热爆炸问题再探
The Thermal Explosion Revisited
AI总结：
该研究修改了长圆柱容器热爆炸经典问题，考虑壁面部分隔热，通过数值方法发现临界半径遵循标度律，且大N时核心温度轴对称、边界层温度变化剧烈。
摘要：
经典的长圆柱形容器中的热爆炸问题被修改，使得容器壁只有一部分比例 $\a$ 是理想导热的，而剩余比例 $1-\a$ 是热隔离的。壁的部分隔离自然降低了容器的临界半径。最有趣的情况是边界结构为周期性结构，即交替的导热部分 $\a$ 和隔离部分 $1-\a$ 共同占据边界的 $2π/N$ 段（$N$ 为段数）。进行了数值研究。结果表明，在小的 $\a$ 和大的 $N$ 下，临界半径遵循一个标度律，其系数依赖于 $N$。对于大的 $N$，得到在容器的中心核心区域温度分布是轴对称的。在靠近壁的边界层中，其厚度约为 $2πr_0/N$（$r_0$ 为容器半径），温度分布在周向方向上变化剧烈。在容器半径的临界值下，轴对称核心中的温度分布是亚临界的。
英文摘要：
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 $2π/N$ ($N$ 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 $\approx 2πr_0/N$ ($r_0$--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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