Piloted ignition at square corners of 2D rectangular solids: Asymptotic and approximate solutions

Edges/corners of combustible solids feature greater ignition propensity when heated compared to a slab due to enhanced heating. However, few studies revealed the ignition mechanism involving such unique geometric structure. This work derived asymptotic solutions for corner temperature and ignition time (t_ig) of a 2D rectangular solid plate (temperature gradient in the other direction is neglected) heated at two neighboring edges with varying dimensions, including thick-thick, thick-int, and int-int, where “thick” and “int” designate thermally thick and thermally intermediate conditions in each direction. Two fundamental scenarios, namely a 1D thermally intermediate case considering only convective heat loss and a simplified 2D case neglecting surface heat loss, were examined first and then used to derive the more complex 2D solutions where two identical heat fluxes and convective heat loss were involved. Critical temperature was employed as ignition criterion, suggesting piloted ignition. For thick-thick structure, t_ig^−0.5 linearly depends on imposed heat flux, agreeing with the conclusion of 1D thermally thick solid. Nevertheless, no such linearity was found for thick-int and int-int scenarios. The obtained solutions were verified by comparing with numerical results and exhibited very high accuracy. When combined heat loss (convection and radiation) was incorporated, a constant radiation approximation coefficient was adopted to linearize the boundary conditions, yielding approximate solutions which roughly captured numerical corner temperature but well estimated t_ig. The proposed methodology can be easily extrapolated to square corners of 3D cuboids with varying dimensions. The proposed solutions may benefit fire risk assessment of solids with square edges/corners and quantitative estimate of accelerated flame spread rate over edges of such solids.