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basics:building_physics_-_basics:thermal_bridges:tbcalculation:examples:unheatedb [2019/01/24 09:30] – cblagojevicbasics:building_physics_-_basics:thermal_bridges:tbcalculation:examples:unheatedb [2022/02/15 18:58] (current) – admin
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 <WRAP centeralign>  <WRAP centeralign> 
-<latex>+$$
 \large{\dfrac{1}{U} = \dfrac{1}{U_f} + \dfrac{A}{(A \cdot U_{bf}) + (z \cdot P \cdot U_{bw}) + (h \cdot P \cdot U_W) + (0{,}33 \cdot n \cdot V)}} \large{\dfrac{1}{U} = \dfrac{1}{U_f} + \dfrac{A}{(A \cdot U_{bf}) + (z \cdot P \cdot U_{bw}) + (h \cdot P \cdot U_W) + (0{,}33 \cdot n \cdot V)}}
-</latex>+$$
 \\ \\
 \\ \\
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 <WRAP centeralign>  <WRAP centeralign> 
-<latex>+$$
 \large{\Phi = L_{iu} \cdot (\theta_i - \theta_u) + L_{ie} \cdot (\theta_i - \theta_e)} \large{\Phi = L_{iu} \cdot (\theta_i - \theta_u) + L_{ie} \cdot (\theta_i - \theta_e)}
-</latex>+$$
 </WRAP> </WRAP>
  
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 <WRAP centeralign>  <WRAP centeralign> 
-<latex>+$$
 \large{\Phi = \left(\frac{L_{iu} \cdot L_{ue}}{L_{iu} + L_{ue}}\right) \cdot (\theta_i - \theta_e) \quad \Rightarrow \quad L_{2d} =  \left(\frac{L_{iu} \cdot L_{ue}}{L_{iu} + L_{ue}} + L_{ie}\right)} \large{\Phi = \left(\frac{L_{iu} \cdot L_{ue}}{L_{iu} + L_{ue}}\right) \cdot (\theta_i - \theta_e) \quad \Rightarrow \quad L_{2d} =  \left(\frac{L_{iu} \cdot L_{ue}}{L_{iu} + L_{ue}} + L_{ie}\right)}
-</latex>+$$
 </WRAP> </WRAP>
  
 Thus $L_{ie}$ , $L_{iu}$ and $L_{ue}$  need to be determined. For this purpose, first the conductances of the separate partial areas are ascertained and the following system of equations is solved: Thus $L_{ie}$ , $L_{iu}$ and $L_{ue}$  need to be determined. For this purpose, first the conductances of the separate partial areas are ascertained and the following system of equations is solved:
  
-<WRAP centeralign>  +<WRAP centeralign> 
-<latex> +$$ 
-$$ \bordermatrix{ +\begin{matrix} 
-    & L_{iu} & L_{ie} & L_{ue} \cr +& \begin{matrix}L_{iu}&L_{ie}&L_{ue}\end{matrix} \\\\ 
-L_1 & 1      & 1      & 0 \cr +\begin{matrix}L_1\\\\L_2\\\\L_3\end{matrix} 
-L_2 & 0      & 1      & 1 \cr +& \begin{pmatrix}1\quad&1\quad&0\quad\\\\0\quad&1\quad&1\quad\\\\1\quad&0\quad&1\quad\end{pmatrix}\\\\ 
-L_3 & 1      & 0      & 1 \cr +\end{matrix}
-}+
 \quad \Rightarrow \quad \quad \Rightarrow \quad
 \begin{matrix} \begin{matrix}
-L_{iu} = 0{.}5 \cdot (L_1-L_2+L_3) \\ +L_{iu} = 0{,}5 \cdot (L_1-L_2+L_3) \\ 
-L_{is} = 0{.}5 \cdot (L_1+L_2-L_3) \\ +L_{ie} = 0{,}5 \cdot (L_1+L_2-L_3) \\ 
-L_{us} = 0{.}5 \cdot (L_2+L_3-L_1)+L_{ue} = 0{,}5 \cdot (-L_1+L_2+L_3)
 \end{matrix} \end{matrix}
 $$ $$
-</latex> 
 </WRAP> </WRAP>
  
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 <WRAP centeralign> <WRAP centeralign>
 **Determining the conductance**  **Determining the conductance** 
-<latex>+$$
 \Large{_{2d}} \Large{_{2d}}
-</latex>+$$
 </WRAP> </WRAP>
  
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 <WRAP centeralign>  <WRAP centeralign> 
-<latex>+$$
 \large{ \large{
-$$L_{iu} = 0{.}5 \cdot (L_1-L_2+L_3) = 0{.}5540 \, \frac{\text{W}}{\text{m} \cdot \text{K}}} $$\\ +L_{iu} = 0{.}5 \cdot (L_1-L_2+L_3) = 0{.}5540 \, \frac{\text{W}}{\text{m} \cdot \text{K}} \\ 
-$$L_{is} = 0{.}5 \cdot (L_1+L_2-L_3) = 0{.}2314 \, \frac{\text{W}}{\text{m} \cdot \text{K}}} $$\\ +L_{is} = 0{.}5 \cdot (L_1+L_2-L_3) = 0{.}2314 \, \frac{\text{W}}{\text{m} \cdot \text{K}} \\ 
-$$L_{us} = 0{.}5 \cdot (-L_1+L_2+L_3) = 2{.}6177 \, \frac{\text{W}}{\text{m} \cdot \text{K}}}$$} +L_{us} = 0{.}5 \cdot (-L_1+L_2+L_3) = 2{.}6177 \, \frac{\text{W}}{\text{m} \cdot \text{K}}} 
-</latex>+$$
 </WRAP> </WRAP>
  
  
 <WRAP centeralign>  <WRAP centeralign> 
-<latex> +$$ 
-\large{L_{2d} =  \left(\frac{L_{iu} \cdot L_{ue}}{L_{iu} + L_{ue}} + L_{ie}\right) = 0{.}6886 \, \frac{\text{W}}{\text{m} \cdot \text{K}}}} +\large{L_{2d} =  \left(\frac{L_{iu} \cdot L_{ue}}{L_{iu} + L_{ue}} + L_{ie}\right) = 0{.}6886 \, \frac{\text{W}}{\text{m} \cdot \text{K}}} 
-</latex>+$$
 </WRAP> </WRAP>
  
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 Therefore: Therefore:
 <WRAP centeralign>  <WRAP centeralign> 
-<latex> +$$ 
-$$\dfrac{1}{U} = \dfrac{1}{U_f} + \dfrac{A}{(A \cdot U_{bf}) + (z \cdot P \cdot U_{bw}) + (h \cdot P \cdot U_W) + (0{.}33 \cdot n \cdot V)} +\dfrac{1}{U} = \dfrac{1}{U_f} + \dfrac{A}{(A \cdot U_{bf}) + (z \cdot P \cdot U_{bw}) + (h \cdot P \cdot U_W) + (0{.}33 \cdot n \cdot V)} 
 \quad \Rightarrow \quad \quad \Rightarrow \quad
-U = 0{.}1273 \, \dfrac{\text{W}}{\text{m}^2 \cdot \text{K}}}$$ +U = 0{.}1273 \, \dfrac{\text{W}}{\text{m}^2 \cdot \text{K}} 
-</latex>+$$
 </WRAP> </WRAP>
  
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 <WRAP centeralign>  <WRAP centeralign> 
-<latex> 
 $$\Psi_g = L_{2d}-l_{AW} \cdot U_{AW}-0{.}5 \cdot B' \cdot U$$ $$\Psi_g = L_{2d}-l_{AW} \cdot U_{AW}-0{.}5 \cdot B' \cdot U$$
-</latex> 
 </WRAP> </WRAP>
  
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 <WRAP centeralign>  <WRAP centeralign> 
-<latex> +$$\Psi_g = 0{.}689 \, \dfrac{\text{W}}{\text{m} \cdot \text{K}} \, - \, 1{.}830 \, \text{m} \, \cdot \, 0{.}120 \, \dfrac{\text{W}}{\text{m}^2 \cdot \text{K}} \, - \, 0{.}5 \, \cdot \, 8 \, \text{m} \, \cdot \, 0{.}1273 \, \dfrac{\text{W}}{\text{m}^2 \cdot \text{K}} = -0{.}042 \, \dfrac{\text{W}}{\text{m} \cdot \text{K}}$$
-$$\Psi_g = 0{.}687 \, \dfrac{\text{W}}{\text{m} \cdot \text{K}}} \, - \, 1{.}830 \, \text{m} \, \cdot \, 0{.}120 \, \dfrac{\text{W}}{\text{m}^2 \cdot \text{K}}} \, - \, 0{.}5 \, \cdot \, 8 \, \text{m} \, \cdot \, 0{.}1273 \, \dfrac{\text{W}}{\text{m}^2 \cdot \text{K}}} = -0{.}042 \, \dfrac{\text{W}}{\text{m} \cdot \text{K}}}$$ +
-</latex>+
 </WRAP> </WRAP>
  
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 <WRAP centeralign> <WRAP centeralign>
 **Determining the conductance**  **Determining the conductance** 
-<latex>+$
 \Large{L_{2d}} \Large{L_{2d}}
-</latex>+$
 </WRAP> </WRAP>
  
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 **Ψ-value (proportion of exterior wall)**  **Ψ-value (proportion of exterior wall)** 
 </WRAP> </WRAP>
 +
 <WRAP centeralign>  <WRAP centeralign> 
-<latex> +$$ 
-\large{\Psi_g = L_{ie}-l_{AW} \cdot U_{AW}$} +\large{\Psi_g = L_{ie}-l_{AW} \cdot U_{AW}} 
-</latex>+$$
 </WRAP> </WRAP>
  
 <WRAP centeralign> <WRAP centeralign>
-<latex>+$$
 \large{\Psi_{exterior wall} = 0{.}231-1{.}830 \cdot 0{.}120 = 0{.}0114} \large{\Psi_{exterior wall} = 0{.}231-1{.}830 \cdot 0{.}120 = 0{.}0114}
-</latex>+$$
 </WRAP> </WRAP>
  
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 <WRAP centeralign>  <WRAP centeralign> 
-<latex>+$$
 \large{\Psi_g = L_{iu}-0{.}5 \cdot B' \cdot U_{basement ceiling}} \large{\Psi_g = L_{iu}-0{.}5 \cdot B' \cdot U_{basement ceiling}}
-</latex>+$$
 </WRAP> </WRAP>
  
 <WRAP centeralign> <WRAP centeralign>
-<latex>+$$
 \large{\Psi_{basement ceiling} = 0{.}5543-0{.}5 \cdot 8 \cdot 0{.}148 = -0{.}0377} \large{\Psi_{basement ceiling} = 0{.}5543-0{.}5 \cdot 8 \cdot 0{.}148 = -0{.}0377}
-</latex>+$$
 </WRAP> </WRAP>
  
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 <WRAP centeralign>  <WRAP centeralign> 
-<latex>+$$
 \large{U_{f,corrected} = U_f + \dfrac{\Psi_{basement ceiling} \cdot P}{A}} \large{U_{f,corrected} = U_f + \dfrac{\Psi_{basement ceiling} \cdot P}{A}}
-</latex>+$$
 </WRAP> </WRAP>
  
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 <WRAP centeralign>  <WRAP centeralign> 
-<latex>+$$
 \large{\theta_{basement} = \theta_i-f_x \cdot (\theta_i - \theta_e) = 20 \, ^\circ C - 0{.}6 \cdot (20 \, ^\circ C - (-10 \, ^\circ C)) = 2 \, ^\circ C} \large{\theta_{basement} = \theta_i-f_x \cdot (\theta_i - \theta_e) = 20 \, ^\circ C - 0{.}6 \cdot (20 \, ^\circ C - (-10 \, ^\circ C)) = 2 \, ^\circ C}
-</latex>+$$
 </WRAP> </WRAP>
  
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 <WRAP centeralign> <WRAP centeralign>
 **Determining the minimum surface temperature and**  **Determining the minimum surface temperature and** 
-<latex>+$$
 \Large{f_{Rsi}} \Large{f_{Rsi}}
-</latex>+$$
 </WRAP> </WRAP>
  
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 <WRAP centeralign>  <WRAP centeralign> 
-<latex>+$$
 \large{f_{Rsi} = \dfrac{17{.}6 - (-10)}{20-(-10)}=0{.}92} \large{f_{Rsi} = \dfrac{17{.}6 - (-10)}{20-(-10)}=0{.}92}
-</latex>+$$
 </WRAP> </WRAP>
  
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 ===== See also ===== ===== See also =====
  
-  * [[basics:building_physics_-_basics:heat_transfer:thermal_bridges:thermal_ bridge_calculation|Thermal bridge calculation]] +  * [[basics:building_physics_-_basics:thermal_bridges:tbcalculation|Thermal bridge calculation]] 
-  * [[basics:building_physics_-_basics:heat_transfer:what_defines_thermal_bridge_free_design:thermal bridges:thermal_bridge_calculation:recommended procedure]] +  * [[basics:building_physics_-_basics:thermal_bridges:tbcalculation:ground_contact:procedure|]] 
-  * [[basics:building_physics_-_basics:heat_transfer:thermal_bridges:thermal_bridge_calculation:examples]]+  * [[basics:building_physics_-_basics:thermal_bridges:tbcalculation:examples|Examples of thermal bridge calculations]] 
 + 
  
basics/building_physics_-_basics/thermal_bridges/tbcalculation/examples/unheatedb.1548318654.txt.gz · Last modified: 2019/01/24 09:30 by cblagojevic