Approximate Analytical Solutions For The Transient Mass Loss Rate And Piloted Ignition Time Of A Radiatively Heated Solid In The High Heat Flux Limit

Abstract

An approximate closed form solution is developed for the mass loss rate of a semiinfinite solid irradiated by a constant net heat flux. The solution is valid at high heat flux levels where surface losses and the endothermic heat sink due to pyrolysis are small in comparison to the applied heat flux. The expression obtained for the mass loss rate is used to develop an explicit closed form relation for the time to piloted ignition using a critical mass flux as the ignition criterion. The resultant formula is identical to that obtained from the classical thermal ignition theory, with the important difference that the surface temperature at ignition is not constant. Rather, it increases with applied heat flux, mass flux at ignition, and activation temperature, and decreases with increasing density, pre-exponential factor, and thermal conductivity. The model predictions are compared to recent high-heat flux ignition measurements for PMMA.