## 5 Conclusions
\begin{tabular}{l l l} \(A\) & lateral Surface of the storage unit & m\({}^{2}\) \\ \(c\) & specific heat capacity & \(\frac{1}{\text{kg}^{\text{K}}}\) \\ \(C_{\text{I}}\) & large constant in the Darcy term \(D\) & \(\frac{\text{kg}}{\text{m}^{\text{s}}}\) \\ \(C_{\text{II}}\) & small constant in the Darcy term \(D\) & \\ \(D\) & Darcy term & \(\frac{\text{kg}}{\text{m}^{\text{s}}}\) \\ \(d\) & air channel thickness & m \\ \(\mathbf{g}\) & gravitational acceleration & \(\frac{\text{m}}{\text{s}^{2}}\) \\ \(h\) & specific enthalpy & \(\frac{\text{kg}}{\text{m}^{\text{s}}}\) \\ \(L\) & specific latent heat of fusion & \(\frac{\text{I}}{\text{kg}}\) \\ \(p\) & pressure & Pa \\ \(\dot{Q}\) & heat flux & W \\ \(R\) & thermal resistance & \(\frac{\text{K}}{\text{W}}\) \\ \(T\) & temperature & K \\ \(T_{l}-T_{s}\) & mushy zone width & K \\ \(t\) & time & s \\ \(U\) & overall heat transfer coefficient & \(\frac{\text{W}}{\text{m}^{\text{K}}}\) \\ \(u\) & velocity & \(\frac{\text{m}}{\text{s}}\) \\ \(\mathbf{u}\) & velocity vector & \(\frac{\text{m}}{\text{s}}\) \\ \(\dot{V}\) & volume flow & \(\frac{\text{m}^{3}}{\text{s}}\) \\ \(y\) & variable & \\ \(z\) & deviation & \\ Greek symbols & & \\ \(\alpha\) & convective heat transfer coefficient & \(\frac{\text{W}}{\text{m}^{\text{K}}}\) \\ \(\alpha_{\text{F}}\) & global liquid fraction & \\ \(\beta\) & thermal expansion coefficient & \(\frac{1}{\text{W}}\) \\ \(\lambda\) & thermal conductivity & \(\frac{\text{W}}{\text{m}^{\text{K}}}\) \\ \(\boldsymbol{\tau}\) & stress tensor (without pressure) & Pa \\ \(\eta\) & dynamic viscosity & Pa-s \\ \(\rho\) & density & \(\frac{\text{kg}}{\text{m}^{3}}\) \\ Subscripts & & \\
0 & reference point & \\ \(amb\) & ambient & \\ \(char\) & charging & \\ \(curve\) & temporal curve & \\ \(dis\) & discharging & \\ \(ext\) & extern & \\ \(HTF\) & Heat Transfer Fluid \\ \(i\) & inner & \\ \(in\) & inlet & \\ \(init\) & initial & \\ \(l\) & liquid, liquidus & \\ \(loss\) & heat loss & \\ \(m\) & melting & \\ \(max\) & maximum & \\ \(mean\) & mean & \\ \end{tabular} \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & **Point** & **Point** & **Point** & **Point** & **Point** & **Mean** & **Unit** \\  & & **B-b** & **D-a** & **D-b** & **D-c** & **F-b** & & **Mean** & **Unit** \\ \hline radial +1 mm & mean & \(-0.33\) & \(-0.67\) & \(-0.38\) & \(-0.21\) & \(-0.41\) & \(-0.40\) & K \\  & maximum & \(4.30\) & \(2.24\) & \(2.84\) & \(5.21\) & \(2.16\) & \(3.35\) & K \\  & standard deviation & \(0.74\) & \(0.84\) & \(0.62\) & \(0.70\) & \(0.49\) & \(0.68\) & K \\ radial \(-1\) mm & mean & \(0.38\) & \(1.01\) & \(0.44\) & \(0.26\) & \(0.49\) & \(0.52\) & K \\  & maximum & \(3.61\) & \(3.10\) & \(2.09\) & \(4.32\) & \(1.47\) & \(2.92\) & K \\  & standard deviation & \(0.74\) & \(1.10\) & \(0.60\) & \(0.68\) & \(0.48\) & \(0.72\) & K \\ vertical +1 mm & mean & \(0.03\) & \(0.02\) & \(0.02\) & \(0.02\) & \(0.03\) & \(0.03\) & K \\  & maximum & \(0.32\) & \(0.33\) & \(0.30\) & \(0.44\) & \(0.37\) & \(0.35\) & K \\ vertical \(-1\) mm & standard deviation & \(0.07\) & \(0.05\) & \(0.05\) & \(0.07\) & \(0.06\) & \(0.06\) & K \\  & mean & \(-0.03\) & \(-0.02\) & \(-0.02\) & \(-0.02\) & \(-0.03\) & \(-0.03\) & K \\  & maximum & \(0.32\) & \(0.33\) & \(0.30\) & \(0.44\) & \(0.37\) & \(0.35\) & K \\  & standard deviation & \(0.07\) & \(0.05\) & \(0.05\) & \(0.07\) & \(0.06\) & \(0.06\) & K \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Temporal mean, maximum, and standard deviation of the temperature measurements with a varied measurement point position with respect to the reference position. **Figure A1. ** Power over time curve for charging of the standard case and the case with a decreased melting enthalpy as well as the regarding relative deviation.