In this analysis, Janssens developed a simplified thermal model for piloted ignition of wood products. The model allows for temperature-dependent thermal properties for the sample and nonlinear boundary conditions. Janssens solved the equations numerically using a finite difference technique. Running the model systematically, a functional relationship was developed between the ignition time and the exterior heat flux. This relationship has been used to correlate experimental data, and Janssens believes this accounts for the temperature-dependent material properties and nonlinear boundary conditions. The functional form of Janssens' correlation is:

Where:

The critical heat flux, , is calculated from the intercept of the ( t _ig) ^?0.547 versus plot. The h _ig is calculated using Equation 16:

Jannsens suggested that ? = 0.88 be used as typical for wood. Equation 15 can be rearranged to solve for t _ig, which results in the following relationship:

Janssens' correlation plots the data as ( t _ig) ^?0.547 versus as shown in Figure 5. The ( x) symbols indicate the data points, and the solid line is the best-fit linear regression line.

Figure 5: Plot of ( t _ig) ^?0.547 Versus for a Thermally Thick Pine Showing the Linear Nature of the Correlation

The apparent k ? c and are calculated from the slope and intercept of the regression line through the data plotted...