(528f) A New Assessment of the Finite Biot Number Correction to Thermal Ignition Tests

Traditionally, effective kinetic parameters for the Frank-Kamenetskii (F-K) thermal explosion model have been obtained through the use of ignition tests on baskets of reactive solid materials. The baskets are inserted into a hot isothermal convection oven, and the outcome is monitored for either subcritical or supercritical (i.e., ignition) behavior. The tests are continued at a fixed basket size by changing the oven temperature for each test in an iterative fashion to bracket the critical ambient temperature for that basket size. After gaining a series of basket size-critical temperature data pairs, a Frank-Kamenetskii graph is used to graphically determine the activation energy and the product of the Arrhenius pre-exponential and heat of reaction. These parameters can then be used in the F-K theory to predict safe storage conditions for larger sizes, different geometries, and different boundary conditions. However, most of the experimental literature ignores the effect of finite heat transfer rates (i.e., finite Biot number) on the reactive material containing baskets even though reasonable correlations have been determined theoretically. There have been a few attempts in the literature to assess the Biot number for the baskets with marginal success. In this paper, wood flour has been utilized as a model compound in F-K basket ignition tests in a large convection oven. The overall heat transfer coefficient was determined experimentally for each of the baskets using an inert solid heating model. The tests were performed at two fan speeds on the oven, and the effect of the finite Biot number is compared to the usual infinite Biot number assumption. If the effects of finite Biot number were neglected, the predicted critical temperature was unacceptably high thus overestimating the safe storage temperature. If standard heat transfer correlations were used for the correction, then critical temperatures were conservatively low yet potentially incurring unnecessary economic penalties. The empirically derived heat transfer corrections provided the best estimates of the true activation energy, yet required significant experimental effort.