The method for thermally thin fuels is derived from the solution of the one-dimensional inert heat transfer equation commonly called the lumped heat capacity18 equation, which assumes a uniform temperature across the sample thickness. The full solution for the temperature of a thin fuel can be found in reference 19. The time to ignition, t ig, is estimated from an approximate solution to the heat transfer equation. When the radiant heat loss from the surface is large compared to the convective heat loss, which is the case in ignition problems, the time to ignition can be approximated using Equation 1:
Where:
| T ig | = | ignition temperature |
| T 0 | = | initial temperature |
| p | = | density of the material |
| c | = | specific heat of the material |
| L 0 | = | thickness of the material |
The ignition temperature, density, specific heat, and critical heat flux are determined experimentally.
When correlating data, Equation 1 is used by plotting the inverse time to ignition (1/t ig) versus externally applied heat flux ( 
) as shown in Figure 1. Where the "best-fit" line intersects the abscissa, the time to ignition goes to infinity, which translates as the critical heat flux, 
. The ignition temperature is difficult to measure but can be obtained experimentally or estimated from 
. The ? and L 0 are considered to be independent but can be difficult to measure for some thin fuels. In addition, the specific heat is a function of the temperature and should be...
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