A novel approach to model the thermal and physical behaviour of swelling intumescent coatings exposed to fire

Abstract

The research study presented herein proposes a finite-difference heat transfer model aimed at simulating the thermal and physical response of swelling intumescent coatings during heating. The numerical model is based on the outcomes of a previous experimental study which analysed the effectiveness of thin intumescent coatings for a range of heating conditions and initial coating thickness. The model solves the one-dimensional heat conduction problem using the finite-difference Crank-Nicolson method, and it assumes that the effectiveness of intumescent coatings is mainly dependent on their ability to develop swelled porous char. Accordingly, the coating swelling is implemented by adding finite elements in the proximity of the substrate-coating interface following empirical correlations, and the intumescent coating is modelled as swelled porous char with constant material properties. The described model offers a performance-based design engineering tool able to characterise the heat transfer through swelling intumescent coatings (i.e. thermal gradient) by predicting the evolution of the coating surface and substrate steel temperatures, and the evolution of the swelled coating thickness. Based on its assumptions, the numerical model defines a quasi-steady-state thermal problem: more accurate for conditions close to steady-state (e.g. high heat fluxes), but it loses accuracy for cases characterised by transient phenomena.