## 3 Results and Discussion
The emissivity values were selected based on the surface finish: \(\varepsilon\approx\) 0.4-0.5 for the polished working surface and \(\varepsilon\approx\) 0.7-0.8 for rougher lateral sides. These values were taken from [30]. The ambient temperature was set to 293 K (20 \({}^{\circ}\)C), consistent with the temperature of the circulating electrolyte. Numerical results demonstrated that accounting for radiation led to a measurable reduction in the calculated surface temperature at U = 250 V, from 1518.5 \({}^{\circ}\)C to 1490.6 \({}^{\circ}\)C--a difference of approximately 28 \({}^{\circ}\)C (1.84%). In contrast, the effect was negligible for lower voltages: 5.9 \({}^{\circ}\)C (0.67%) for 200 V, and 1.2 \({}^{\circ}\)C (0.25%) for 150 V.  
Given these results, radiative losses were included in the model only for the 250 V mode, where their impact on accuracy is most significant. For lower-voltage modes, radiation was omitted to avoid unnecessary model complexity, as its influence on the results was within the numerical error margin. After calculating and summarizing all energy terms in Table 1, these values were used to define the third kind of boundary conditions in the Elcut 6.6 program. Figure 8 illustrates the temperature distribution graphs along the sample depth at \(t\) = 10 s for three processing modes of 20 GL steel, measured precisely along the line \(x=a/2\), which is at the sample's midpoint. Following the heating phase, the cooling of the part after voltage removal was simulated using the Elcut 6.6 program, with \(q\) = 0 while maintaining the established boundary conditions. Figure 9a depicts the temperature distribution pattern relative to the sample's depth (on the line \(x=a/2\)) during cooling at different time intervals, as well as the tem  
Figure 8: Temperature profiles across the sample depth following a 10 s heating period for three distinct processing modes. perature distribution pattern across the sample's cross-section 5 s after the voltage was disconnected (Figure 9b). To ensure a valid comparison, the numerical calculation results were analyzed at a depth of 2 mm, consistent with the experimental temperature measurements obtained using a thermocouple. However, the interpretation of experimental data must consider the inherent measurement inertia; the MEGEON26003 thermocouple's response time is approximately 4 s, according to its technical specifications. Consequently, the thermocouple readings may lag behind the actual temperature of the sample, particularly under the rapid heating conditions characteristic of electrolytic plasma hardening. Figure 9: Temperature distribution within the sample at a voltage of 200 V after switching off the electric voltage: (**a**) by depth; (**b**) in the cross-section after 5 s of cooling. To estimate this delay, a classical model, described by a linear differential equation of the first order, was used to represent the response of the inertial measuring device. The solution to such an equation is an exponential approximation:  
\[T_{tc}(t)=T_{real}(t)\cdot(1-e^{-\frac{t}{t}}), \tag{23}\]  
where \(T_{tc}\) represents the thermocouple reading, \(T_{real}\) represents the true temperature within the sample, \(t\) is the current time, and \(\tau\) is the thermocouple time constant. This expression was detailed in several authoritative sources, including standard manuals on measurement systems and heat transfer [31]. For the 200 V processing mode at 10 s, corresponding to the end of heating, the numerical calculation predicted a steel temperature of approximately 698.6 \({}^{\circ}\)C at a depth of 2 mm. Concurrently, the thermocouple recorded 592 \({}^{\circ}\)C. When accounting for the exponential delay, a recalculation using the formula suggests the actual temperature in the part at that time could be around 645 \({}^{\circ}\)C, indicating a relative deviation of approximately 7.7% from the numerical prediction.