## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c} \hline
**Parameter/Mode** & **150 V** & **200 V** & **250 V** \\ \hline Electrical energy input, \(Q_{\sigma}\), J & 12,038 \(\pm\) 722.2 & 20,905 \(\pm\) 1254.3 & 34,549.5 \(\pm\) 2072.9 \\ \hline Electrolyte heating, \(Q_{hr}\), J & 1086.3 \(\pm\) 152.1 & 2716.2 \(\pm\) 380.2 & 6518.8 \(\pm\) 912.6 \\ \hline Vaporization heat, \(Q_{\sigma}\), J & 2351.1 \(\pm\) 21.2 & 2766 \(\pm\) 24.9 & 2351.1 \(\pm\) 21.2 \\ \hline Workpiece heating, \(Q_{k}\), J & 8675.6 \(\pm\) 738.3 & 15,507.8 \(\pm\) 1310.9 & 25,775.6 \(\pm\) 2265 \\ \hline Heat flux density, \(q\), W/m\({}^{2}\) & \((17\pm 1.6)\cdot 10^{5}\) & \((31\pm 2.9)\cdot 10^{5}\) & \((51\pm 4.9)\cdot 10^{5}\) \\ \hline Heat transfer coefficient to & & 339 \(\pm\) 1.8 & \\ electrolyte, \(\alpha\), W/(m\({}^{2}\cdot\)K) & & & \\ \hline \end{tabular}
\end{table} 
Table 1: Summary energy characteristics of EPH for three modes. In our case, the surface roughness was estimated as Ra \(\approx\) 1 \(\upmu\)m for the 20 GL steel sample (sides roughly grounded but not polished), and Ra \(\approx\) 3-5 \(\upmu\)m for the stainless steel holder (as-manufactured). The contact pressure was estimated to lie between 0.4 and 1.2 MPa, based on the tightening torque (1-1.5 N\(\cdot\)m) applied during assembly, assuming a thread friction coefficient of \(\upmu\approx\) 0.2 and a contact area of 125 mm\({}^{2}\). According to [PERSON]'s empirical formulation for plastically deformable rough surfaces, the thermal contact conductance can be approximated by  
\[\alpha_{cl}=1150\cdot P^{0.94}, \tag{21}\]  
where \(P\)--contact pressure, MPa. Substituting the estimated pressure values yields \(\alpha_{cl}\approx 500-2000\) W/m\({}^{2}\cdot\)K, which is consistent with the empirical range found in prior experimental and theoretical studies for similar materials and conditions. To validate the robustness of the model, a sensitivity analysis for the U = 200 V regime was performed by varying \(\alpha_{cl}\) within this range (Table 2). The results indicated that surface temperatures changed to 12.8 \({}^{\circ}\)C, and internal temperatures also remained moderately affected. These findings suggest that the simulation is only weakly sensitive to this parameter, and the selected range is both physically justified and numerically stable. In further numerical calculations, the value of contact conductivity was taken as \(\alpha_{cl}=500\) W/m\({}^{2}\cdot\)K.  
To enhance the accuracy of the thermal model in the high-temperature regime (U = 250 V), radiative heat losses from the exposed surfaces of the sample were incorporated into the boundary conditions. The radiation condition was written as follows  
\[q_{r}=\varepsilon\cdot\sigma_{0}\cdot\left(T^{4}-T^{4}_{amb}\right), \tag{22}\] \begin{table}
\begin{tabular}{c c c c} \hline
**Contact Conductivity \(\alpha_{cl}\)/W/m\({}^{2}\cdot\)K** & **T Surface**, \({}^{\circ}\)C & **T Middle**, \({}^{\circ}\)C & **T Back**, \({}^{\circ}\)C \\ \hline
500 & 875.45 & 438.29 & 335.81 \\ \hline
1000 & 871.28 & 432.74 & 329.03 \\ \hline
1500 & 867.15 & 428.56 & 322.84 \\ \hline
2000 & 862.63 & 423.16 & 316.73 \\ \hline \end{tabular}
\end{table} 
Table 2: Effect of contact conductivity \(\alpha_{cl}\) on the surface and internal temperatures of the sample (U = 200 V). Figure 7: Determination of the duration of growth and existence of the vapor–gas shell (case for U = 250 V; red area represents the time interval during which the vapor–gas shell is formed). where \(\varepsilon\)--emissivity coefficient; \(\sigma_{0}\)--Stefan--[PERSON] constant; \(T\)--current surface temperature; \(T_{amb}\)--the temperature of the environment where the radiation goes. This modification addresses the increasing significance of radiative dissipation above 1000 \({}^{\circ}\)C, where the discrepancy between simulated and experimental temperatures becomes more pronounced if radiation is neglected. Radiation boundary conditions were applied to both the heated surface in contact with the electrolyte and the lateral surfaces exposed to air.