## 3 Results  
### Fouling Resistance Analysis  
The fouling resistance indicates the decrease in heat transfer efficiency due to deposits on the heat transfer surface of the heat exchange device, that is, the heat transfer resistance of the deposit on the heat transfer surface [2]. The real-time fouling resistance was calculated using Equations (2) and (3) and is shown in Figures 3 and 4. A time interval, which is called the initiation period or delay time, generally occurs from the start of the experiment to the detection of the fouling resistance [4]. However, no remarkable delay time was observed in this experiment due to the high hardness of the circulating cooling water. Magnesium ion concentration, as an important role, affects the fouling resistance. Figure 3 depicts that the fouling resistance of the control group changed and remarkably increased with time. The increase in No. 3 control group was significantly greater than that in the two other groups. Compared with that of No. 3 control group, the magnesium ion concentration of No. 2 control group inhibited the growth of the adherent scale. In the final stage, the fouling resistance curve tends to be gentle. This phenomenon occurred because the shearing force of the water transports some of the scales from the copper tube wall, and the quality of the subsequently formed scale is equivalent to the mass of the part that was removed. Hence, the two form a dynamic balance, and fouling resistance stops increasing. Figure 4 depicts the change in the fouling resistance of the experimental groups with time. At the beginning of the experiment, the fouling resistance of the three experimental groups showed different degrees of decline. [PERSON] et al. [23] believed that this result occurs because the increase in the number of bubble nucleation sites during this time period affects the heat transfer coefficient near the heat exchanger until the sediment becomes the dominant heat transfer coefficient. No similar phenomenon was observed in the control group. Hence, AEFT was speculated to increase the bubble nucleation sites at the initial stage of the experiment. Compared with the control groups, the experimental groups exhibited fouling resistance at the beginning of the period for approximately 50-100 min at a low level and then increased significantly, indicating that AEFT can delay the fouling time. [PERSON] [4] also observed a similar phenomenon in the study of electromagnetic field scale inhibition. Although many studies confirmed that the high-frequency electric fields of suitable frequency have significant scale inhibition effects [2; 10], the present experimental results showed that AEFT has a slight promoting effect on the formation of scale. For the three experimental groups with AEFT, the fouling resistance curves of Nos. 1 and 2 exhibited a large degree of coincidence. At the end of the experiment, the fouling resistance of No. 1 experimental group was \(2.24\times 10^{-4}\) m\({}^{2}\)K/W, and that of No. Figure 4: Real-time fouling resistance of experimental groups. Figure 3: Real-time fouling resistance of control groups. 1 control group was \(1.99\times 10^{-4}\) m\({}^{2}\)K/W, exhibiting an increase of approximately 12.56%. For No. 2 experimental group, the final fouling resistance was \(2.00\times 10^{-4}\) m\({}^{2}\)K/W, and that of No. 2 control group was \(1.53\times 10^{-4}\) m\({}^{2}\)K/W, exhibiting an increase of 30.71%. In the case of constant magnesium ion concentration, the increase in fouling resistance indicated that AEFT has a certain promoting effect on the formation and growth of adherent scale. The fouling resistance of No. 2 experimental group was nearly twice that of No. 1 experimental group, indicating that the presence of magnesium ions at a concentration of 4 mmol/L enhanced the growth and adhesion of AEFT to the scale. When the magnesium ion concentration was increased, the effect of AEFT on the fouling resistance was quite different. The final fouling resistance of No.