Ten Fundamental Principles on Defining and Expressing Thermal Exposure as Boundary Conditions in Fire Safety Engineering

Predicting the temperature of exposed objects is one of the most-common and fundamental tasks in fire safety engineering. As a first step, thermal exposure must be specified. That can be done by measurements, fire modeling or standard specifications. These must be clear, well-defined and consistent. However, how these are interpreted is often clouded by a lack of common understanding of how the exposure parameters shall be used to estimate and calculate the temperature of exposed bodies. This deficiency hinders a sound development of fire safety engineering (FSE).

Fire safety engineers typically use gas temperature, incident heat fluxes and — lately — adiabatic surface temperature (AST) to express thermal exposure. However, since approaches are not always consistent, the task group on Local Fire Exposures of the SFPE Standards-Making Committee on Calculating Fire Exposures has formulated 10 key fundamental principles for how to define and express thermal boundary conditions in FSE.

The principles are general and can be applied to material reaction fire problems, such as time to ignition estimates and fire resistance of structures under very high temperature exposures.¹

The 10 principles are shown in bold type with comments providing additional explanation.²

Principle 1
Thermal exposure is governed by two independent parameters: incident radiant heat flux (or irradiance)

and gas temperature T_g .

Since

 and T_g are independent, they must be treated separately and cannot, in principle, be replaced by one single parameter, such as fire temperature or heat flux, as is often seen in FSE literature.  

Principle 2
Heat is transferred to solid surfaces by radiation and convection here denoted

 where the net radiation is the difference between the absorbed and emitted radiation, i.e.

.

The net radiation

is the difference between the two independent entities, absorbed radiant heat

 and the emitted radiant heat

. Convection heat flux, on the other hand, depends on the difference between the gas and surface temperatures. The heat flux

 is proportional to the solid surface temperature gradient.

Principle 3
The incident radiation can be expressed as

. The radiation temperature

may be either greater or smaller than the gas temperature

.

The term radiation temperature is to be used as an alternative to incident radiation. It includes the contributions from all surfaces, gas masses, flames, etc., that might radiate onto a surface.

Principle 4
The heat transfer

 to solid surfaces consists of three independent components: heat absorbed by radiation

, heat emitted by radiation

 and heat transferred by convection

, i.e.

.

Thus, the three parameters — incident radiation, surface temperature and difference between gas and surface temperatures — govern the heat transferred. Heat transfer by convection cannot be split into positive and negative physical quantities as can be done for radiation.

Principle 5
Gas temperature T_g can be measured with very thin or aspirating thermocouples. Incident radiation

or T_r can be measured using radiometers.

Thermocouples influenced by the radiation and gas temperatures adapts to temperatures between T_g and T_r. The thinner they are, the closer they measure gas temperature.

Water-cooled heat flux meter measures the heat flux to a small surface at a temperature near that of the cooling water. When placed in room temperature they measure incident radiation. However, when placed in hot gases the heat transfer by convection to the sensor may be of the same order of magnitude as that by radiation, and the output is in practice more or less impossible to interpret in terms of incident radiation.

Incident radiation can be measured with plate thermometers (PT). These have a large exposed surface and therefore the contribution by convection is small. Combined with gas temperature measurements, plate thermometers can be used to attain incident heat flux and adiabatic surface temperatures in both ambient air and hot fire gases.

Principle 6
Heat flux (radiation plus convection) is often measured in Fire Safety Engineering (FSE) with water-cooled Heat Flux Meters (HFM). Given an exposed surface is assumed to have the same emissivity and convection heat transfer coefficient as the HFM sensor, the heat transfer to an exposed surface can be calculated as

 where

 is the temperature of the sensor surface.

Thus, when using data from water-cooled HFM assumptions must be made concerning the convection heat transfer coefficient and the emissivity of the sensor surface.³ 

Principle 7
With a given relation

 a single ‘effective’ exposure temperature, the adiabatic surface temperature

, can be defined by the relation

 or

.

is always between T_g and T_r.

When a solid surface has the adiabatic surface temperature, the sum of the heat transfer by radiation and convection is zero. The AST is always between the gas and radiation temperatures. The AST can be measured with PTs made of thin metal plates insulated on the back side.

Principle 8
The heat flux to a surface with a temperature T_s can be calculated as

.

AST can replace the radiation and gas temperatures and be used as single parameter boundary condition.

Unfortunately, in many standards on calculation of temperature in fire exposed structures the boundary conditions are specified imprecisely as ‘heat flux’ or implicitly ‘heat flux to a surface at ambient temperature’ or similar. This type of boundary conditions is generally not possible to apply for calculations and should be avoided.

Principle 9

can be measured with Plate Thermometers. PTs have large surfaces to get a convection heat transfer coefficient as well as an emissivity like a real exposed body. The PT sensing plate is thin to achieve a fast time response (a short time constant). As incident radiation depends on directions, the PT temperature T_PT and

 depend on orientation.

 The AST measured with PTs can be the basis for calculation of the heat flux to fire exposed bodies. In many cases of severe fire conditions PT measurements are in practice the only way of getting input data to be used for calculation of temperature of for example steel structures.

Principle 10
Given the HFM and PT are assumed to have the same emissivities and convection heat transfer coefficients,

_.

 Under certain conditions there is a one-to-one relation between the heat flux measured with an HFM and the temperature measured with a PT. Thus, ‘incident heat flux’ or shorter ‘heat flux’ to a cooled surface as given in a standard can be interpreted as an AST and used for calculations.

Ulf Wickström, FSFPE is with Luleå University of Technology and TASEF Fire Consulting

References

¹ Wickström, U., Temperature Calculation in Fire Safety Engineering, Springer International Publishing. 2016.

>²Wickström U, Hunt S, Lattimer B, Barnett J, Beyler C. Fire and Materials. 2018;1–4.

³ Brian Y. Lattimer, “Heat Transfer from Fires to Surfaces,” in Hurley, et al., Eds. (2015). SFPE Handbook of Fire Protection Engineering, 5th Ed. Gaithersburg, MD: SFPE.