## 2 Materials and Methods
### Flow Resistivity
The heated air is forced through a porous metal foam sample and the static pressure drop along the sample is recorded using a Mensor pressure gauge 2101 in differential mode with a range between \(-1000\,\mathrm{Pa}\) and \(3500\,\mathrm{Pa}\). The accuracy is \(\pm 0.01\,\%\) of the full scale (FS) corresponding to \(0.45\,\mathrm{Pa}\)[23]. The two pressure measurement points are located \(5\,\mathrm{cm}\) upstream and downstream of the porous sample, respectively. The porous samples have a diameter of \(5.5\,\mathrm{cm}\) and their thickness is varied from \(1\,\mathrm{to}\,6\,\mathrm{cm}\) to assess entrance and exit effects on the permeability and form coefficient. In the following, normalized pressure drops from converged measurements with \(t=6\,\mathrm{cm}\) are presented [24]. A Bronkhorst F-202 AV mass flow controller (range: 0 to 260 ln/min air; uncertainty: \(\pm 0.5\,\%\) of measurement value \(\pm 0.1\,\%\) FS [25]) is used to ensure constant air supply at a prescribed mass flow rate \(\dot{m}\). The full-scale contribution to the inaccuracy amounts to \(\pm 5.6\times 10^{-6}\,\mathrm{m}^{3}\,\mathrm{s}^{-1}\) for the given air properties. The air temperature, required to calculate the volumetric flow rate \(\dot{Q}\), is measured \(1\,\mathrm{cm}\) downstream of the porous sample by using a type-K thermocouple. The seepage velocity through the porous sample follows from dividing the volumetric flow rate by the pipe cross-section \(v_{s}=\dot{Q}/A_{p}\). Assuming ideal gas behavior, the seepage velocity can be expressed in terms of the mass flow rate through  
\[v_{s}=\frac{\mu R_{air}T_{\infty}}{A_{p}p_{\infty}}\,. \tag{3}\]  
For the air temperatures \(22\,^{\circ}\mathrm{C}\), \(50\,^{\circ}\mathrm{C}\) and \(90\,^{\circ}\mathrm{C}\), the mass flow rate set-point is varied in a range between \(1.5\times 10^{-4}\,\mathrm{kg}\,\mathrm{s}^{-1}\) and \(4.5\times 10^{-3}\,\mathrm{kg}\,\mathrm{s}^{-1}\) while the pressure drop is recorded. Quadratic least-square curve fitting of the experimental data to Equation (1) in the form \(\Delta p=C_{a}v_{s}+C_{b}v_{s}^{2}\) is applied to the measurement points in order to retrieve the linear and quadratic coefficients \(C_{a}\) and \(C_{b}\) which can be related to the material parameters in Equation (1). For every measurement point, the quantities \(\dot{m}\) and \(\Delta p\) are obtained by averaging 50 data points which are recorded within \(10\,\mathrm{s}\). Data points are only acquired for converged flow conditions i.e., when the mass flow rate is within \(\pm 0.04\,\%\) FS around the set point. From the normally distributed data points, the standard deviation is used to specify the random measurement uncertainty of measured quantities. The standard deviation of temperature, seepage velocity and pressure drop, are obtained by taking error propagation from directly measured quantities into account. The uncertainty of the \begin{table}
\begin{tabular}{c c c c c} \hline
**Nominal Pore Size \(d_{p,0}\)** & **Porosity \(\varphi\)** & **Resistivity \(R\)** & **Permeability \(K\)** & **form Coefficient \(C\)** \\ \hline \(800\,\mathrm{\SIUnitSymbolMicro m}\) & \(91.65\,\%\) & \(6728\,\mathrm{N}\mathrm{s}\mathrm{m}^{-4}\) & \(27.1\times 10^{-10}\,\mathrm{m}^{2}\) & \(2612.54\,\mathrm{m}^{-1}\) \\ \hline \end{tabular}
\end{table} 
Table 1: Characterizing properties of the porous metal foam P800 for a sample thickness of \(6\,\mathrm{cm}\) as characterized by [PERSON] et al. [16]. curve fitting parameters \(C_{a}\) and \(C_{b}\) can be computed via Monte Carlo sampling with \(\Delta p\) and \(v_{s}\) being independent, normally distributed input variables. A total of 1000 simulations is launched and the standard deviation of the coefficients is defined as the interval containing 68 % of the simulated data points. The uncertainty of form coefficient and permeability includes curve-fitting error and random errors from the measurement of the viscosity and density.