The Thermal Explosion Revisited

Details The Thermal Explosion Revisited The Thermal Explosion Revisited

1999-09-17

arxiv.org/abs/math/9909103v1

Mathematics

Numerical Analysis

9 pages

Scientific paper

The classical problem of the thermal explosion in a long cylindrical vessel is modified so that only a fraction $\a$ of its wall is ideally thermally conducting while the remaining fraction $1-\a$ is thermally isolated. Partial isolation of the wall naturally reduces the critical radius of the vessel. Most interesting is the case when the structure of the boundary is a periodic one, so that the alternating conductive $\a$ and isolated $1-\a$ parts of the boundary occupy together the segments $2\pi/N$ ($N$ is the number of segments) of the boundary. A numerical investigation is performed. It is shown that at small $\a$ and large $N$ the critical radius obeys a scaling law with the coefficients depending upon $N$. For large $N$ is obtained that in the central core of the vessel the temperature distribution is axisymmetric. In the boundary layer near the wall having the thickness $\approx 2\pi r_0/N$ ($r_0$--the radius of the vessel) the temperature distribution varies sharply in the peripheral direction. The temperature distribution in the axisymmetric core at the critical value of the vessel radius is subcritical

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