The temperature decomposition method for periodic thermal flows with conjugate heat transfer

Abstract

Periodic structures are often found in many industrial applications. Simulations for such systems can be performed over a one-module domain when neglecting variation in fluid properties, and the results can be applied to a multiple-module flow passage. This approach is widely found in previous studies; however, it is limited to systems with relatively simple boundary situations: either the temperature or heat flux can be specified over the wall surfaces. Recently Li and Zhang (J. Heat Transf. 140:112002, 2018; Numer. Heat Tr. B Fund. 74:559, 2018) have proposed a temperature decomposition method, which makes the one-unit simulations possible for the above situations. However, the conjugate heat transfer, for example, between the flowing fluid and the structure materials (solid structure), has not been considered. In this study, we extend the temperature decomposition method to periodic thermal flows with conjugate heat transfer between the fluid and structure. The physical temperature is split into two parts, namely the transient part and the equilibrium part. The governing equations and conjugate relations at the interface for each temperature parts are established, and the corresponding inlet/outlet boundary conditions are proposed. It can be mathematically shown that the temperature obtained from this method satisfies the original energy equation in the fluid and solid domains, the thermal boundary conditions on the system walls, and the conjugate relations at the solid-fluid interfaces. Physical interpretations and numerical implementation steps are also provided. Several simulations are conducted to verify and demonstrate the validity, accuracy, and potential usefulness of our method, and the results and discussions clearly show that the TDM method correctly reflects the underlying relationship in temperature, which otherwise is not available, for conjugate periodic thermal systems.