## 1 Introduction  
At present, high-temperature solar-thermal conversion processing is accomplished mainly by the concentrated solar collection technologies [1; 2], with the implementation forms including the parabolic trough collector system, tower collector system, dish collector system, and linear Fresnel collector system [3; 4; 5]. With the increasing market values, the concentrated solar collection technologies develop fast and are popularly applied into solar-thermal utilizations such as solar heating/cooling in buildings, solar desalination, concentrated solar power (CSP) [6; 7; 8], etc. The parabolic trough collector (PTC) is the most mature technology and is popularly employed all over the world. The PTC system is mainly composed of trough mirrors, heat collecting elements (HCEs), structural support, and a sun-tracking system [9]. In the heat collection process of the PTC system, solar rays projected on the trough mirrors are reflected and concentrated onto the HCEs, the most of rays would pass through the glass envelope, and are blocked and absorbed by the absorber tube deposited with solar selective-absorbing coating (SSC) [10], then the solar energy absorbed is eventually converted into the heat energy of heat transfer fluid (HTF) flowing inside of absorber tube. At present, the operating temperature of PTC system approximately reaches 400 and even 550 \({}^{\circ}\)C as the HTFs are therminol oil or molten salt [11; 12; 13]. Under such high temperatures, HCEs face with many challenges. Besides the structural deformation and poor reliability of HCEs at high operating temperatures [14], considerable heat loss is another knotty and urgent problem. According to the study conducted by National Renewable Energy Laboratory [15], the heat loss increases rapidly with the absorber temperature raised to fourth power, which accounts for almost 19.4% of solar irradiance by the HCE at absorber temperature of 550 \({}^{\circ}\)C, i.e., absolute decrease of thermal efficiency by 19.4% would occur in the PTC system due to excessive heat loss. Therefore, the reduction of heat loss in HCEs at high operating temperature is definitely vital for the further development of the PTC system. Material properties enhancements of the key components in the HCE are the solutions popularly employed by researchers to reduce the heat loss of HCEs. For instance, SSC with lower emittance has been studied and developed for a long time. Up to now, the emittance of state-of-the-art SSC is about 0.09 at 400 \({}^{\circ}\)C [16]; the room for the further decrease of emittance is small because the absorptance of SSC would suffer much with the lower emittance. Therefore, the solution by enhancing the properties of materials hardly exerts effective role in reducing the heat loss. In our previous study [17], we discovered and proposed the negative thermal-flux region (negative energy-flow region) which occurs in approximately upper half of HCE; the discovery of the negative thermal-flux region (NTR) spawned novel optimization methods to effectively reduce the heat loss and improve the overall performance of HCEs. Taking the EuroTrough collector and Schott PTR70 solar receiver as an example [18]: due to the special structural characteristics of the PTC system, the HCE receives 80 times direct normal irradiance (80\(\times\) DNI) at the approximately lower half of the HCE facing the trough mirrors, but only receives one direct normal irradiance (1\(\times\) DNI) at the upper half of the HCE facing the sun as shown in Figure 1. This fact causes a phenomenon that the heat loss of the HCE in the upper half would exceed the absorbed solar energy in this part when the operating temperature is high enough. Consequently, the phenomenon of negative net heat gain in the upper half occurs, and this part in the HCE is thus named as the negative thermal-flux region (see literature [17] for more detail information). Therefore, the reduction of heat loss is vital for the improvement of the net heat gain of the HCE in the NTR.