A fire experiment with wood crib was conducted in a concrete building under low ambient temperature of −10 °C to explore fire development and temperature distribution. The concrete building consists of a two-storey compartment with the size of 9.0 m by 5.0 m by 4.8 m high and a four-storey stairwell with the size of 5.0 m by 2.4 m by 10.0 m high. The fuel mass loss rate and temperatures at different positions were measured. Two fire cases, with different assumed ambient temperatures of −10 °C and 20 °C respectively, were then simulated by using FDS software to investigate the effect of ambient temperature and compare with the experimental results. The numerical results show that the calculated heat release rate is in reasonably good agreement with the measured full-scale result before water suppression. The calculated temperatures in the hot combustion gas layer at different positions agree also very well with the measured values. However, the measured fresh air temperature at the floor level near the fire source is higher than the calculated value. This discrepancy may partly depend on measuring errors as analyzed in the paper.

Adiabatic surface temperature is an efficient way of expressing thermal exposure. It can be used for bridging the gap between fire models and temperature models, as well as between fire testing and temperature models. In this study, a full-scale compartment fire experiment with wood crib fuel was carried out in a concrete building. Temperatures were measured with plate thermometers and ordinary thermocouples. Five plate thermometers and five thermocouples with a diameter of 0.25 mm were installed at different positions. These two different temperature devices recorded different temperatures, especially near the floor surface. The adiabatic surface temperature was derived by a heat balance analysis from the plate thermometer measurements. The thermal inertia of the plate thermometer was taken into account to correct the measured results. In addition, the fire experiment scenario was also simulated with fire dynamics simulator. The fire source was specified as a given heat release rate, which was calculated from the measured mass loss rate of the wood fuel. The adiabatic surface temperatures at these measuring positions were simulated by the fire dynamics simulator model and compared with the experimental adiabatic surface temperatures. The comparative results showed that fire dynamics simulator predicted the adiabatic surface temperature accurately during the steady-state period.

Two temperatures govern heat transfer to a surface of a solid body. One is the gas temperature which can be measured with thermocouples (TC) and the other the black body radiation temperature. The latter can also be expressed as the incident radiant heat flux. It is difficult to measure as radiometers cannot be used under hot fire conditions. Indirectly the radiation temperature can be obtained by measuring the Adiabatic Surface Temperature (AST) with plate thermometers (PT) for example as defined in the fire resistance furnace standards EN 1363-1 and ISO-834-1 combined with measurements of gas temperature with thin TC. In the test reported here a smaller gauge is used to measure adiabatic surface temperature at surfaces. It has been named copper disc Plate Thermometer (cdPT). Then a thin copper disc with an attached TC is mounted flush at the surface to obtain the AST in e.g. cone calorimeters according to ISO 5660. A main advantage of the cdPT is that it can record the AST before as well after a material has ignited. It can thereby be used to indicate ignition as well as continue recording the thermal exposure thereafter when ignition occurs the cdPT reacts immediately by displaying a quick temperature rise.

A localized fire is a fire which in a compartment is unlikely to reach flash-over and uniform temperature distribution. Designing for localized fires is generally more difficult than for flash-over compartment fires because of the complexity of the problem. There is also a lack of experimental data. We report here on a full scale test series on a steel column exposed to localized fires. The setup is a 6 meters tall hollow circular column, ϕ = 200 mm with a steel thickness of 10 mm. The unloaded column was hanging centrally above different pool fires. Temperatures of gas and steel were measured by thermocouples, and adiabatic surface temperatures at the steel surface were measured by plate thermometers of various designs. The results are compared with estimates based on Eurocode 1991-1-2 which in all cases studied overestimate the thermal impact for this setup. The input from plate thermometers was used to compute the steel temperatures using finite element methods. Excellent agreement was found if the radiation exchange within the column due to asymmetry of the exposure was taken into account.

In this paper we report on a series of experiments which were conducted in the large fire hall of SP’sThe unprotected steel column with Ø=200 mm and thikness 10 mm was placed with its base in a pan with the fuel and exposed to fires of various liquid fuels and magnitudes. Temperatures were recorded in the gas phase and in the steel. In the gas phase temperatures were measured with traditional thermocouples and Plate Thermometers (PTs). It was observed that measured temperatures were much lower than the correspond temperatures calculated based on the formulas presented in Eurocode 1991-1-2. For a better estimation of the steel temperatures the emissivity of the flame should be taken into account.

A localized fire is a fire in a compartment which is unlikely to reach flash-over or a uniform temperature distribution. Designing for localized fires are generally more difficult than for a typical room fire both because of the complexity of the problem as well as the lack of experimental data. We reports on a full scale test on a steel column exposed to a localized fire. The setup is a 6 meters hollow circular column, Ø=200 mm with a steel thickness of 10 mm. The unloaded column was hanging centrally above different pool fires. We report temperatures of gas and steel as well as those measured by plate thermometer of the somewhat asymmetric fires. The results are compared with estimates based on Eurocode 1991-1-2 which in all cases studied overestimates the thermal impact for this setup.

This paper shows and demonstrates how an analysis of the energy and mass balance of a fully developed (ventilation controlled) compartment fire can be used as a basis for simple and accurate predictions of fire temperatures. The model has been applied on compartments of light weight concrete structures. A finite element FE analysis has been used to solve the heat transfer equation. Effects of moisture were considered for material properties of the surrounding structure. The results were validated with experiments. The model then accurately predicted the fire temperatures and among other things it showed the influence of moisture in the surrounding structure on the fire temperature. Parametric temperature curves according to EN 1991-1-2, 2002 were shown to overestimate the fire temperature.

This paper describes and validates by comparisons with tests a one-zone model for computing temperature of fully developed compartment fires. The model is based on an analysis of the energy and mass balance assuming combustion being limited by the availability of oxygen, i.e. ventilation controlled fire. It is demonstrated that the model can be used to predict fire temperatures in compartments with semi-infinitely thick boundaries as well as with boundaries of insulated and uninsulated steel sheets where the entire heat capacity of the surrounding structure is assumed to be concentrated to the steel core. That is so called lumped heat capacity is assumed.

When developing the fire model a maximum fire temperature was defined depending on combustion efficiency and opening heights only. This temperature was then used as a thermal boundary condition to calculate the temperature of the surrounding structure. The fire temperature was then derived to be a weighted average between the maximum fire temperature and the current calculated surrounding structure surface temperature.

A general finite element solid temperature calculation code (TASEF) was used to calculate the temperature in the boundary structure. With this code it is possible to analyze surrounding structures of various kinds comprising materials with properties varying with temperature as well as assemblies of various materials.

The experiments referred to were accurately defined and surveyed. In all the tests a propane diffusion burner was used as the only fire source. Temperatures were measured with thermocouples and plate thermometers at several positions [1].

The concept of Adiabatic Surface Temperature (AST) opens possibilities to calculate heat transfer to a solid surface based on one temperature instead of two as is needed when heat transfer by both radiation and convection must be considered. The Adiabatic Surface Temperature is defined as the temperature of a surface which cannot absorb or lose heat to the environment, i.e. a perfect insulator. Accordingly, the AST is a weighted mean temperature of the radiation temperature and the gas temperature depending on the heat transfer coefficients. A determining factor for introducing the concept of AST is that it can be measured with a cheap and robust method called the plate thermometer (PT), even under harsh fire conditions. Alternative methods for measuring thermal exposure under similar conditions involve water cooled heat flux meters that are in most realistic situations difficult to use and very costly and impractical.This paper presents examples concerning how the concept of AST can be used in practice both in reaction-to-fire tests and in large scale scenarios where structures are exposed to high and inhomogeneous temperature conditions.

A pool fire test was conducted in an uninsulated steel container under low ambient temperature condition, at −20°C. The heat balance of the enclosure fire was analyzed. The size of the container was 12 m × 2.4 m and 2.4 m high, and it was made of 3-mm-thick steel. During the fire test, the fuel mass loss rate was recorded and the temperatures at different positions were measured with high-temperature thermocouples and plate thermometers. The fire scenario was simulated by using fire dynamics simulator software, and the simulated and measured results were compared. The coarse high-temperature thermocouple responded slower, and therefore, temperature measured by the high-temperature thermocouple was corrected to eliminate the effect of the thermal inertia. Furthermore, a simple two-zone model was proposed for estimating gas temperature in the enclosure of the highly conductive steel walls assuming a constant combustion rate. The convective and radiative heat transfer resistances at the inside and outside surfaces of the enclosure were analyzed.

This paper presents a model for estimating temperatures in pre-flashover fires where the fire enclosure boundaries are assumed to have lumped heat capacity. That is, thermal inertia is concentrated to one layer with uniform temperature and insulating materials are considered purely by their heat transfer resistance. The model yields a good understanding of the heat balance in a fire enclosure and was used to predict temperatures in insulated and non-insulated steel-bounded enclosures. Comparisons were made with full scale experiments and with other predictive methods, including CFD modeling with FDS and the so called MQH relationship. Input parameter values to the model were then taken from well-known literature and the heat release rates were provided from the experiments. The fire temperature predictions of the model matched very well with experimental data. So did the FDS predictions while the original MQH relationship gave unrealistic results for the problems studied. Major benefits of using the model in comparison with CFD modeling are its readiness and simplicity as well as the negligible computation times needed. An Excel application of the presented pre-flashover fire model is available on request from the author.

The EN 50399 cable test is used for classification of cables within the European construction products regulation. Means to predict a cables performance in this test, based on material data and small scale test results is of great value for the development of new cable materials. A first step in developing a prediction tool should be to understand the heat exposure on the cables in the EN 50399 test apparatus. The heat load in e.g. the cone calorimeter is very well characterized whereas for EN 50399 only the burner power (20.5 kW) is known. In the cone calorimeter the heating is solely by radiation, whereas for the EN 50399 test a large fraction of the heat exposure depends on feed-back from the cable fire. This paper presents a measuring method for characterizing the thermal exposure inside the EN 50399 cable test apparatus without cables and with a cable rated Euroclass Dca. A new instrument for measuring thermal exposure simultaneously in several directions was developed for the purpose, and thereby the non-isotropic exposure on the cables at different position on the ladder could be investigated

The plate thermometer is a device used mainly to measure temperatures in fire resistance tests according to ISO 834-1 and EN 1363-1 and to measure the so-called adiabatic surface temperature. However, it can also be used to measure incident radiant heat flux (q̇″inc) as a simpler, more robust and less-expensive alternative to water-cooled heat flux meters. The accuracy of the measured q̇″inc is subject to simplifications in the heat transfer analysis model and uncertainties of parameters 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 physical surrounding, by comparing a simple one-dimensional model to the results of finite element modelling. The so-obtained model includes a heat transfer coefficient due to heat losses of the plate 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 field experiments.

Equations are given in the Eurocode standard EN 1993-1-2 on the estimation of temperature in insulated steel cross sections when assuming uniform steel section temperature, sometimes called a lumped heat capacity assumption. When deriving these equations the temperature of the exposed insulation surface is assumed equal the surrounding fire gas temperature. That is a simplification that may provide inaccurate results for heavily insulated steel sections, when the heat capacity of the insulation is considerably higher than that of the steel section. Therefore, a new lumped mass formulation suited for heavily insulated steel sections is proposed in this paper. It accounts for the heat transfer resistance between the fire and the insulation surface as well as for the heat capacity of the insulation. The accuracy of the predictions made with the proposed new formulation are compared with results of accurate 1-D finite element numerical analyses considering insulation materials with several combinations of thermal properties and thicknesses. Analyses with the proposed formulation is shown to yield accurate and generally on the safe side estimations of steel temperature in comparison to the finite element (FE) calculations. The new formulation is applicable to lightly as well as heavily insulated steel sections.

There are numerous methods in structural fire safety engineering to assess a time-temperature input for structural calculations in fire enclosures but there is very little on design fires for CFD calculations. This study is an attempt to explore a simpler form of design fire. The simplified approach consists of two main features, a travelling behaviour and a heat release rate specified by the user

The temperature in the lower chord of steel trusses subjected to localized fires is difficult to estimate as most thermal exposure correlation formulas presented in the literature focus on heating along the ceiling where the temperature is very different from that of the lower chord [1], [2]. At the same time as the upper chord is engulfed in a ceiling jet from a localized fire, the lower chord may be surrounded by air at ambient temperature.

Two existing methods by Zhang and Usmani [3] and Guowei et al. [4], [5] along with one new approach for calculating the thermal exposure of the lower chord are presented in this paper and compared to the results from experiments conducted in Trondheim 2015 [6].

A new approach presented in this paper is evaluated based on two separate assumptions of the thermal exposure. Outside the plume, the radiative contribution is assumed originating from the plume in the form of a cylinder and inside the plume, the temperature is assumed decreasing according to a Gaussian shape from the central axis temperature to the temperature down to the temperature from the first part of the model at the transition between inside and outside the plume.

All models provide good correlation to the experimental data outside the plume perimeter. Inside the plume perimeter, the thermal impact depends to a high degree to the relation between the flame height and the height of the horizontal surface of interest.

Evaluation of steel temperature for small and complex structural elements directly in FDS introduces local effects which can lead to over prediction of the solid temperatures. The sol-id temperature calculation in FDS is based on a one dimensional assumption and cannot handle all the aspects of heat loss due to conduction. FDS is therefore likely to over predict the temperature in, for example, the web in open cross sections. In this paper, this issue is demonstrated and handled with by the use of shadow effects in FE analysis. Two different methods handling the local effects are presented. The different methods show different lev-els of accuracy presenting a more complete method for thermal response calculations based on numerical calculations of experimental data.

By using advanced FEA techniques, the predicted temperature in steel elements can be reduced significantly (see paper by Ulf Wickström). By in addition assuming a performance based fire exposure obtained with numerical fire models such as Fire Dynamics Simulator, FDS, the steel temperatures can be even further reduced.

Most calculation methods assume the fire exposure of the steel sections to be uniform. By using section factors A/V, i.e. the circumference over the area, and the most onerous of the fire exposing temperatures from computer fluid dynamics, CFD, calculations, the temperatures is over-estimated which leads to very conservative and costly solutions.

By considering the cooling effect of concrete structures and shadow effects, the temperatures can be reduced in the steel. By combining differentiated fire exposing temperatures from CFD calculations with consideration to shadow effects and the cooling of concrete, the temperature in the steel beam can be reduced even further.

Structural stability is not necessarily required for buildings where life safety is the sole structural fire safety objective. However, a structural collapse is only acceptable in an area where lethal fire conditions have developed. Therefore, structural failures due to fire resulting in risks of progressing outside of the area of lethal fire conditions need to be addressed. Thus, a new type of design principles for the life safety objectives is presented here which enables an evaluation of more precise risk assessments and more cost-efficient solutions without compromising human safety.

As for any building material, verification of fire resistance is mandatory for separating and loadbearing timber members. While non-standard fire design for steel members has long tradition, the corresponding possibilities for timber members are limited. Reasons for this can be found in the degree of complexity of the material and the limited research done in the field. This paper summarizes selected outcomes of tests investigating the influences on the charring behavior varying the oxygen content and the gas velocity. Besides the charring rate the char layer depth was the focus of this study to investigate char contraction (consumption of the char layer). In general, measurements are in line with previous results reported in literature. Results show that charring is predominantly depending on the fire compartment temperature. Results show further that for gas oxygen contents below 15 percent the gas velocity has no influence on the charring. However, at higher oxygen rates char contraction was observed affecting the protective function of the char layer. Thus, the charring and the temperature distribution was affected and the residual cross-section was decreased. In fully developed fires increased charring due to char contraction may not be observed due to the low oxygen contents. Contrary, in travelling fires or in the decay phase char contraction may be considered. This may have significant impact to Performance Based Design using non-standard temperature fire curves where the complete fire duration has to be taken into account.

Purpose

The purpose of this study is to investigate the influencing factors on the charring behaviour of timber, the char layer and the charring depth in non-standard fires.

Design/methodology/approach

This paper summarizes outcomes of tests, investigating the influences on the charring behavior of timber by varying the oxygen content and the gas velocity in the compartment. Results show that charring is depending on the fire compartment temperature, but results show further that at higher oxygen flow, char contraction was observed affecting the protective function of the char layer.

Findings

In particular, in the cooling phase, char contraction should be considered which may have a significant impact on performance-based design using non-standard temperature fire curves where the complete fire history including the cooling phase has to be taken into account.

Originality/value

Up to now, some research on non-standard fire exposed timber member has been performed, mainly based on standard fire resistance tests where boundary conditions as gas flow and oxygen content especially in the decay phase are not measured or documented. The approach presented in this paper is the first documented fire tests with timber documenting the data required.

Linear response theory is widely used in science and engineering but its use in fire sciences is rare. This communication reviews shortly the Duhamel superposition technique for solving problems in fire sciences where the response of a material maybe assumed linear but the boundary conditions (BC) are non-linear. The method can be used as an alternative to e.g. finite element methods for problems where analytical solutions are not available. Examples include temperature distribution in solids with time-varying and non-linear heat flux boundaries using a simple spreadsheet solution technique. Supplementary material contains an Excel spreadsheet solving problems with non-linear BC

A series of room fire tests for enclosures with different wall materials have been conducted for the purpose of supplying validation data for enclosure fire models. The wall materials are varied between light weight concrete, mineral wool insulation, bare 3 mm steel, and finally insulated steel. All tests used a propane gas burner with a well-defined mass flux as a fire source. Temperatures of thermocouples and plate thermometers were measured as well as oxygen concentrations in the opening. For some tests the heat release rate (by oxygen consumption calorimetry) as well as O2, CO2 and CO concentrations were measured in addition.This report describes the instrumentation, fire scenarios, enclosure materials, and results from all the tests. All results are readily available as spreadsheet data for downloading. The report also contains short description showing the influence of different factors such as wall materials, heat release rates and burner placements.

A summary of the three kinds of boundary conditions as outlined in Sect. 1.​1.​3 is shown in Table 4.1. The third kind of BC sometimes called natural BC is by far the most important and common boundary condition in fire protection engineering, while the first and second kinds of BCs can rarely be specified. The third kind of BC may be divided into three subgroups, (a), (b) and (c). The subgroup (b) and (c) are particularly suitable for fire engineering applications. Subgroup (a) is applied when the heat transfer coefficient may be assumed constant as assumed in Chaps. 2 and 3. T g is then the surrounding gas temperature. In fire protection engineering it is, however, generally not accurate enough to assume a constant heat transfer coefficient as in particular heat transfer by radiation is highly non-linear, i.e. the heat transfer coefficient varies with the surface temperature. Therefore the subgroups (3b) and (3c) are the most commonly applied. They consist of a radiation term and a convection term with the corresponding emissivity ε and convection heat transfer coefficient h, respectively. The subgroup (3b) presupposes a uniform temperature T f , i.e. the radiation temperature and the gas temperature are equal. This is assumed, for example, when applying time–temperature design curves according to standards such as ISO 834 or EN 1363-1 for evaluating the fire resistance of structures, see Chap. 12. The subgroup (3c) is a more general version of (3b) as it allows for different gas T g and radiation T r temperatures, so-called mixed boundary conditions. Alternatively σ⋅T 4 r σ⋅Tr4 may be replaced by an equivalent specified incident radiation q . ′′ inc q.inc′′ according to the identity q . ′′ inc ≡σ⋅T 4 r q.inc′′≡σ⋅Tr4 (Eq. 1.​17). As shown in Sect. 4.4 all boundary conditions of subgroup 3 may be written as type 3a. That means momentarily a single effective temperature named the adiabatic surface temperature (AST) with a value between the radiation and gas temperatures as well as a corresponding total heat transfer coefficient can always be defined, see Sect. 4.4.

When exposed to fire structures deform and lose load-bearing capacity which must be considered in design processes. It is then exposures to the more severe fires which are of interest such as post-flashover compartment fires and large flames for longer times. Pre-flashover fires do in general not create thermal conditions that can jeopardize the function of structural elements in a building. For design purposes it is therefore in general exposures relevant for post-flashover compartment fires that are specified in various standards and guidelines in the form of time–temperature curves. These curves are then used for controlling fire resistance test furnaces, see Fig. 12.1.

In previous chapters heat transfer by convection or just convection was treated only to the extent that it provides a linear boundary condition of the 3rd kind for conduction problems when the heat transfer coefficient is assumed constant. In this chapter the physical phenomenon of convection is described in more detail.

Heat transfer by thermal radiation is transfer of heat by electromagnetic waves. It is different from conduction and convection as it requires no matter or medium to be present. The radiative energy will pass perfectly through vacuum as well as clear air. While the conduction and convection depend on temperature differences to approximately the first power, the heat transfer by radiation depends on the differences of the individual body surface temperatures to the fourth power. Therefore the radiation mode of heat transfer dominates over convection at high temperature levels as in fires. Numerical applications of radiation heat transfer in FSE are outlined in Sect. 4.​1.

Temperature is the dominating factor in determining the rate and extent of chemical reactions including breakdown of organic compounds and deteriorations of strength and stiffness of structural materials such as steel and concrete. Phase change phenomena including ignition as well as severe loss of strength of materials are often related to specific elevated temperature levels. Temperatures of fire gases are also of crucial importance as they initiate gas movements thereby spread of smoke and toxic fire gases. Fire temperatures vary typically over several hundred degrees. Therefore a number of thermal phenomena need special attention such as phase changes of materials and heat transfer by radiation when calculating temperature of fire-exposed materials.

In FSE temperature is nearly always measured with thermocouples as described in Sect. 9.1. Heat flux measured in different ways is most commonly measured as the sum of the net heat flux by radiation and convection to a cooled surface. The principles are briefly outlined in Sect. 9.2. Alternative methods incident radiation heat flux as well AST using so-called plate thermometers has also been developed as a practical alternative to heat flux meters as outlined in Sect. 9.3

The fire resistance of structural elements is traditionally determined by standard fire endurance tests. However, there is also a need to be able to predict the response of structures of various designs when exposed to alternative design fire conditions. Accurate and robust analytical methods are then needed. Such methods may also be used for predicting standard tests of, for example, structural elements that cannot be tested due to their size or for extending test results to modified structures.

An analytical closed form formula is presented for explicitly calculating time to reach ignition temperature of semi-infinite solids exposed to constant incident radiation and gas temperature as for example in the cone calorimeter. The non-linear boundary condition due to the emitted radiation from the surface being proportional to the surface temperature raised to the fourth power according to the Stephan–Boltzmann law is accurately considered. The formula works for a wide range of the parameter values like the thermal inertia of the solid, the emissivity of the exposed surface and the convective heat transfer coefficient. They are all assumed constant. The new formula contains a single constant coefficient, which has been derived by comparing results obtained by accurate numerical finite element simulations using two different codes, comsol and TASEF, as well as calculations based on a Duhamel superposition scheme. Thus, the formula can be classified as semi-empirical. It offers a simple approximate solution of a non-linear problem that requires cumbersome numerical calculation methods to obtain more exact results. Any exact analytical solution is not available. The new method is carefully verified by comparisons with numerical solutions. However, as it is an analysis of well-defined theoretical methods, any validation and comparisons with test data are not required and has therefore not been made.In comparison with other similar approximation formulas found in the literature, the accuracy as well as simplicity of applying the new formula is outstanding

The analytical methods outlined in Chaps. 2 and 3 presume that the material properties and heat transfer coefficients are constant. That is, however, not possible in most cases in fire protection engineering as the temperature then varies within a wide range and therefore both material properties and boundary conditions vary considerably. Phase changes or latent heat due to water vaporization or chemical reactions of materials (see Sect. 14.​1 on concrete) must in many cases be considered to achieve adequate results. Furthermore in particular radiation heat transfer coefficients vary considerably with temperature. As shown in Sect. 4.​1 it increases with the third power of the temperature level. In addition geometries being considered are not as simple as assumed above. Often they are in two or three dimensions, and then analytical methods can seldom be used for practical temperature analyses. Therefore numerical methods involving computer codes are frequently used in fire protection engineering. In some cases in particular for 0-dimension problems (lumped-heat-capacity) relatively simple so-called spreadsheet codes such as Excel may be used. For problems with more complex geometries and boundary conditions computer codes based on finite difference or finite elements methods are needed. Several computer codes based on these methods are commercially available, see Sect. 7.3.2. The superposition technique as presented in Sect. 7.2 may be seen as a combination of a numerical and an analytical method.

FSE and design of structures and structural elements are in most cases made with a procedure including tests and classification systems. Fire resistance or endurance tests are specified in standards such as ISO 834, EN 1363-1 or ASTM E-119. In these standards time–temperature curves are specified representing fully developed compartment fires to be simulated in fire resistance furnaces for prescribed durations.

Two-zone models are applied to pre-flashover fires, i.e. compartment fires which have not reached ventilation controlled combustion conditions as defined in Chap. 10. Several more or less advanced computer codes have been developed to calculate temperature under such assumptions. The most fundamental principles of the theory are outlined below.

In one dimension in the x-direction the rate of heat transfer or heat flux is expressed according to Fourier’s law as outlined in Sect. 1.​1.q . ′′ x =−k⋅dTdx q.x′′=−k⋅dTdxwhere k is the thermal conductivity. For simplicity the mathematical presentation of the heat transfer phenomena is here in general made for one-dimensional cases only. Corresponding presentations in two and three dimensions can be found in several textbooks such as [1, 2].

This book provides a consistent scientific background to engineering calculation methods applicable to analyses of materials reaction-to-fire, as well as fire resistance of structures. Several new and unique formulas and diagrams which facilitate calculations are presented. It focuses on problems involving high temperature conditions and, in particular, defines boundary conditions in a suitable way for calculations. A large portion of the book is devoted to boundary conditions and measurements of thermal exposure by radiation and convection. The concepts and theories of adiabatic surface temperature and measurements of temperature with plate thermometers are thoroughly explained.Also presented is a renewed method for modeling compartment fires, with the resulting simple and accurate prediction tools for both pre- and post-flashover fires. The final chapters deal with temperature calculations in steel, concrete and timber structures exposed to standard time-temperature fire curves. Useful temperature calculation tools are included, and several examples demonstrate how the finite element code TASEF can be used to calculate temperature in various configurations. Temperature Calculation in Fire Safety Engineering is intended for researchers, students, teachers, and consultants in fire safety engineering. It is also suitable for others interested in analyzing and understanding fire, fire dynamics, and temperature development. Review questions and exercises are provided for instructor use.

Steel is sensitive to high temperature. The critical temperature of a steel member is the temperature at which it cannot safely support its load.

Modelling the thermal behaviour of wood is complicated as phenomenas such as moisture vaporization and migration, and the formation of char have decisive influences on the temperature development within timber structures. Nevertheless it has been shown that general finite element codes can be used to predict temperature in, for example, fire-exposed cross sections of glued laminated beams [52], provided, of course, that apparent thermal material properties and appropriate boundary conditions are used. Other specialized numerical codes for timber structures have been developed, e.g. by Fung

Reinforced concrete structures are sensitive to fire exposure of mainly two reasons. They may be subject to explosive spalling, and they may lose their load-bearing capacity due to high temperatures. Spalling is particularly hazardous as it may occur more or less abruptly and unanticipated. It usually starts within 30 min of severe fire exposure. It may depend on several mechanisms or combinations thereof such as pore pressure, stresses due to temperature gradients, differences of thermal dilatation and chemical degradations at elevated temperatures. Reinforcement bars of steel lose their strength at temperature levels above 400 °C. Prestressed steel may even loose strength below that level. Concrete loose as well both strength and stiffness at elevated temperature.

The concept of adiabatic surface temperature (AST) opens possibilities to calculate heat transfer to a solid surface based on one temperature instead of two as is needed when heat transfer by both radiation and convection must be considered. The adiabatic surface temperature is defined as the temperature of a surface which cannot absorb or lose heat to the environment, i.e. a perfect insulator. Accordingly, the AST is a weighted mean temperature of the radiation temperature and the gas temperature depending on the heat transfer coefficients. A determining factor for introducing the concept of AST is that it can be measured with an inexpensive and robust method called the plate thermometer (PT) even under harsh fire conditions. Alternative methods for measuring thermal exposure under similar conditions involve water cooled heat flux meters that are in most realistic situations difficult to use and very costly and impractical. This paper presents examples concerning how the concept of AST can be used in practice both in reaction-to-fire tests and in large scale scenarios where structures are exposed to high and inhomogeneous temperature conditions

The expression ‘heat flux’ without any qualifier like ‘to a surface at ambient temperature’ as frequently used in fire safety science and engineering literature and standards is ambiguous and misleading. Boundary conditions in fire safety engineering problems cannot be expressed as a given heat flux (or net heat flux), as the heat flux depends on and varies with the exposed surface temperature and thereby the properties of the target body. Therefore, it is important that the terminology is reviewed and that an agreement is reached on how to express thermal exposure in a well-defined and unambiguous way. A proposal is given on how the boundary conditions can be defined in a consistent way that is applicable to fire resistance and reaction-to-fire problems

The various aspects of the subject ignition of unwanted fires has been thoroughly investigated by Babrauskas and presented in the comprehensive Ignition Handbook. This book is concentrating on the calculation of the development of surface temperature. Despite many limitations, it is often assumed that a solid ignites due to external heating when its exposed surface reaches a particular ignition temperature.

When a body is exposed to unsteady or transient thermal conditions, its temperature changes gradually, and if the exposure conditions remain constant it will eventually come to a new steady state or equilibrium. The rate of this process depends on the mass and thermal properties of the exposed body, and on the heat transfer conditions. As a general rule the lighter a body is (i.e. the less mass) and the larger its surface is, the quicker it adjusts to a new temperature level, and vice versa. The temperature development is governed by the heat conduction equation (Eq. 1.29) with the assigned boundary conditions. It can be solved analytically in some cases, see textbooks such as [1, 2], but usually numerical methods are needed. This is particular the case in fire protection engineering problems where temperature generally varies over a wide range, often several hundred degrees.

A new more insulated and faster responding plate thermometer (PT) is introduced, which has been developed for measurements particularly in air at ambient temperature. It is a cheaper and more practical alternative to water‐cooled heat flux meters (HFMs). The theory and use of PTs measuring incident radiation heat flux and adiabatic surface temperature are presented. Comparisons of measurements with PTs and HFMs are made. Finally, it is concluded that incident radiation in ambient air can be measured with HFMs as well as with the new insulated type of PT. In hot gases and flames, however, only PTs can be recommended. At elevated gas temperatures, convection makes measurements with HFMs difficult to interpret and use for calculations. However, they can be used in standard or well‐defined configurations for comparisons.

In this paper a new simple calculation method for compartment temperatures is derived. The method is applicable to post-flashover ventilation controlled fires. A parameter termed the ultimate compartment fire temperature is defined as the temperature obtained when thermal equilibrium is reached and thick compartment boundaries cannot absorb any more heat from the fire gases. This temperature depends only on the product of the heat of combustion and the combustion efficiency over the specific heat capacity of air. It is, however, independent of the air mass flow rate, and of the fire compartment geometry and the thermal properties of the compartment boundary materials. These parameters on the other hand govern the rate at which the fire temperature is increasing towards the ultimate temperature. It is shown how the fire temperature development as a function of time in some idealized cases may be calculated by a simple analytical closed form formula.The fire temperature developments of two types of compartment boundaries are presented, semi-infinitely thick and thin structures. It is also shown that for the semi-infinite case, the solution resembles the standard ISO 834/EN 1363-1 curve and the parametric fire curves according to Eurocode 1, EN 1991-1-2.

This paper describes and validates by comparisons with test results a one-zone model for computing temperatures of compartment fires where flashover is reached. The model is based on an analysis of the energy and mass balance of a fully developed (ventilation controlled) compartment fire. It is demonstrated in this paper that the model can be used to predict fire temperatures in compartments with semi-infinite boundaries as well as with boundaries of insulated or uninsulated steel sheets where so called lumped heat capacity can be assumed. Comparisons are made with a series of experiments in compartments of light weight concrete, and insulated and non-insulated single sheet steel structures. A general finite element code has been used to calculate the temperature in the surrounding structures. The in this manner calculated surface temperatures yield the fire temperature as a function of time. By using a numerical tool like a finite element code it is possible to analyse fire compartment surrounding structures of various kinds and combinations of materials.Two new characteristic compartment fire temperatures have been introduced in this paper. They are the ultimate compartment fire temperature, which is the temperature reached when heat losses to surrounding structures as well radiation out through openings can be neglected, and the maximum compartment fire temperature, which is the temperature when only the losses to surrounding structures are neglected.The experiments referred to were accurately defined and surveyed. In all the tests a propane gas burner was used as the only fire source. Temperatures were measured with thermocouples and plate thermometers at several positions, and oxygen concentrations were measured in the fire compartment only opening. In some tests the heat release rate as well as the CO2 and CO concentrations were measured as well (Sjöström, et al., 2016).