Combustion waves in two dimensions and their one-dimensional approximation

A two-dimensional reaction-diffusion system, describing combustion waves in a fuel layer or cylinder is studied. The results are compared with those obtained from a one-dimensional approximate model, where the approximation is motivated by centre manifold reduction. From the comparison it is clear that the one-dimensional approximation is accurate when the heat loss from the layer to the environment is not too large or when the layer is large enough such that the one-dimensional adiabatic approximation is appropriate. This is usually the case in experimental work, but it is not necessarily appropriate to asymptotic calculations. Differences between the one-and two-dimensional models in the size of the layer leading to quenching of the combustion are seen to be significant for certain values of the fuel parameter and heat loss.