Analytical solutions for prediction of the ignition time of wood particles based on a time and space integral method

The main idea of this paper is to establish a simple approach for prediction of the ignition time of a wood particle assuming that the thermo-physical properties remain constant and ignition takes place at a characteristic ignition temperature. Using a time and space integral method, explicit relationships are derived for computation of the ignition time of particles of three common shapes (slab, cylinder and sphere), which may be characterized as thermally thin or thermally thick. It is shown through a dimensionless analysis that the dimensionless ignition time can be described as a function of non-dimensional ignition temperature, reactor temperature or external incident heat flux, and parameter K which represents the ratio of conduction heat transfer to the external radiation heat transfer. The numerical results reveal that for the dimensionless ignition temperature between 1.25 and 2.25 and for values of K up to 8000 (corresponding to woody materials), the variation of the ignition time of a thermally thin particle with K and the dimensionless ignition temperature is linear, whereas the dependence of the ignition time of a thermally thick particle on the above two parameters obeys a quadratic function. Furthermore, it is shown that the transition from the regime of thermally thin to the regime of thermally thick occurs at Kcr (corresponding to a critical size of particle) which is found to be independent of the particle shape. The model is validated by comparing the predicted and the measured ignition time of several wood particles obtained from different sources. Good agreement is achieved which indicates that the presented ignition time relationships can be used by process engineers and reactor designers for interpretation of ignition data.