# The Impact of Internal Insulation on Heat Transport through the Wall: Case Study
## 3 Results and Discussion
### Simulations
Therefore, the obtained value of thermal transmittance of the outer wall (after insulation) was U\({}_{\delta 1}=0.56\) W/(m\({}^{2}\cdot\)K). Such an insulation method generates lower values of heat loss \(\Phi=59.20\) W, \(L^{2D}=3.04\) W/(m\(\cdot\)K) than for the case without insulation. It should be noted that such a connection generates additional heat loss with linear thermal transmittance \(\Psi=1.13\) W/(m\(\cdot\)K)--i.e., the value higher than that in the initial variant without insulation. This is due to the calculation method of the coefficient \(\Psi\). On the inner surface of the envelope at the connection \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & & & & & \\ \hline \multicolumn{6}{c}{**Physical Parameters**} \\ \cline{2-7} \multicolumn{1}{c}{\(U_{c}\)} & \(U_{c}\) & \(\Phi\) [W] & \(L^{2D}\) & \(\Psi_{i}\) & \(t_{min}\) [\({}^{\circ}\)C] & \(f_{Rsi(2D)}\) [-] \\ \hline \multicolumn{6}{c}{**before thermal simulation**} \\ \hline \multirow{3}{*}{(a)} & U\({}_{s}=2.37\) & 85.14 & 5.13 & 0.603 & \multirow{3}{*}{12.45} & \multirow{3}{*}{0.587} \\  & U\({}_{s}=2.37\) & \(\Phi_{d}=46.69\) & \(\mathrm{L_{d}}^{2D}=2.81\) & \(\Psi_{i,d}=0.44\) & & \\ \cline{1-1}  & & \(\Phi_{g}=38.45\) & \(\mathrm{L_{g}}^{2D}=2.31\) & \(\Psi_{i,g}=0.163\) & & \\ \hline \multicolumn{6}{c}{**after thermal simulation**} \\ \hline \multirow{3}{*}{(b)} & U\({}_{s}=0.56\) & 35.71 & 1.83 & 0.768 & \multirow{3}{*}{0.80} & \multirow{3}{*}{0.542} \\  & U\({}_{s}=0.56\) & \(\Phi_{d}=22.04\) & \(\mathrm{L_{d}}^{2D}=1.13\) & \(\Psi_{i,d}=0.578\) & & \\ \cline{1-1}  & & \(\Phi_{g}=13.67\) & \(\mathrm{L_{g}}^{2D}=0.70\) & \(\Psi_{i,g}=0.190\) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Physical parameters obtained by the simulation. Figure 12: Simulated temperature distribution of the connection of outer walls: (**a**) simulations without thermal insulation; (**b**) simulations with thermal insulation. point of the outer wall with the window, the minimum temperature is \(t_{min}\) = 5.79 \({}^{\circ}\)C, which brings about the risk of surface condensation (the risk of mold and mildew fungi development)--Table 8.  
The connections of outer walls in the corner with the window before the insulation generate higher heat losses involving heat flux \(\Phi\), thermal coupling coefficient \(L^{2D}\) than in the case of insulation from the inside. However, as in the first calculation example, additional heat losses regarding linear thermal transmittance are higher \(\Psi\) = 1.29 W/(m-K) than in the variant before the insulation \(\Psi\) = 0.62 W/(m-K). In addition, the applied insulation brings about a significant reduction of temperature on the inner surface (at the junction outer wall--window) \(t_{min}\) = 5.80 \({}^{\circ}\)C--Table 9.  
And for the connection of the outer wall with the ceiling, the application of insulation from the outside brings about the reduction in heat loss involving heat flux \(\Phi\), thermal coupling coefficient \(L^{2D}\) and the decrease in temperature on the inner surface of the envelope in the bottom surface of the ceiling \(t_{\min}\) = 8.08 \({}^{\circ}\)C--Table 10.