Approximate solutions for the ignition of a solid as a function of the Biot number

Abstract

The ignition of a finite planar 1-dimensional solid is addressed for constant applied radiant heat flux. An ignition temperature criterion is used, with constant properties, and linearized reradiation. An approximate integral analysis leads to analytic formulas to predict the ignition time in terms of Biot (Bi) number and heat flux. The accuracy of the integral solution is found to be good compared to the exact infinite series solution for the conduction equation. The integral model is then used to assess the accuracy of common ideal thick and thin formulas for ignition. There is a domain of heat flux and Bi where the ideal formulas are not accurate. An example is given where the integral model is accurately applied to ignition data to illustrate the range where the ideal formula is not accurate.