## 3 Results
### Effective Radiation Coefficient  
For investigation of the electrically heated storage system, a detailed detection of the heat transport mechanisms inside the effective radiation coefficient \(k_{rad}\) is necessary, requiring a geometry-, process- and material-based parametrization. Extensive simulation studies (Table 2) on the relevant influencing factors were performed and \(k_{rad}\) was iteratively \begin{table}
\begin{tabular}{c c c c c c} \hline  & \(\rho\) [kg/m\({}^{3}\)] & \(c\) [J/kgK] & \(\lambda\) [W/mK] & \(\beta\) & \(\kappa\) [\(\Omega\) mm\({}^{2}\)/m] \\ \hline Honeycomb (S) & 3991 & 1169 & 11.1 & 0.8 & - \\ \hline Heating Wire (P) & 7250 & 690 & - & 0.7 & 1.4 \\ \hline Thermal Insulation (Ins) & 225 & - & 0.03 & - & - \\ \hline \end{tabular}
\end{table} 
Table 1: Temperature-averaged material properties in a range between \(-10\)\({}^{\circ}\)C to 1000 \({}^{\circ}\)C.  
determined by minimizing the temperature deviations between the porosity based and the detailed based model. The variations include the solid mass (\(m_{S}\)), the length to diameter ratio (\(L\)/\(D\)), the specific surface (\(a_{V}\)) and the void fraction (\(\epsilon\)) of the honeycomb structure as well as the heating wire assignment (\(x\)), its diameter (\(d_{P}\)) and the charging duration (\(\tau\)). Here, the heating wire temperature (\(T_{P}\)) was set constant at a maximum permitted value of 1000 \({}^{\circ}\)C.  
For an exemplary case, Figure 3 shows the resulting temporal temperature characteristics for four specific surfaces of the honeycomb structure. The squares represent the results based on the detailed model with the pure radiation coefficients \(C_{nd}\) and local thermal conduction, the solid lines the results based on the porosity model with the iteratively determined effective radiation coefficients \(k_{nd}\). In addition, the corresponding coefficients \(C_{rad}\) and \(k_{nd}\) are summarized in Table 3.  
The results show with increasing specific surfaces significant higher temporal temperature characteristics as well as rapprochements between the iteratively determined radiation coefficients \(k_{nd}\) to the pure radiation coefficient \(C_{rad}\) (Table 3). These results are associated with an increasing heat transport due to two central effects: a total higher number of honeycomb channels with heating wires and decreasing wall thicknesses of the honeycomb structure, thus negligible thermal conduction resistances. Comparable characteristics of different magnitude are also evident in other results within the variation matrix. Additionally, a good agreement in the temporal heating characteristic between the detailed and the porosity model with maximum deviations of lower 5% are reached. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(m_{S}\) [kg] & \(L\)/\(D\) [-] & \(\mathbf{a_{V}}\) [\(\mathbf{\tau}\)] & \(\epsilon\) [\%] & \(x\) [\%] & \(\frac{d_{P}}{2\tau_{0}}\)[\%] & \(\mathbf{\tau}\) [min] \\ \hline
5–15 & 0.5–4 & 50–600 & 20–80 & 10–90 & 0.05–0.5 & 15–180 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Variation matrix. Figure 3: Comparison of temporal temperature characteristics: porous model (solid lines) vs. geometry-resolved model (squares) for an exemplary case at \(x=10\%\), \(\frac{d_{P}}{2\tau_{0}}=25\%\), \(m_{S}=10\) kg, \(L/D=2\), \(\epsilon=60\%\), \(\tau=60\) min. Due to the large number of geometric, process and material configurations, a parameterization of \(k_{rad}\) is needed in order to enable a computationally efficient and detailed investigation of the electrically heated storage system throughout the porosity model.