无界域—维热平流热传导问题的解析人工边界条件

摘要

以核废料处置库近场环境的对流传热过程为研究对象,采用解析法,推导了无界域内一维热平流热传导过程的准确人工边界条件.针对饱和多孔介质的一维水流传热问题,考虑半无界域内的温度边界情况和无界域内的热流集度情况,分别采用准确人工边界条件和下游特定位置处的温度人工边界条件,利用有限差分法计算任意时刻的温度分布.通过与半无界域内一维水流传热问题的解析解对比,验证了准确人工边界条件的可用性和准确性.结果表明,采用温度人工边界条件计算时,如果传热时间足够长,则温度计算点离人工边界位置越近,计算误差就越大；相比之下,采用准确人工边界条件计算时,计算误差很小,并与人工边界的具体位置无关.%Taking the advective-conductive heat transfer in the near filed of nuclear waste repositories as the subject of study, an analytical exact artificial boundary of 1-D advective-conductive heat transfer in unbounded domain is proposed in this paper. According to the 1-D advective-conductive heat transfer of porous media in unbounded domain, two numerical examples are solved by finite different method, in which an exact artificial boundary and a Dirichlet boundary condition are adapted. The first example with Dirichlet boundary condition in semi-infinite extent is provided for illustration of the proposed boundary condition with comparison of an analytical solution, and the second example takes into account of contributed heat sources in unbounded domain. The result indicates that the error of temperature, solved by the Dirichlet boundary condition, is greater with the position closer to the artificial boundary on a long enough time of heat transfer. In contrast, the error, calculated with the proposed exact artificial boundary, is very small and has no correlation with the position of the artificial boundary.