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basics:building_physics_-_basics:thermal_bridges:tbcalculation:examples:unheatedb [2016/08/09 16:16] – mschuerenbasics:building_physics_-_basics:thermal_bridges:tbcalculation:examples:unheatedb [2022/02/15 18:58] (current) – admin
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 ====== Unheated basement ====== ====== Unheated basement ======
  
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 Active temperature control does not take place in unheated basements. As a rule, lower temperatures prevail in these, therefore thermal separation of the basement from the heated part of the building is necessary. In energy balances the unheated basement is not taken into account in the treated floor area, but it does represent an additional heat transfer resistance between the heated interior space and the outdoor air which has to be taken into account. Active temperature control does not take place in unheated basements. As a rule, lower temperatures prevail in these, therefore thermal separation of the basement from the heated part of the building is necessary. In energy balances the unheated basement is not taken into account in the treated floor area, but it does represent an additional heat transfer resistance between the heated interior space and the outdoor air which has to be taken into account.
  
-{{ :picprivate:unbeheizter_keller_abb_1.png?nolink&800 |}}+{{ :picopen:unbeheizter_keller_abb_1.png?800 |}}
  
 This transfer resistance is assigned to the boundary surface between the basement and the interior space (see figure above). This is expressed by the following U-value: This transfer resistance is assigned to the boundary surface between the basement and the interior space (see figure above). This is expressed by the following U-value:
  
 <WRAP centeralign>  <WRAP centeralign> 
-<latex> +$$ 
-$$\frac{1}{U} = \frac{1}{U_f} + \frac{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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 $U_f$  is the heat transfer resistance of the basement ceiling. $U_{bf}$ and $U_{bw}$ are the U-values of the basement floor slab and the basement wall respectively and are based in turn on the approximation function of the norm for taking into account of the ground. Ventilation of the basement is also taken into account. In order to allow energy-relevant evaluation of the connection situation between the basement and the interior space, another Ψ-value must be calculated for the energy balance. Several methods exist for this purpose which are demonstrated on the basis of the following detail: $U_f$  is the heat transfer resistance of the basement ceiling. $U_{bf}$ and $U_{bw}$ are the U-values of the basement floor slab and the basement wall respectively and are based in turn on the approximation function of the norm for taking into account of the ground. Ventilation of the basement is also taken into account. In order to allow energy-relevant evaluation of the connection situation between the basement and the interior space, another Ψ-value must be calculated for the energy balance. Several methods exist for this purpose which are demonstrated on the basis of the following detail:
   
-{{ :picprivate:unbeheizter_keller_abb_2.png?nolink&400 |}}+{{ :picopen:unbeheizter_keller_abb_2.png?400 |}}
 \\ \\
-{{ :picprivate:unbeheizter_keller_abb_3a.png?nolink&800 |}} +{{ :picopen:unbeheizter_keller_abb_3a.png?800 |}} 
-{{ :picprivate:unbeheizter_keller_abb_3b.png?nolink&800 |}} +{{ :picopen:unbeheizter_keller_abb_3b.png?800 |}} 
-{{ :picprivate:unbeheizter_keller_abb_3c.png?nolink&800 |}} +{{ :picopen:unbeheizter_keller_abb_3c.png?800 |}} 
-{{ :picprivate:unbeheizter_keller_abb_3d.png?nolink&800 |}}+{{ :picopen:unbeheizter_keller_abb_3d.png?800 |}} 
  
 \\ \\
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 ==== Calculation of the conductance ==== ==== Calculation of the conductance ====
  
-{{ :picprivate:unbeheizter_keller_abb_4.png?nolink&200|}}+{{ :picopen:unbeheizter_keller_abb_4.png?200|}}
 For the unheated basement, the overall value $L_{2d}$ must also be calculated as it is for the floor slab and the heated basement. The required heat flow from the heated space consists of the conductances $L_{ie}$  and $L_{iu}$: For the unheated basement, the overall value $L_{2d}$ must also be calculated as it is for the floor slab and the heated basement. The required heat flow from the heated space consists of the conductances $L_{ie}$  and $L_{iu}$:
  
 <WRAP centeralign>  <WRAP centeralign> 
-<latex> +$$ 
-$$\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> +$$ 
-$$\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> +$$ 
-$L_{2d}$  +\Large{_{2d}} 
-</latex>+$$
 </WRAP> </WRAP>
  
-{{ :picprivate:unbeheizter_keller_abb_5a.png?nolink&600 |}} +{{ :picopen:unbeheizter_keller_abb_5a.png?600 |}} 
-{{ :picprivate:unbeheizter_keller_abb_5b.png?nolink&600 |}}+{{ :picopen:unbeheizter_keller_abb_5b.png?600 |}}
  
 <WRAP centeralign>  <WRAP centeralign> 
-<latex> +$$ 
- +\large{ 
-$$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_2-L_3+L_1) = 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> +$$ 
-$$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> +$$ 
-$$\frac{1}{U} = \frac{1}{U_f} + \frac{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 \, \frac{\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> +$$\Psi_g = L_{2d}-l_{AW} \cdot U_{AW}-0{.}5 \cdot B' \cdot U$$
-$$\Psi_g = L_{2d}-l_{EW} \cdot U_{EW}-0{.}5 \cdot B' \cdot U$$ +
-</latex>+
 </WRAP> </WRAP>
  
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 <WRAP centeralign>  <WRAP centeralign> 
-<latex> +$$\Psi_g = 0{.}689 \, \dfrac{\text{W}}{\text{m} \cdot \text{K}} \, - \, 1{.}830 \, \text{m} \, \cdot \, 0{.}120 \, \dfrac{\text{W}}{\text{m}^2 \cdot \text{K}} \, - \, 0{.}5 \, \cdot \, 8 \, \text{m} \, \cdot \, 0{.}1273 \, \dfrac{\text{W}}{\text{m}^2 \cdot \text{K}} = -0{.}042 \, \dfrac{\text{W}}{\text{m} \cdot \text{K}}$$
-$$\Psi_g = 0{.}687 \, \frac{\text{W}}{\text{m} \cdot \text{K}}} \, - \, 1{.}830 \, \text{m} \, \cdot \, 0{.}120 \, \frac{\text{W}}{\text{m}^2 \cdot \text{K}}} \, - \, 0{.}5 \, \cdot \, 8 \, \text{m} \, \cdot \, 0{.}1273 \, \frac{\text{W}}{\text{m}^2 \cdot \text{K}}} = -0{.}042 \, \frac{\text{W}}{\text{m} \cdot \text{K}}}$$ +
-</latex>+
 </WRAP> </WRAP>
  
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 <WRAP centeralign> <WRAP centeralign>
 **Determining the conductance**  **Determining the conductance** 
-<latex> +$ 
-$L_{2d}$  +\Large{L_{2d}} 
-</latex>+$
 </WRAP> </WRAP>
  
-{{ :picprivate:unbeheizter_keller_abb_6a.png?nolink&600 |}} + 
-{{ :picprivate:unbeheizter_keller_abb_6b.png?nolink&600 |}}+{{ :picopen:unbeheizter_keller_abb_6a.png?600 |}} 
 +{{ :picopen:unbeheizter_keller_abb_6b.png?600 |}}
  
 <WRAP centeralign>  <WRAP centeralign> 
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 <WRAP centeralign>  <WRAP centeralign> 
-<latex> +$$ 
-$$\Psi_g = L_{ie}-l_{EW} \cdot U_{EW}$$ +\large{\Psi_g = L_{ie}-l_{AW} \cdot U_{AW}} 
-$$\Psi_{exterior wall} = 0{.}231-1{.}830 \cdot 0{.}120 = 0{.}0114$$ +$$ 
-</latex>+</WRAP> 
 + 
 +<WRAP centeralign> 
 +$$ 
 +\large{\Psi_{exterior wall} = 0{.}231-1{.}830 \cdot 0{.}120 = 0{.}0114} 
 +$$
 </WRAP> </WRAP>
  
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 <WRAP centeralign>  <WRAP centeralign> 
-<latex> +$$ 
-$$\Psi_g = L_{iu}-0{.}5 \cdot B' \cdot U_{basement ceiling}$$ +\large{\Psi_g = L_{iu}-0{.}5 \cdot B' \cdot U_{basement ceiling}} 
-$$\Psi_{ basement ceiling } = 0{.}5543-0{.}5 \cdot 8 \cdot 0{.}148 = -0{.}0377$$ +$$ 
-</latex>+</WRAP> 
 + 
 +<WRAP centeralign> 
 +$$ 
 +\large{\Psi_{basement ceiling} = 0{.}5543-0{.}5 \cdot 8 \cdot 0{.}148 = -0{.}0377} 
 +$$
 </WRAP> </WRAP>
  
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 <WRAP centeralign>  <WRAP centeralign> 
-<latex> +$$ 
-$$U_{f,corrected} = U_f + \frac{\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> +$$ 
-$$\theta_{Keller} = \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> +$$ 
-$f_{Rsi}$  +\Large{f_{Rsi}} 
-</latex>+$$
 </WRAP> </WRAP>
  
-{{ :picprivate:unbeheizter_keller_abb_7a.png?nolink&400 |}}+{{ :picopen:unbeheizter_keller_abb_7a.png?400 |}}
  
-{{ :picprivate:unbeheizter_keller_abb_7b.png?nolink&400 |}}+{{ :picopen:unbeheizter_keller_abb_7b.png?400 |}}
  
 <WRAP centeralign>  <WRAP centeralign> 
-<latex> +$$ 
-$$f_{Rsi} = \frac{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.1470752191.txt.gz · Last modified: 2016/08/09 16:16 by mschueren