Burn angle in forced and natural convection: a simplified scaling approach

The surface regression of burning solid fuels facing a forced flow has been observed and measured by several authors, because of its connection with mass burning rate and heat transfer between flame and fuel. The pyrolysis region of non-spreading flames is not uniform in space and changes in shape with time. On the contrary, for moving flames experiments showed that the competition between surface regression and spread rate causes the pyrolysis region to assume a steady-state geometry. In particular, the declination of the pyrolysis surface is constant for given burning conditions, although it is highly influenced by their variations. The geometry of the pyrolysis region is characterised by the surface declination angle, called burn angle, which can be used to study the relation between mass burning rates and flame spread rates. Despite the amount of experimental work in literature, a theoretical description of the burn angle and its dependence on burning parameters such as flow velocity is still missing....