Numerical heat transfer model for swelling intumescent coatings during heating

Abstract

This research study presents a heat transfer model aimed at estimating the thermal and physical response of intumescent coatings. The numerical model is inspired by the outcomes of an experimental study focused on analysing the insulating effectiveness of a commercial intumescent coating 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. The coating swelling is implemented in the model by adopting an approach based on expanding the mesh representing the physical domain in proximity to the substrate-coating interface. The model described herein offers researchers and engineers a tool to estimate the heat transfer of swelling intumescent coatings (i.e. in-depth thermal gradient). Outcomes of the analysis shown herein demonstrate that the heat conduction within intumescent coatings is governed by the physical coating swelling and the thermal conditions at the coating-substrate interface. The numerical model shows that its accuracy is highly influenced by the coating thickness ahead of the reaction zone. Consequently, the coating swelling rate plays a key role, while the thermo-physical properties of the intumescent coating have a secondary effect. According to its assumptions, the model defines a quasi-steady-state thermal problem: it is more accurate for conditions close to steady-state (e.g. high heat fluxes), but it loses accuracy for cases characterised by transient phenomena (e.g. phases prior to the onset of swelling and low heat fluxes).