Researches about comprehensive, systemic and multi-level assessment methods are limit. Therefore, a comprehensive assessment method of heat exchangers based on extension theory is proposed. Heat transfer, pressure drop, mechanism, safety and reliability, economy, structure, mechanism and production performance are considered and evaluated in detail. By using this method, the comprehensive performances of the shell-tube and printed circuit heat exchangers as the intermediate heat exchanger of the accelerator driven sub-critical system are evaluated for comparison. The results show that the economy performance and pressure drop for the shell-tube heat exchanger attain the highest grades because the processing technology is mature and flow velocity is lower. However, the structure performance parameter is the lowest level due to its large volume and mass. For the printed circuit heat exchanger, the safety and reliability performance attains the lowest grade due to its easily blocked mini-channels and the manufactured thin plate. However, the mechanism performance shows the highest grade. In addition, the pressure drop performance also attains the highest grade due to its large cross-sectional area and low flow velocity. In conclusion, the comprehensive performance of the printed circuit heat exchanger is theoretically better than the shell-tube heat exchanger.
As a clean and renewable source of energy, nuclear energy has the unique advantage and development potential on reducing the emissions of greenhouse gases and mitigating the pressure of energy transmission effectively [1,2]. Currently, how to dispose the nuclear waste has the constraint on the development of nuclear energy. Through the collision of proton beam generated by the accelerator with the spallation target of lead-bismuth eutectic (LBE), the accelerator driven sub-critical system (ADS) could drive and sustain the process of the nuclear transmutation, and reduce the life and radioactive property of nuclear wastes, and therefore is one of the effective resolutions . In this system, LBE is adopted as not only the medium of the spallation target but also the coolant of the reactor due to its good thermal-physical properties [, , ]. The heat produced by the reactor is transferred from LBE to the working fluid of the power generating system through the intermediate heat exchanger (IHE), and the performance of the IHE plays significant impacts on the functions of the ADS and the power generating system. Therefore, systematic and reasonable performance evaluation on the IHE is of great significance.
At first, the performance assessment on the IHE with LBE is from the first principle of thermodynamics. Heat transfer rate, heat transfer coefficient and pressure drop are directly adopted to present heat transfer and flow characteristics of heat exchangers. For example, Ma et al.  experimentally investigated the effect of the straight and U-type tubes on the performance of the IHE with LBE. The heat transfer coefficients and pressure drops are compared between these two heat exchangers. Xi et al.  experimentally tested the performance of a shell-and-tube heat exchanger (STHE) with LBE and helium. The heat transfer rate, the overall heat transfer coefficient and pressure drop of the heat exchanger are obtained with increasing the Reynolds number and inlet temperature. In order to increase commonality, parts of research investigate the dimensionless performance parameters related to heat exchangers, such as Nusselt number, friction factor, effectiveness and number of transfer units (NTU). Chen et al.  numerically simulated a STHE with LBE and they utilized the overall heat transfer coefficient to compute the NTU and effectiveness of the heat exchanger for evaluation. Wang et al.  compared the effectiveness and friction factor of the STHE with LBE and helium with those concluded from correlations. Khan et al.  designed a compact heat exchanger with LBE and the heat transfer coefficient and Nusselt number are adopted to evaluate the performance of the heat exchanger. In order to fully consider the flow and heat transfer characteristics of the IHE, a comprehensive performance evaluation criterion (PEC) is introduced. Zhao et al.  changed straight tubes with twisted tubes for the IHE. The results show that the PEC of the twist-tube heat exchanger is improved by 1.2–1.7 times compared with the straight-tube one. Yang et al.  numerically studied the STHE with LBE and water, and the PEC is analyzed to optimize the inlet velocity of LBE.
In this study, through the analysis on matter element model, a comprehensive evaluation system of heat exchangers is built. The classical and joint domains are confirmed according to the databases and expert opinion. The weights of the performance indexes of the heat exchanger are set based on fuzzy analytic hierarchy process. The correlated function and evaluation grade are defined. At last, a comprehensive evaluation method of heat exchangers based on extension theory is proposed.
The SHTE and PCHE are chosen as the IHE with LBE and helium of the ADS for theoretical comparison. Although the flow channel in the SHTE is larger and that in the PCHE, the pressure drop performance for these two heat exchangers show the same grade. This is because the cross-sectional area of the PCHE is large and therefore the fluid flow velocity is low. The mechanism performance of the PCHE attains the highest grade because the plates are welded by the vacuum diffusion bonding. In conclusion, these two heat exchangers show the same evaluation grade. However, the comprehensive performance of the PCHE is theoretically better than that of the STHE due to the larger characteristic value. With the develop of the processing technology and the wide application of the PCHE, the production cycle is shortened and the manufacture and cost is deduced. In the future, the comprehensive performance of the PCHE would be even better.