复合球体非稳态导热的理论解及实例分析

针对二层复合球体在第三类边界条件下的导热微分方程进行了分析求解．以法国Cristopia公司的C．00型蓄冷冰球为例，对温度函数进行求解，分析了温度函数中特征值、指数值的变化规律．当水分别处于固态和液态时，画出了3个典型时刻冰和水的温度曲线．结果表明，在相同的表面传热条件下，冰和水的最外层几乎同时达到0℃．冰内温度变化比水内变化更剧烈，水开始结冰比冰开始融化需要更长的时间．提供的理论解可用于对相关导热问题的求解，以及为近似解或数值解的准确性提供检验标准．

Analytical Solution for the Heat Conduction Problem in a Compound Sphere and its Applications to an Incapsulated PCM

The transient energy equation of a hollow sphere filled with phase change material （PCM） used to store thermal energy is analytically resolved under the third boundary condition, with no phase change taking place. The temperature function is resolved with a typical ice cool storage sphere, and some characteristics of the eigenvalue, and the value of the index function are presented, with the C. 00 type of stored ice ball of a French company of Cristopia as an example. When water is in solid state and liquid stale, the temperature curves of water and ice are drawn at 3 typical temperatures. Under the same heat transfer conditions, it was found that the time needed for water to freeze is much longer than the time needed for ice to melt, and the time needed for the most outsides of water and ice to reach the phase change temperature are almost the same. The temperature field in ice shows a more sharp change than that in water during the same time. The analytical solution can be used to resolve the transient conduction problem in a hollow sphere, and it can provide a standard for evaluating the results of some approximate methods, such as integral methods and numerical methods.