Thermal analysis of heat transfer in pipe cooling concrete structure by a meshless RBF-FD method combined with an indirect model

Numerical simulation of heat conduction in the concrete structure with cooling pipes is meaningful and full of challenges. In this paper, the radial basis function finite difference method (RBF-FD) combined with a self-correcting prediction model (SCM) is proposed for thermal analysis of heat transfer in concrete structures with pipe cooling system. Using the Multiquadric radial basis function (MQ-RBF), the SCM is proposed to give full play to advantages of the localized meshless method. This technique allows use of more number of nodes in the whole domain to solve the ill-conditioning problem associated with multiple regions of rapid variation and increases the accuracy of models. A multiple-scale technique is applied to determine the shape parameter in the MQ-RBF and the fictitious nodes method is modified by using just one fictitious node outside the domain to deal with boundary conditions of the third kind in tiny holes. To show the flexibility and efficiency of the proposed scheme, we consider several examples with different number, size, and positions of pipes. Meanwhile, a guidance of determination of effected area near a tiny hole is provided and a simple optimization design of cooling pipe system is performed. The results demonstrate advantages of the proposed model which can effectively handle heat conduction problem with multiple holes subjected to the third kind boundary conditions. •The indirect scheme is simple, accurate and avoids the difficulty of adaptive collocation procedure.•The RBF-FD-SCM is accurate and efficient for the problem with many tiny pipes.•The proposed scheme is flexible to use just a set of fixed collocation points, even for multi-pipe cases.