rst method proposes the use of risk factors to classify buildings in terms such as low, medium, and high risk. Each class of building would be assigned a risk adjustment factor. Similar to safety factors, risk adjustment factors would be applied during deterministic building "re safety design to provide an increased level of safety in buildings where the risk perceptions would mandate greater safety. The second method would be used with a probabilistic-based building "re safety design approach, and uses risk factors to develop risk conversion factors (RCFs). In the probabilistic approach, a maximum expected-risk-to-life (ERL) value would be established by the code, with appropriate RCFs being applied to adjust maximum ERL values depending on how the building's "re safety risk is perceived.
Fire Safety Journal, 2008
... View Within Article. Fig. 3 shows the historical Tewarson data for free burn conditions (no a... more ... View Within Article. Fig. 3 shows the historical Tewarson data for free burn conditions (no applied heat flux) of thermally thick behaving samples with a physical thickness of 2.5 cm. ... Fig. 3. Mass loss flux for free burn black PMMA as a function of oxygen concentration. ...
Fire Safety Journal, 2005
A new approach to modeling soot formation and oxidation in non-premixed hydrocarbon flames has be... more A new approach to modeling soot formation and oxidation in non-premixed hydrocarbon flames has been developed and subjected to an initial calibration. The model considers only the phenomena essential for obtaining sufficiently accurate predictions of soot concentrations to make CFD calculations of fire radiation feasible in an engineering context. It is generalized to multiple fuels by relating the peak soot formation rate to a fuel's laminar smoke point height, an empirical measure of relative sooting propensity, and applying simple scaling relationships to account for differences in fuel stoichiometry. Soot oxidation is modeled as a surface area independent process because it is controlled by the diffusion of molecular oxygen into the zone of active soot oxidation rather than being limited by reaction of OH Á radicals with the available soot surface area. The soot model is embedded within a modified version of NIST's Fire Dynamics Simulator and used for a comparison of predicted and measured temperatures, soot volume fractions, and velocities in laminar ethylene, propylene, and propane flames. The
Fire Safety Journal, 1998
ABS¹RAC¹ ¹his paper presents results from Cone Calorimeter testing of two types of cored composit... more ABS¹RAC¹ ¹his paper presents results from Cone Calorimeter testing of two types of cored composite materials used in shipbuilding: a GRP/Balsa-cored sandwich and a GRP/P»C foam-cored sandwich. ¹he observed phenomena of delamination, melting and charring of the core materials, and edge effects are discussed in the context of how they affect test results. ¹he ''standard'' ignition data analysis method specified in AS¹M E 1321 and Janssens' ''improved'' method of analysis were both used to derive effective material ignition properties such as ignition temperature and k c. ¹he findings of the study indicate that Janssens' method is well suited for analyzing the ignition data of cored composite materials. Derived material properties are used as input to Quintiere's fire growth model in order to evaluate their influence on time to flashover predictions in the ISO 9705 Room-Corner test scenario. 1998 Elsevier Science¸td. All rights reserved. NOTATION Bi Biot number c Specific heat (J/kg K) C Constant, eqn (2) h Convective heat transfer coefficient (W/m K) h Total heat transfer coefficient at ignition (kW/m K) k Thermal conductivity (W/m K) k c Effective thermal property [(kW/m K) s] l Characteristic length (m) Effective heat of gasification (kJ/g) n Exponent, eqn (2) 137 q Critical irradiance for ignition (curve-fitting parameter) (kW/m) qR Measured incident irradiance (kW/m) q Critical irradiance for ignition (kW/m) q Minimum irradiance for ignition (kW/m) t Time (s) ¹ Ignition temperature (K or°C) ¹ Minimum temperature for flame spread (K or°C) ¹ Ambient temperature (K or°C) Greek letters Thermal diffusivity (m/s) Thickness (m) H Effective heat of combustion (MJ/kg) Surface emissivity Flame heating parameter (kW/m) Density (kg/m) Stefan-Boltzmann constant (5.67;10\ kW/m K)