含义Meaning
放热反应的发热随温度指数增长，而冷却移热随温度线性增长。两曲线相切时为临界条件，超过则发生热失控（谢苗诺夫，1928）。是化工过程安全的基础。
Heat generation rises exponentially with temperature while cooling rises linearly. Tangency of the two curves is critical; beyond it thermal runaway occurs (Semenov, 1928) — a foundation of process safety.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(U\) | 传热系数heat-transfer coefficient | W·m⁻²·K⁻¹ |
| \(A\) | 传热面积heat-transfer area | m² |
| \(T_c\) | 冷却介质温度coolant temperature | K |
推导Derivation
稳态要求 \(Q_\text{gen} = Q_\text{rem}\) 且 \(dQ_\text{gen}/dT < dQ_\text{rem}/dT\)（稳定交点）。
Stable steady states need equal heat rates and a steeper removal line.
临界时两曲线相切：值相等且斜率相等，用 \(dk/dT = kE_a/RT^2\)。
At criticality values and slopes match.
大活化能近似下得到 \(T_\text{crit} - T_c \approx RT_c^2/E_a\)（约 20–30 K），即“谢苗诺夫数” \(\psi = 1/e\)。
For large Ea the critical temperature rise is ≈ RT²/Ea.
适用条件与局限Assumptions & limitations
均匀温度（强搅拌）假设；非均匀体系用弗兰克–卡缅涅茨基理论。忽略反应物消耗。
Uniform temperature; non-uniform systems use Frank-Kamenetskii theory; reactant consumption ignored.