Discussion on numerical treatment of periodic boundary condition for temperature

For periodic fully developed fluid flow and heat transfer problems, it is sufficient to confine attention to a single cycle. The temperature periodic conditions at the computational domain inlet/exit for fluid temperature can be implemented by two methods: either by extending the computational domain by several control volumes and replacing the field data at the domain inlet and outlet by each other, or by using linear interpolation while restricting the computation within one module. By carefully examining the numerical solutions of the fluid streamwise bulk temperature obtained from the two methods, it is found that at the fluid bulk temperature varies abruptly at the domain exit. A comprehensive analysis reveals that this abnormal phenomenon is caused by the fact that the domain exit fluid bulk temperature is actually not updated with iteration. A remedy is proposed: The domain exit bulk temperature is updated by an upwind-based interpolation method. Numerical examples show that the second-order interpolation method is feasible and reliable.