Quick estimation of f(E) in the distributed activation energy model (DAEM): an inverse problem approach

Abstract

An inverse problem in distributed activation energy model is the problem of estimating unknown activation energy distribution of a thermoactive material from the measured volatile fractions emitted under heating. In this work, a closed-form approximation to the problem is derived by establishing a mathematical analogy with the inverse Fermi system problem in physics. The new solution allows for deriving distribution function f(E) from a single set of non-isothermal linear, parabolic or exponential heating data with a constant k0, compared with the existing iso-conversional integral methods in which at least three sets of linear heating data are needed. An error analysis and comparison of the proposed method along with the Miura’s is performed through case studies covering a wide range of model parameters, showing that our method is accurate enough and applicable in thermal analysis. Besides, physical implications drawn from present exploration are discussed.