The results of the application of the similarity theory of thermophysical processes to the modeling of hydrodynamics and heat transfer in liquid metals in intricately shaped channels and rod systems (reactor cores) as well as the temperature and velocity fields in the top chamber of a fast reactor in different operating regimes are reported. Direct modeling can be used without restrictions only for processes in which the characteristic similarity numbers are functions of only the geometric simplexes of the system and one determining criterion. The presence of two determining criteria, such as, for example, the Reynolds and Prandtl numbers, in the case of heat transfer appreciably complicates the modeling. In the case of three determining criteria, direct modeling is usually unfeasible. In such cases, systematic multivariate experiments must be performed. The task of such experiments is to determine the effects that are allowed by the general mathematical model but are not reproducible, at the current level of mathematical technologies, either analytically or in numerical studies.

将热物理过程的相似性理论应用于复杂形状的通道和棒系统（反应堆堆芯）中液态金属的流体力学和传热建模以及快速反应器顶室中的温度和速度场的应用结果在不同的操作方式下都有报道。直接建模可以不受限制地仅用于特征相似度数仅是系统的几何单纯形和一个确定标准的函数的过程。在传热的情况下，两个确定标准的存在，例如雷诺数和普朗特数，明显使模型复杂化。对于三个确定标准，直接建模通常是不可行的。在这种情况下 必须进行系统的多元实验。这种实验的任务是确定在分析或数值研究的当前数学技术水平下，通用数学模型所允许但不可再现的效果。