Cluster mathematical model for conjugate thermal processes of the isothermal bodies system in the fluid flow

Abstract

Abstract There has been developed a cluster mathematical modelling method for non-stationary thermal processes, occurring in complex technical system structures, which thermal models represent a system of clusters. Each cluster has a core, combining the heat-emitting elements that fall into the said cluster, a shell of the cluster, and a fluid, flowing through the cluster. The state of the thermal process in each cluster at any specific time is characterized by three state variables, namely, by the temperatures of the core, the temperatures of the shell and the ambient temperature. At that, the elements of each cluster (core, shell, fluid flow) exchange heat with each other and the elements of the adjacent clusters. As opposed to existing methods, the cluster method allows modelling thermal processes that occur in complex technical systems, taking into account non-uniform temperature distribution in the fluid flow, conjugate nature of heat transfer between the fluid flow, the cores and the shells of the clusters. The mathematical model, describing state variables of thermal processes in the cluster thermal model, represents a system of block matrix differential equations with matrix and vector blocks, corresponding to the respective clusters of the thermal model. The solution of equations of the mathematical model is the values of the state variables of the thermal processes in the clusters. The methodology of the application of the cluster method is shown on the example of a real technical system.