Transient Conduction With Pyrolysis (Approximate Solutions for Charring of Wood Slabs)

The rate of charring of a heated one-dimensional, wood-like solid slab is predicted by solving the transient conduction equation with a phase-change energy sink term. This solution procedure uses an integral method with spatially-linear-temperature profiles. Two types of front-face boundary conditions are considered—prescribed temperature and prescribed heat flux. The backface is insulated. The prescribed temperature condition leads to the conclusion that for all reasonable exposure temperatures, the slab would only partially char. The maximum char depth is most sensitive to the char conductivity and exposure temperature and less sensitive to the char specific heat and charring endothermicity. Results of the constant flux are in reasonable agreement with the available experimental data both qualitatively and quantitatively.