Abstract
A practical method to calculate some properties for the evaluation of flashover, such as the criterion on or the temperature at its occurrence, from Control Volume mathematical models of fire is derived based upon the characterization of flashover by thermal instability. The method is based on the mathematical optimization to estimate the extremum of an objective function, but it is emphasized that this should be done without calculating the differentials of the basic equations of fire, because mathematical fire models are being developed to be too complicated for analytical operations to be applicable. The report shows, by using a simple model to which analytical treatments are applicable, that the combination of the augmented Lagrangian function method and Hooke-Jeeves algorithm for direct search is appropriate for this purpose, and it studies some problems to improve the precision of the estimation. The established method was applied to the Quintiere et al's quasi-steady model which is too complicated for analytical treatments to be applicable.
