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热源为时间的任意函数时,导出了圆柱形燃料棒热传导方程解析解的普遍公式。热源为简单的阶跃常源时,其解只是本文结果的一个特例。假定热源在燃料棒中为均匀分布,单位体积单位时间的热源密度为q(τ),只与时间τ有关,且为τ的任意连续函数。又假定棒外的冷却剂的温度T_m不随时间变化。初始条件为当τ≤0时整个系统处于稳定状态。当τ>0时由于热源变化而引起棒内温度T(r,τ)变化,其中r为棒内每点的空间位置。
When the heat source is an arbitrary function of time, a general formula for the analytical solution of the heat conduction equation for a cylindrical fuel rod is derived. When the heat source is a simple step-source, the solution is only a special case of the results in this paper. Assuming that the heat source is uniformly distributed in the fuel rod, the heat source density per unit volume per unit time is q (τ), only related to time τ, and is any continuous function of τ. Also assume that the temperature of the coolant outside the stick, Tm, does not change with time. The initial condition is that the whole system is in a steady state when τ≤0. When τ> 0, the internal temperature T (r, τ) changes due to the change of heat source, where r is the spatial position of each point in the rod.