Reaction–diffusion systems are known to admit travelling wave solutions which can be interpreted as combustion waves if the reaction term is exponential in temperature following the Arrhenius law. The speed of such combustion waves and its parameter dependence is of considerable interest both as a fundamental mathematical problem in combustion and for comparison with experimental results on simple fuels.
In certain fuel systems radiation transfer of heat is as likely a preheating mechanism as conduction of heat. By formulating the appropriate (approximate) one–dimensional equations and solving them numerically it is shown that radiation transfer results in order of magnitude larger speeds for combustion waves. For systems where radiative heat transfer is important, such as a porous solid fuel bed, radiation is shown to be equivalent to a large nonlinear diffusion term.