## 2 Experimental Setup and Data Reduction  
Figure 4 shows the schematic of the experimental setup to study the thermo-physical behavior of supercritical carbon dioxide (s-CO\({}_{2}\)). Firstly, the liquid carbon dioxide was poured into the accumulator (High-pressure laboratory, Xi'an, China). The whole system was then evacuated to 2 Pa. Then, the working fluid was pumped from the tank into the circulation system using a high-pressure constant flow pump (Elite Analytical Instruments Co. Ltd., Dalian, China). Carbon dioxide was cooled/heated when passing through the low-temperature bath (Hepu biotechnology Co. Ltd., Xi'an, China), and reached the desired test conditions. It then flowed into the test section, which was electrically heated using an alternating current (in the range of 0-500 A) at low voltages. Then, the working fluid from the exit of the test section flowed through another constant temperature bath, and was returned to the tank. In this system, all of the connecting tubes were thermally insulated using glass wool to minimize heat losses. A Micro Motion Coriolis flow meter and a transmitter (Emerson, St. Louis, MO, USA) were used to measure the mass flow rate in the system. The flow meter was capable of measuring flow rates up to 0.1 kg/s with a \(\pm\)0.01% full-scale accuracy. The pressure was monitored through Rosemount gauge pressure transducers (Emerson, St. Louis, MO, USA) with the manufacturer's specified accuracy  
Figure 4: Schematic of the experimental setup used to study the heat transfer behavior of Supercritical carbon dioxide (s-CO\({}_{2}\)). AC: Alternating Current; DAS: Data Acquisition System. of \(\pm\)0.04% of full scale. The temperature in the loop was controlled using two constant-temperature baths (Hepu biotechnology Co. Ltd., Xi'an, China). The bath was used to increase or decrease the temperature of s-CO\({}_{2}\) to the desired test section inlet temperature. Several K-type thermocouples (OMEGA Engineering Inc., Shanghai, China) installed in the outer surfaces were used to monitor the amount of energy put into and removed from the flow. Thirty-five (35) K-type thermocouples' wires (OMEGA Engineering Inc., Shanghai, China) were welded on the outer wall's surface, and were 20 mm apart from each other, starting from the inlet. These K-type thermocouple wires had the uncertainty of \(\pm\)0.5 \({}^{\circ}\)C. The bulk temperatures of the fluid at the inlet and outlet were monitored using K-type sheathed thermocouples with the maximum uncertainty of \(\pm\)0.5 \({}^{\circ}\)C. These thermocouples were calibrated against a high oil bath to quantify the systematic error. The material of the test section was a 304 stainless steel circular pipe (Changtai precision alloy Co. Ltd., Xi'an, China) with an outer diameter (OD) and ID of 6 mm and 5 mm, respectively, and a length of 730 mm, as seen in Figure 5. The test section was directly heated by an AC power supply (0-12 V, 0-500 A) to provide the required constant heat flux. The heat flux to the test section was varied by adjusting the current between copper plates at the ends of the pipe. The accuracy of the voltage control was \(\pm\)0.01% of full scale, while that of the current control was \(\pm\)0.04% of full scale. A 20-mm long developing section was provided to ensure that the flow was hydrodynamically fully developed at the entrance of the test section. Furthermore, the test section was electrically and thermally insulated from the rest of loop by using dielectric fitting at the end of the test section. A series of integral experiments were performed by changing the mass flow rate and heat flux for the operating pressures of 7.5, 8.0, 8.5, and 9.0 MPa. The inlet temperature to the test section was varied from \(-\)50 \({}^{\circ}\)C to 100 \({}^{\circ}\)C in order to cover the whole range of bulk temperature spanning the pseudocritical temperature. The mass flux was varied in the range of 100-200 kg/m\({}^{2}\)s, while the heat flux was varied in the range of 5-120 kW/m\({}^{2}\).