To study the heat transfer of pipe cooling process in concrete, an effective model combined with a radial basis function collocation method (RBFCM) is proposed. In this model, a replicable fictitious structure is imported that allows a set of fixed points to supersede the complicated adaptive remeshing or redistributing points, which significantly saves a lot of time and effort in the pre-processing of the numerical algorithm. Moreover, a relation between the mean temperature of water flow and the heat flux is derived from a heat balance equation. The validity of the proposed model is demonstrated in simulation of a typical three-dimensional problem. Numerical solutions are compared with those obtained by the finite element method and some experimental data. To find the optimum design, 32 cases involving 1 to 7 pipes under certain constraints are considered as follows: the quantity of water flow remains unchanged, the volume occupied by pipes keeps the same, and the same initial temperature of water is used for cooling. Since number, size, and positions of pipes are always changing during the design process, the ability of this approach is further illuminated. Finally, the effect of water flow with several conversing frequencies is investigated. As expected, the maximum temperature difference in concrete can be further controlled by enlarging conversing frequency. Numerical results reveal that the optimal design of pipe cooling system can not only minimize temperature, but also control temperature difference of the concrete structure. The process of design is useful for guidance of engineering practice to improve the structural safety and the economy of the whole building process.

为了研究混凝土中管道冷却过程的热传递，提出了一种结合径向基函数配置法（RBFCM）的有效模型。在该模型中，导入了可复制的虚拟结构，该结构允许一组固定点取代复杂的自适应重划或重新分配点，从而大大节省了数值算法的预处理时间和精力。此外，从热平衡方程式导出水的平均温度与热通量之间的关系。仿真一个典型的三维问题证明了所提出模型的有效性。将数值解与通过有限元法获得的解和一些实验数据进行了比较。为了找到最佳设计，在一定的约束下，涉及32个案例，涉及1到7个管道，如下：水流量保持不变，管道所占的体积保持不变，并且使用相同的水初始温度进行冷却。由于管道的数量，尺寸和位置在设计过程中总是在变化，因此这种方法的能力得到了进一步的阐明。最后，研究了几种转换频率下水流的影响。如预期的那样，可以通过增加转换频率来进一步控制混凝土的最大温差。数值结果表明，管道冷却系统的优化设计不仅可以使温度降到最低，而且可以控制混凝土结构的温差。