1. CE 808 : Structural Fire Engineering Ch 3. FIRE AND HEAT
V. Kodur, Professor
Dept of Civil and Env. Engineering
Michigan State University

2. Ch 3. FIRE AND HEAT Fuels Combustion Fire Initiation
Pre-flashover Fires
t-squared Fires
Basics of Heat Transfer
CE 808 – Chapter 3

3. Fuels - Materials
Material available as fuel are part of the building structure, lining materials, or contents of the building
All materials are hydrocarbons, their molecules consisting mainly of carbon & atoms, with the addition of oxygen, nitrogen & others in some cases
Heat release rates (HRR) from combustion depend on the nature of the burning material, the size of the fire, and the amount of air available
calorific value
CE 808 – Chapter 3

4. Fuels - Calorific Value
The calorific value or heat of combustion is the amount of heat released during complete combustion of a unit mass of fuel
Most solid, liquid and gaseous fuels have a calorific value between 15 and 50 MJ/kg
Net calorific values Hc (MJ/kg) for a range of common fuels
See distributed Table (Table 3.1 in Text Book)
For materials containing moisture the effective calorific value Hc,n (MJ/kg) is
Hc,n = Hc ( mc) mc
mc is the moisture content given by
mc = 100 md / (100 + md)
md is the moisture content as percentage of dry weight
CE 808 – Chapter 3

5. Fuels - Calorific Value
For typical dry wood fuel with a moisture content of md = 12% and Hc = 19 MJ/kg
mc = 10.7% and Hc,n = 16.7 MJ/kg
Max. possible energy, E (MJ), that can be released when fuel burns is the energy contained in the fuel, & is given by:
E = M Hc,n
M is the mass of the fuel (kg)
CE 808 – Chapter 3

6. Fuels – Fire Load
Fire load in buildings is usually expressed as Fire Load Energy Density (FLED) per floor area
For each room, FLED - ef (MJ/m2 floor area) is given by:
ef = E/Af
Af is the floor area of the room
Some references express fire load as energy density per total room bounding surfaces - et (MJ/m2 total room surface area) is given by:
et = E/At
At is the total area of the bounding surfaces of the room (floor, ceiling and walls, including window openings)
CE 808 – Chapter 3

7. Fuels – Fire Load ef is larger than et by the ratio At/Af
It is important to know which fuel load density is being used in any given situation
Major errors can be caused if the distinction is not clear
Results of several fuel load surveys are shown in tables distributed (Appendix B in textbook)
CE 808 – Chapter 3

8. Fuels – Fire Load Design fire loads
should be determined in a similar way to design loads (earthquake load vs. extreme likely design fire scenario)
should reflect almost the max. fire load expected in building life
Both fixed and moveable fire loads should be included
Should be less than 10% probability being exceeded in 50 Yrs
When fire load is determined from representative surveys, the design load should be the 90-percentile value of surveyed loads (about 1.65 to 2.0 the average value)
Therefore, the recommended design fire load is twice the average values given in tables distributed (Appendix B in textbook)
CE 808 – Chapter 3

9. Fuels – Heat Release Rate (HRR)
For a fire, the average HRR - Q (MW) is given by:
Q = E/t
E is the total energy contained in the fuel (MJ)
t is the duration of the burning (s)
CE 808 – Chapter 3

10. Combustion - Chemistry
Combustion of organic material is a chemical reaction involving oxidation of hydrocarbons to produce water vapour and carbon dioxide
Exothermic reaction
For example, the chemical reaction for the complete combustion of propane is:
C3H8 + 5O2  3CO2 + 4H2O
However, in many fires, incomplete combustion occurs leading to production of CO or carbon as soot particles
CE 808 – Chapter 3

11. Combustion - Phase Change & Decomposition
Gases can mix with air to burn directly without any phase change
Solid and liquid fuels must be converted to the gaseous phase before they can burn
Some solid fuels melt when heated
Some other fuels, thermally decompose with a transition directly from solid to gaseous phase
Ex: thermally decomposition of wood
Referred to as pyrolysis for wood
CE 808 – Chapter 3

12. Combustion - Flame Temperature
The max. temp. reached in a flame is known as the adiabatic flame temp.
Adiabatic flame temp. may be reached in a small region in the flame centre
Average temp. of the flame will be considerably less
CE 808 – Chapter 3

13. Combuston - Smouldering Combustion
Smouldering is a flameless combustion
Ex: burning of a cigarette
Slower than flaming combustion & temp. are low & do not affect the structure
Very hazardous, specially for sleeping occupants
Smoke from smouldering combustion will activate smoke detectors but not heat detectors
Smoldering fires – Ground Zero Fires
CE 808 – Chapter 3

14. Fire Initiation - Ignition
Ignition occurs when a combustible mixture of gases is heated to temp. that will trigger an exothermic reaction of combustion
Ignition almost always requires external heat source
Pilot ignition occurs in the presence of a flame or spark
Auto-ignition causes a spontaneous ignition which is self heating within solid materials
After ignition, initial fire spread occurs from the burning object to adjacent ones
Flames tend to spread rapidly on surfaces having high temp. rate increase on exposure to heat flux
CE 808 – Chapter 3

15. Fig. – HRR for furniture items
Burning Objects
If an object such as a furniture item is ignited and allowed to burn freely in the open, the HRR tends to increase exponentially as the flames get larger & they radiate more heat back to the fuel
A peak HRR is usually reached, followed by steady- state burning and eventual decay
Fig. – HRR for furniture items
CE 808 – Chapter 3

16. Table: Burning rates for liquid and solid fuels
Burning Objects
Table: Burning rates for liquid and solid fuels
CE 808 – Chapter 3

17. t-Squared Fires
t-squared fires are characterized by a parabolic curve with the HRR proportional to the time squared
The t-squared HRR is given by: Q = (t/k)2 = ( t)2
Q is HRR (MW), t is time (s), k is a growth constant (s/MW1/2),  is fire intensity coefficient (MW/s2)
CE 808 – Chapter 3

18. Figure - t-squared fire (Calculation of HRR)
t-Squared Fires
Figure - t-squared fire (Calculation of HRR)
characterized by parabolic curve with HRR proportional to the t2
used to calculate fire growth (design fires) in rooms in the pre-flashover phase
CE 808 – Chapter 3

19. t-Squared Fires - Calculations
Figure- HRR for a fire in office furniture with slow, medium and fast fire growth rates – (fire load of 3200 MJ)
The peak HRR has been taken as 9MW
The furniture item weighs 160kg with a calorific value of 20 MJ/kg, giving a total energy load of 3200 MJ, which is the area under each curve shown
CE 808 – Chapter 3

20. Fire Spread to Other Items
t-squared fires are generally used to describe the HRR for burning of a single object
Fire can spread from the first burning object to a second object by flame contact or by radiant heat transfer
The time to ignition of a second object depends on the intensity of radiation from the flame & distance between objects
When the time to ignition of the second object has been calculated, the combined HRR can be added at any point in time to give the total HRR for these two, and subsequent objects
This combined curve is the input design fire for room under consideration
CE 808 – Chapter 3

21. Fire Spread to Other Items
Fig - t-squared HRR (fire) separately & combined for two objects
The first object burns with medium growth rate for 10 min, followed by 1 minute of steady burning at its HRR of 4.0 MW
The second object ignites after 3 min, burning with fast growth rate for 4 min followed by steady burning at 2.5 MW for 2 min
CE 808 – Chapter 3

22. Room Fires
The t-squared design fires all assume open-air burning with unlimited ventilation, and no suppression by sprinklers or firefighters
When these burning objects are in a room they burn differently, with the burning rate enhanced by radiation, but limited by the available ventilation
The design fires are used as input to room fire models to calculate fire development
CE 808 – Chapter 3

23. Heat Transfer - Conduction
Conduction is the mechanism for heat transfer in solid materials
factor in the ignition of solid surfaces, & in the fire resistance of barriers & structural members
Thermal properties needed for heat transfer calculations in solid materials include:
density,  (kg/m3), specific heat, Cp (J/kg-K),
thermal conductivity, k (W/m-K),
Also often needed are:
thermal diffusivity,  = k/Cp (m2/s), and
thermal inertia, kCp (W2s/m4K2)
function of temp.
CE 808 – Chapter 3

24. Heat Transfer - Conduction
Table - Thermal properties of common materials
CE 808 – Chapter 3

25. Heat Transfer - Conduction
In the steady-state situation, heat transfer by conduction is given by:
q" = k dT/dx
q" is the heat flow per unit area (W/m2)
k is the thermal conductivity (W/m-K)
T is the temp. (oC or K)
x is the distance in heat flow direction (m)
CE 808 – Chapter 3

26. Heat Transfer - Conduction
For transient heat flow, a 1-D heat transfer by conduction is given by:
2T/x2 = 1/ T/t
t is time (s) &  is thermal diffusivity (m2/s)
Materials with low  conduct more heat than materials with high 
Equations can be extended to 2-D and 3-D
Heat transfer Eqns. by conduction can be solved using:
simple formulae
use of design charts
numerical analysis
Refer to textbook for more information on calculation methods
CE 808 – Chapter 3

27. Heat Transfer - Convection
Convection is heat transfer by the movement of fluids, either gases or liquids
Heat transfer by convection is an important factor in flame spread and in upward transport of smoke and hot gases to the ceiling or out of the window from a room fire
Convective heat transfer is usually taken to be directly proportional to the temp difference between 2 materials as
q"=hT
q" (W/m2) heat flow per unit area
h is the convective heat transfer coefficient (W/m2K)
T is the temp. difference betn. surface of solid & fluid (oC or K)
A typical value of h for fire-exposed str elements is 25 W/m2K
CE 808 – Chapter 3

28. Heat Transfer - Radiation
Radiation is the transfer of energy by waves
is very important in fires because it is the main mechanism for heat transfer from:
flames to fuel surfaces,
hot smoke to building objects, &
a burning building to an adjacent building
The radiant heat flux q" (W/m2) at a point on a receiving surface is given by
q" =  e  Te4
 - Configuration or view factor
e - Emissivity of the emitting surface
 - Stefan-Boltzmann constant (5.67 x 10-8 W/m2K4)
Te - Absolute temp. of the emitting surface (K)
CE 808 – Chapter 3

29. Heat Transfer - Radiation
The resulting heat flow q" (W/m2) from the emitting surface to the receiving surface is:
q" =    (T e4 - T r4)
Tr - absolute temperature of the receiving surface (K), and
 - resultant emissivity of the two surfaces (range from 0 to 1), given by:
 = 1 / (1/e + 1/r -1)
r - emissivity of the receiving surface
The view factor  is a measure of how much of the emitter is seen by the receiving surface
CE 808 – Chapter 3

30. Heat Transfer - Radiation
In the case of 2 parallel surfaces, view factor, , can be expressed as
 = 1/90 [ x/1+x2 tan-1(y/1+x2) +
y/1+y2 tan-1(x/1+y2)]
x=H/2r, y=W/2r, H and W are height & width of rectangular source
Fig – View factor - Emitting & receiving surfaces
CE 808 – Chapter 3

31. Example 3.1
(a) Calculate the average HRR when 200 kg of paraffin wax burns in half an hour
Mass of fuel M = 200 kg
Calorific value Hc = 46 MJ/kg
Energy contained in the fuel
E = M Hc = 200 x 46 = 9200 MJ
Time of burning t = 1800 s
HRR
Q = E/t = 9200/1800 = 5.11 MW
CE 808 – Chapter 3

32. Example 3.1
(b) Calculate the fuel load energy density in an office 5 m x 3 m containing 150 kg of dry wood and paper & 75 kg of plastic mater-ials. Assume calorific values of 16 MJ/kg & 30 MJ/kg respectively.
Mass of wood Mwood = 150 kg
Calorific value Hc,wood = 16 MJ/kg
Energy contained in the wood
Ewood = M Hc = 150 x 16 = 2400 MJ
Mass of plastic Mplastic = 75 kg
Calorific value Hc,plastic = 30 MJ/kg
Energy contained in plastic,
Eplastic = M Hc = 75 X 30 = 2250 MJ
Total energy in fuel E = Ewood + Eplastic = = 4650 MJ
Floor area Ar = 5 x 3 = 15m2
Fuel load energy density
ef = E/Af = 4650/15 = 310 MJ/m2
CE 808 – Chapter 3

33. Example 3.2
A room in a storage building has 2000 kg of polyethylene covering the floor. Calculate the HRR & duration of burning after the roof collapses in a fire. The room is 6.0 m by 10.0 m. Use the open-air burning rates from Table 3.2 in textbook.
Mass of polyethylene M = 2000 kg
Calorific value Hc = 43.8 MJ/kg
Energy content of fuel E = M Hc = 2000 x 43.8 = MJ
Surface burning rate q = kg/s/m2 (Table 3.2)
Floor area Af = 6.0x10.0 = 60.0m2
Specific HRR Qs = qHc = x 43.8 = 1.36 MW/m2
Total HRR Q =Qs Af = 1.36x60 = 81.6 MW
Duration of burning
t = E/Q = 87600/81.6 = 1074 sec = 18 min.
CE 808 – Chapter 3

34. Example 3.3
(a) Calculate the HRR for 160 kg of office furniture with an average calorific value of 20 MJ/kg, if it burns as a 'fast' t2-fire with a peak HRR of 9.0 MW.
Mass of fuel M = 160 kg
Calorific value Hc = 20 MJ/kg
Energy contained in fuel
E = M Hc = 160 x 20 = 3200 MJ
Growth factor for fast fire k = 150 s/MW
Peak HRR Qp = 9.0 MW
Time to reach peak heat release
t1 =kQp= 150x9 = 450s
Energy released in time t1
E1 = t1 Qp/3 = 450 x 9/3 = 1350MJ
E1 < E so there is steady burning
CE 808 – Chapter 3

35. Example 3.3 Energy released in steady burning
E2 = E - E1 = = 1850 MJ
Duration of steady burning
tb = E2 / Qp = 1850/9 = 206 s
See Fig. for HRR curve for this “fast” fire
CE 808 – Chapter 3

36. Example 3.3
(b) Repeat calculations in (a) for a 'slow' t2 fire growth rate.
Growth factor for slow fire k = 600 s/MW
Time to reach peak HRR
t1 = kQp = 600 x 9 = 1800s
Energy released in time t1
E1 = t1 Qp/3 = 1800 x 9/3 = 5400 MJ
E1 > E, so fire does not reach steady-burning time for all fuel to burn
tm =(3E k2)1/3 = (3 X 3200 X 6002)1/3 = 1512s
Heat release at time t1
Qm = (tm/k)2 = (1512/600)2 = 6.3 MW
See Fig 3.5 in textbook for HRR curve (shown as the 'slow' fire)
CE 808 – Chapter 3

37. Example 3.4
(a) Calculate the steady-state heat transfer through a 150 mm thick concrete wall if the temperature on the fire side is 800°C & the temperature on the cooler side is 200°C.
Wall thickness x = 0.15m
Temperature difference
T = = 600°C = 600 K
Temperature gradient
dT/dx = 600/0.150 = 4000 K/m
Thermal conductivity
k = 1.0 W/m-K (from Table 3.4 in textbook)
Heat transfer
q" = k dT/dx = 1.0 x 4000 = 4000 W/m2 = 4 MW/m2
CE 808 – Chapter 3

38. Example 3.4
(b) Calculate the convective heat transfer coefficient on the cool side of the wall if the ambient temperature is 20°C and all the heat passing through the wall is carried away by convection.
Temperature of wall Tw = 200°C
Ambient temperature Ta = 20°C
Temperature difference
T = Tw- Ta = = 180°C= 180K
Heat transfer q" = 4000 W/m2
Convective heat transfer Coefficient
h = q” / T = 4000/180 = 22.2 W/m2K
CE 808 – Chapter 3

39. Example 3.5
Calculate the radiant heat flux from a window in a burning building to the surface of an adjacent building 5.0 m away. The window is 2.0 m high by 3.0 m wide and the fire temperature is 800°C. Assume an emissivity of 0.9.
Emitter height H = 2.0 m
Emitter width W = 3.0 m
Distance from emitter r = 5.0 m
CE 808 – Chapter 3

40. Example 3.5 Height ratio x = H/2r = 2/(2 x 5) = 0.20
Width ratio y = W/2r = 3/(2 x 5) = 0.30
Configuration factor
 = 1/90 [x/1+x2 tan-1(y/1+x2) + y/1+y2 tan-1(x/1+y2)] =
Emitter temperature T = 800°C = 1073K
Emissivity  = 0.9
Stefan-Boltzmann constant
 = 5.67x10-8 W/m2K4
Radiant heat flux
q” =    T4 = x 0.9 x 5.6 x 10-8 x 10734/1000
= 4.69 kW /m
CE 808 – Chapter 3