โ Scribed by G.N. Gorelov; V.A. Sobolev
No coin nor oath required. For personal study only.
The singularly perturbed system of differential equations describing thermal explosion is analyzed. Critical and transient regimes are modeled by means of integral manifolds theory methods. The mathematical objects are introduced for the nth order reactions and for the autocatalytic case. These objects make it possible to follow the continuous transition of reaction from the slow regime to the explosive one. For the nth-order reaction the critical regime is modeled by the phase trajectory of the system, which includes the unstable integral manifold. In the autocatalytic case the critical regime is modeled by the mathematical object called duck-trajectory in the modern mathematical literature. Such trajectories pass from the stable integral manifold to the unstable one. Systems' trajectories, passing some part of its way along critical trajectories, belong to the transient regimes. Thus the transient region is separated into the region of slow transient regimes and the region of the explosive transient regimes. The asymptotic formulae for the calculation of the critical values of heat loss parameter were obtained.
๐ SIMILAR VOLUMES
A technique for predicting critical points for thermal ignition by solving specific extended systems of equations is presented. In particular, two extended systems for locating limit points and nondegenerate hysteresis points are discussed. These are implemented in a finile-element formulation, whic