Solid Ignition TimeThermally thin and thermally thick ignition

What this calculates

This sheet uses basic conduction equations to estimate the time at which a solid will ignite when subjected to a given heat flux. A good example would be if you had a burning pool fire of gasoline, used the “Radiation Pool Fire” spreadsheet to determine the heat flux some distance away where another fuel package was (A wood chair, an upholstered sofa, some cotton drapes, etc.) and used this sheet to determine when that second fuel package would ignite.

We must treat thermally thin items differently than thermally thick items, so there are two different equations provided on this sheet. The thermally thin equation should be used when the item is less than 1/16” thick, anything thicker should use the other equation.

There is one block of cells for thermally thin items, and two blocks of cells on the sheet used for ignition of thermally thick items (the 2nd and 3rd blocks). The two thermally thick blocks are both the same; the only difference is that the first requires user input for the material properties; the other performs the same calculation but uses a dropdown box to select a material and automatically populate the material properties from a table.

How to use it

Determine whether the solid material you are interested in is thermally thin or thick. If it is thin, put the material thickness and thermal properties for density, specific heat, and ignition temperature into the top section. A good place to find these values for some materials would be Quintiere table 3-1 and 4-3 or in Appendix B of the SFPE Handbook. If you can’t find paper, something like wood might be an appropriate substitution. Use the best data you can find and make note of any assumptions that you have made along the way. Determine the heat flux exposure to enter; in the field, this would often come from a radiation calculation (such as the one in the “Radiation Pool Fire” spreadsheet).

For a thermally thick item, check the dropdown box in the bottom section for the material you are interested in. If it (or something close) is there, choose that, then enter the ambient temperature and the heat flux exposure; the ignition time will be reported at the bottom.

If the thermally thick item that you are interested in is not available in the dropdown box, then you will need to look up the appropriate material properties somewhere else and populate the middle block to get your result.

Variables

t_ig

Time to ignition [s]

k

Thermal conductivity [kW/m·K]

ρ

Density of material [kg/m³]

c

Specific heat [kJ/kg·K]

kρc

Thermal inertia (tabulated, thermally thick) [(kW/m²·K)²·s]

T_ig

Ignition temperature [°C]

T_a

Initial / ambient temperature [°C]

ℓ

Material thickness (thin case) [m]

q″

Heat flux exposure [kW/m²]

q″_cr

Critical ignition flux (tabulated) [kW/m²]

C

Constant — π/4 (no losses) or π/6 (some losses) [—]

Equations

Discussion

A thermally thin object assumes that the item is thin enough that the temperature almost instantly becomes the same on the backside as on the front. As a material gets thicker it becomes less like a thermally thin object. Therefore, we need to account for some length (thickness).

For thermally thick items we are assuming that the backside never heats up to the surface temperature, so mathematically the thickness drops out (we only care about the surface where the ignition is happening here). What comes in though in this case is the thermal conductivity, because now we care how fast heat is conducting away from the surface (where as in the thin case there is nowhere for the heat to go).

The material properties referenced by the drop-down box are from 4-3 of Quintiere’s “Principals of Fire Behavior”.

Worked example