ABSTRACT

We have done several studies of condensed-phase combustion (as well as gas-phase combustion). In one of those studies, which we summarize here, we relied heavily on MAPLE. The problem we set out to investigate was suggested by some experiments done in the Soviet Union in the 1970s. The physical problem concerned the propagation of a combustion front down a cylindrical solid fuel element. Experimental observations suggested that the combustion front could propagate in a number of ways. One mode of propagation was that of a uniformly propagating plane front. However, under specific circumstances, which could be controlled by the experimenter by varying the amount

The mathematical model consists of two partial differential equations, one for a suitably nondimensionalized temperature, 0, and another for the position of the combustion front, IP. It is derived on the assumption that the activation energy, which is needed to get the chemical reaction to go, is large (but not necessarily infinite). The independent variables are the time t, the angular variable 'lj; (0 :$ 'lj; < 21r ), and the axial variable z ( -oo < z < oo ). Both 0 and IP are 27r-periodic functions of 'lj;. The radius of the cylindrical fuel element is p. '