1. Heat Transfer in Structures
Dr M Gillie

2. Heat Transfer Fundamental to Fire Safety Engineering
Three methods of heat transfer
Radiation - does not require matter
Conduction – within matter (normally solids)
Convection – as a result of mass transfer

3. CONDUCTION

4. Some Physics Heat flow proportional to thermal gradient
Heat flows from hot to cold
k thermal conductivity (material property)
c specific heat capacity give amount of heat needed to change temperature of mass m by ΔT as:

5. Fourier’s Law Heat flux per unit area Heat flow proportional
to temperature gradient
Heat flowing from hot
To cold
Insulated a
Constant
Temp
Constant
Temp
q’’
Steady-state conditions
Insulated

6. Steady-state 1-d Heat Flow
Assume total heat in bar
does not change with
Time – steady state
Insulated A T1
q’’
Steady-state conditions T2 L

7. Transient Heat Flow 1-d
Insulated A T1 T2
Varying heat
flow x dx L

8. Transient Heat Flow 1-d
Insulated A T1 T2
Varying heat
flow x dx L

9. CONVECTION

10. Convection
Heat transfer from solid to fluid as a result of mass transfer
Can be “forced” or “natural”
First studied by Newton for cooling bodies
Governed by
Fluid at T2
Solid at T1
h= convective heat transfer coefficient

11. h Convective heat transfer coefficient depends on
Temperature
Free or forced convection
Turbulence
Geometry
Viscosity
Etc etc
Difficult to determine accurately. “Engineering” values often used.

12. Radiation

13. What is Radiative Heat Transfer?
Electromagnetic radiation emitted on account of a body’s temperature
Requires no medium for transfer
Only a small portion of spectrum transmits heat ( um)

14. Preliminaries – Absolute Temperature
Absolute temperature needed for radiative heat transfer problems
Measured in Kelvin (K)
0 K at “Absolute 0” - all atomic motion ceases
A change of 1K equals a change of 1ºC
0 ºC equals K

15. Preliminaries – “Black bodies”
Black bodies are hypothetical but useful for analysis of radiation
Absorb all incoming radiation
No body can emit more radiation at a given temperature and wavelength
Are diffuse emitters
The Sun is very close to being a black body

16. Stefan-Boltzmann Equation

19. Stefan-Boltzmann Equation in Action
Question: What is the net incident
radiation arriving at B?
Each “piece” of area emits
uniformly in all directions
according to E=εσT4 B T2 A A T1
Hot surface

20. Stefan-Boltzmann Equation in Action
Question: What is the net incident
radiation arriving at B?
Answer depends on
The relative temperatures A and B
radiation is a two way process
-The geometry of the system –
configuration factors B T2 d
Some radiation
“escapes” and does
not reach B A T1

21. Configuration Factors
Take account of the geometry of radiating bodies
Allow calculation of net radiation arriving at a surface
Calculation involves much integration – only possible for simple cases
Details not needed for this course
Two kinds
Point to surface (eg fire to ceiling)
Surface to surface (e.g. smoke layer to ceiling)

24. For compartment fires Thick layer of hot gas, opaque Fire compartment
Hot gases are radiating and so
Ceiling “sees” all of the area of
The room. Therefore configuration
factor~1.
Local fire or
flashed over fire

25. Heat Transfer to Steel Structures
Several cases - insulated, uninsulated etc
Simple solution methods presented
More advanced solutions possible but require LOTS more analysis
Approach is to make conservative assumptions

26. Un-insulated Steel Assume constant temperature in cross-section
lumped capacitance
Apply energy balance to the problem
Solve for small time-steps to get approximate solution
Involves use of radiative and convective heat transfer equations

27. Un-insulated steel q’’ consists of two parts
Heat flowing into a unit length of section in time Δt is equal to the energy stored in the section
Assume steel
at uniform
temperature, Ts
Perimeter=H
Area=A
q’’ consists of two parts
convection
radiation
Convection and
radiation to steel from
gas at Tg
Substituting and rearranging results

28. Section Factors Give a measure of how rapidly a section heats
Normally ratio of heated perimeter to area
Given in some tables
Various other measures and symbols used
Area to volume

29. Insulated Steel-Sections (1)
Insulation has no thermal capacity (e.g. intumescent paint)
Same temp as gas at outer surface
Same temp as steel at inner surface
Therefore conduction problem
Perimeter=H
Area=A

30. Insulated Steel-Sections (1)
Energy balance approach used again
q’’ now as a result of conduction only
Perimeter=H
Area=A
Which gives
Insulation thickness d

31. Insulated Steel-Sections (2)
Insulation has no thermal capacity (e.g. cementious spray)
Assume linear temperature gradient in insulation
Perimeter=H
Area=A

32. Insulated Steel-Sections (2)
Energy balance approach used again
Perimeter=H
Area=A
q’’ now
energy in
insulation
Insulation thickness d
Which gives

33. Heat Transfer in Concrete
Very large thermal capacity
Heat slowly
Lumped mass approach not appropriate
Complicated by water present in concrete
Usually need computer analysis for non-standard situation
Results are published for Standard Fire Tests

34. Heat penetration in concrete beams

35. Heat penetration in concrete slabs
(mm)