Analytical Solution of Problems about the Radiative and Radiative–Conductive Stationary Heat Transfer in a Medium with an Arbitrary Dependence of the Scattering and Absorption on Frequency Boundary Conditions

We defined a method for the analytical solution of problems on stationary radiative and radiative–conductive heat transfer in a medium with an arbitrary frequency dependence of absorption and scattering near its boundary. We obtained formulas for the heat conductance of the remote surface and the thickness of the radiative–conductive relaxation of the medium. We determined characteristics of radiant heat transfer from the medium to free space such as the radiation spectrum, the radiation temperature and the medium outer boundary temperature. In addition, we solved the problem on the radiative–conductive heat transfer from one of two parallel surfaces to another with a medium between them.

Study of Flow and Heat Transfer Characteristics of Lead-Based Liquid Metals in a Turbulent Tube Flow and the Impacts of Roughness

Lead-based liquid metals (LLMs) such as lead–bismuth eutectic (LBE) and lead, are currently the most interesting candidate coolants for fast reactors because of their excellent physical properties, which can improve safety and reduce costs. However, in comparison to other liquid metals, previous research on the flow and heat-transfer characteristics of LLMs has been limited. Therefore, this work carried out flow and heat-transfer experiments in LBE flowing through a circular tube in the Natural Circulation Capability Loop (NCCL) facility. The results show a significantly higher friction factor than that of water flowing in a smooth pipe. Furthermore, the Nusselt numbers were found to be lower than those found in data in the literature for experiments carried out in a smooth tube at low Péclet numbers, while they were higher at high Péclet numbers. Therefore, theoretical analyses were performed for LLMs flowing in both smooth and rough pipes, and the impacts of roughness on the heat transfer of an LLM were examined. The theoretical relations for a smooth pipe and a rough pipe were validated using experimental data from the literature and the results of the NCCL experiments, respectively. The results of the theoretical relation for a smooth pipe fitted the literature data well. The derived theoretical relation for a rough pipe with a relative roughness of 0.004 fitted the NCCL data best. Moreover, it was established from the theoretical analysis that roughness has two competitive impacts on the heat transfer of an LLM: it reduces conductive heat transfer while enhancing convective heat transfer. Because conductive heat transfer is important for liquid metals, even with turbulent flow, a small roughness will lead to heat-transfer deterioration at low Péclet numbers, and it may even deteriorate across the whole typical Péclet-number range. This discovery has important implications for the thermal–hydraulic design of LLM reactors, because corrosion and erosion by an LLM will lead to a rough surface after long operating times.