## 3 Results
### Electrochemical Impedance Spectroscopy (EIS)  
Figure 5 shows the Nyquist plots for the API 5L X65 samples under different flow and magnetic field conditions. Evidently, all the graphs show a regular capacitive loop of a single semicircle due to the double layer interface formed between the metal and solution interface for different conditions. The equivalent circuit, generated using Gamry Echem Analyst software, used to analyze the curves obtained from the Nyquist plot, is given in Figure 6, where R\({}_{\rm s}\) is the solution resistance, C\({}_{\rm f}\) is the capacitance due to the corrosion product, R\({}_{\rm f}\) is the film resistance, R\({}_{\rm ct}\) is the charge transfer resistance, and a CPE (constant phase element) is used to obtain the double layer capacitance Q. From Figure 5a-c, it is evident that the capacitance arc decreases as the flow velocity is increased and it decreases when the magnetic field is applied. After fitting the equivalent circuit, the obtained EIS kinetics parameters are listed in Table 3.  
From Figure 5a, where the velocity is 0 m/s, the R\({}_{\rm ct}\) value for the no magnetic condition is found as 3310 \(\Omega\)cm\({}^{2}\), which is highest from A1 to C3. For the same velocity of 0 m/s, when an N-S magnetic field is applied, the value decreases to 2330 \(\Omega\)cm\({}^{2}\), whereas, for the N-N magnetic field, the R\({}_{\rm ct}\) values decrease again to 1800 \(\Omega\)cm\({}^{2}\). This depicts that the charge transfer is higher when a magnetic field is applied to the API 5L X65 samples. As the velocity gets increased to 1 m/s and 2 m/s, the R\({}_{\rm ct}\) values decrease significantly, showing that flow can cause higher electron transfer in the presence of a magnetic field. By analyzing Figure 5b, it can be observed that, for sample B1, the R\({}_{\rm ct}\) value decreases to 1420 \(\Omega\)cm\({}^{2}\), which is almost half of the R\({}_{\rm ct}\) obtained at A1. A similar result is observed for B2 and B3, where the R\({}_{\rm ct}\) decreases again to 870.4 \(\Omega\)cm\({}^{2}\) and 698.5 \(\Omega\)cm\({}^{2}\). The same kind of reaction kinetics as with B1-B3 is obtained for samples at 2 m/s. For sample C1 at 2 m/s, the R\({}_{\rm ct}\) value decreases to 723.9 \(\Omega\)cm\({}^{2}\), whereas, for C2 and C3, the R\({}_{\rm ct}\) values again decrease to 683.7 \(\Omega\)cm\({}^{2}\) and 304.2 \(\Omega\)cm\({}^{2}\). The characterization results depict that there is a significant increase in corrosion as the charge transfer rate is decreased when a magnetic field is applied. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Sample Name** & **Flow Vel. ** & **Magnet** & \(\beta_{\rm a}\) & \(\beta_{\rm c}1\) & \(\beta_{\rm c}1\) & \({\rm I}_{\rm corr}\) & \({\rm E}_{\rm corr}\) (mV vs. & \({\rm R}_{\rm p}\) (\(\Omega\)cm\({}^{2}\)) & **Corrosion Rate (mmpy)** \\ \hline A1 & 0 & No Magnet & \(5.76\times 10^{-1}\) & \(2.13\times 10^{-1}\) & 19.4 & \(-\)478 & 2879 & 0.28 \\ \hline A2 & 0 & N–S & \(3.71\times 10^{-1}\) & \(1.94\times 10^{-1}\) & 21.4 & \(-\)505 & 1998 & 0.33 \\ \hline A3 & 0 & N–N & \(5.43\times 10^{-1}\) & \(5.04\timesFigure 5: _Cont._  
Figure 5: EIS Nyquist plots (**a**) 0 m/s, (**b**) 1 m/s, (**c**) 2 m/s.