# Dynamic Heat Transfer Calculation for Ground-Coupled Floor in Emergency Temporary Housing
## 3 Numerical Evaluation and Validation
### Validation
#### 3.2.2 Comparison with Fluent Simulated Results  
With the numerical evaluation method discussed above, the soil temperature could be easily calculated by the Matlab tool. Table 1 lists the thermophysical properties of soil and ground surfaces. The temperatures in the range of \(-10\) m \(\leq x\leq 10\) m were calculated. The step size was \(\Delta x\) = 0.05 m, and the time step size was \(\Delta t\) = 86,400 s. The Ansys Fluent software based on the finite volume method was utilized to validate the accuracy of the analytical solution and its numerical evaluation. A two-dimensional rectangular physical model was established, as diagonal stripes filled the region in Figure 1. Detailed sizes were that the indoor floor length was \(L\) = 5 m, the outdoor ground length was \(X\) = 5 m, and the soil depth was \(Z\) = 5 m. Then, regular mesh with step sizes of 0.1 m on both horizontal and vertical directions, as well as time step size \(\Delta t\) = 259,200 s, were chosen.  
Figure 4: Daily mean ground surface temperature in Chengdu.  
Figure 5: Outdoor ground surface temperatures and indoor air temperatures.  
Figures 6 and 7 described, respectively, the soil temperature distribution along the \(x\) dimension and the temperature variation over time. At \(x\rightarrow+\infty\), the soil heat conduction could be thought of as one-dimensional in Equation (8). Its temperature distribution along the \(z\)-axis was calculated by Equation (12), which was marked with solid red circles in the figures. While, at \(x\rightarrow-\infty\), the soil temperature also conformed to a one-dimensional heat transfer model. [PERSON] and [PERSON] analyzed it and obtained the solution in the integral form [37], which was calculated and marked with solid red circles as well.  
As shown in Figure 6, both at a soil depth of \(z=0.05\) m and \(z=0.55\) m, the numerical temperature results calculated by Matlab were in accord with the data simulated by Fluent. At the same time, for three time points (April, August, and December), their temperature trends, both in the positive and negative direction, were close to the exact solutions (red circle marks). It is worth mentioning that the FVM computation by Fluent took about  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **Units** & **Value** & **Parameters** & **Units** & **Value** \\ \hline Soil heat conductivity (\(\lambda\)) & W/(m\(\cdot\)K) & 2 & Ground surface absorptivity (\(\gamma\)) & - & 0.8 \\ \hline Soil density (\(\rho\)) & kg/m\({}^{3}\) & 1500 & Outdoor convective heat transfer coefficient (\(h_{\mathrm{o}}\)) & W/(m\({}^{2}\cdot\)K) & 23 \\ \hline Soil specific heat (\(c_{\mathrm{p}}\)) & J/(kg\(\cdot\)K) & 1350 & Indoor convective heat transfer coefficient (\(h_{\mathrm{i}}\)) & W/(m\({}^{2}\cdot\)K) & 8.7 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Detailed thermophysical properties of ground-coupled floors [28; 36].  
Figure 6: Soil temperature distribution along \(x\) dimension at (**a**) \(z=0.05\) m; (**b**) \(z=0.55\) m.  
Figure 7: Soil temperature variation over time at (**a**) \(z=0.05\) m; (**b**) \(z=0.55\) m.  
several minutes, and the current method spent about several seconds. Therefore, it proved that the analytical solution evaluated numerically was accurate and efficient.  
Figure 7 shows the soil temperatures varied with time at eight points (\(-1.0\), \(0.05\)), (\(-0.05\), \(0.05\)), (\(0.05\), \(0.05\)), (\(1.0\), \(0.05\)), (\(-1.0\), \(0.55\)), (\(-0.05\), \(0.55\)), (\(0.05\), \(0.55\)), and (\(1.0\), \(0.55\)). As was seen in the figure, the calculated temperatures by Matlab agreed well with the data by Fluent. It also could be found that the temperatures at \(x=1.0\) m and \(x=-1.0\) m were closed to the exact solutions (red circle marks), which meant that the heat of the indoor floor and outdoor ground exchanged mainly around walls within the range of \(1\) m. Thus, calculating the heat transfer of the ground-coupled floor in temporary buildings by the current method was reliable.