## 2 Related Theories and Sample Preparation
### Preparation of FIRCs  
This study used TiO\({}_{2}\) (TG-P25, Tokyo, Degussa, Japan) and MWCNTs (OD: 20-30 nm; Cheap Tubes, Grafton, VT, USA) as FIRMs, and the transmission electron microscope (TEM; H-7100, Hitachi, Saitama, Japan) image of these FIRMs are shown in Figure 1. The particle size of TiO\({}_{2}\) and the outer diameter of MWCNTs are about 30 nm and are in compliance with the specifications marked by the manufacturer. First, this study added 10 wt % FIRMs to the water and used an electromagnetic stirrer (PC420D with 600 rpm, Corning, Corning, NY, USA), an ultrasonic cleaner (5510R-DTH, Branson, St. Louis, MO, USA), and a high-speed homogenizer (YOM300D Yotec, Taiwan) with 3000 rpm to stir and disperse the FIRMs for 30 min by each dispersion equipment. Finally, the well-dispersed FIRM aqueous suspension was added to water-based acrylic paint (Asahipen, Osaka, Japan) at a ratio of 1:4 (\(w/w\)) to form FIRCs with a FIRMs concentration of approximately 2.5 wt %. Then, this study used the above dispersion equipment to alternately disperse FIRCs three times (each equipment is executed for 30 min each time), in order to uniformly disperse the FIRMs in FIRC and maintain superior suspension performance. At this time, the preparation procedure of FIRCs is completed.  
Two FIRCs were evenly coated on the surface (single side) of #304 stainless steel sheets (W \(\times\) L \(\times\) T: 160 \(\times\) 370 \(\times\) 0.18 mm, weight: 80.02 \(\pm\) 0.15 g) by the brushing method. After each coating was completed, it was heated and dried (50 \({}^{\circ}\)C) by a heating oven and weighed with an electronic balance (GX-6100, A&D, Tokyo, Japan; accuracy of \(\pm\)0.1 g, resolution of \(\pm\)0.01 g), and if the weight was insufficient, it was coated again. In order to compare the difference between samples with and without coatings, and coatings with and without FIRMs, the test samples also included uncoated stainless steel plates (Blank) and stainless steel plates coated with 25% water-based acrylic paint (Base). The coating weights of all coated samples (Base, TiO\({}_{2}\)-FIRC, MWCNTs-FIRC) were controlled within 2.25 \(\pm\) 0.03 g. Figure 2 shows three coated test samples, where the coating weights of the Base, MWCNTs-FIRC, and TiO\({}_{2}\)-FIRC are 2.28, 2.24 and 2.23 g, respectively.  
Figure 1: TEM image of FIRMs: (**a**) TiO\({}_{2}\); (**b**) MWCNTs.  
Figure 2: The coated test samples: (**a**) Base; (**b**) MWCNTs; (**c**) TiO\({}_{2}\).  
Figure 3 shows the emissivity (\(\varepsilon\)) of the coated test samples with Base, TiO\({}_{2}\)-FIRC, and MWCNTs-FIRC at the sample temperatures of 40 and 80 \({}^{\circ}\)C. The emissivity of the samples were measured at different wavelengths using an FT-IR spectrometer (VERTEX 70, Bruker, Ettlingen, Germany). According to [PERSON]'s displacement law, the wavelength of the maximum radiation energy corresponding to 25-65 \({}^{\circ}\)C (approximate temperature range of hot water heater) is 9.72-8.57 \(\upmu\)m. The average \(\varepsilon\) of the Base, TiO\({}_{2}\)-FIRC, and MWCNTs-FIRC at wavelengths of 9.72-8.57 \(\upmu\)m under the average sample temperature were 0.82, 0.97, and 0.94, respectively.