basics:building_physics_-_basics:thermal_bridges:tbcalculation:examples:unheatedb
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basics:building_physics_-_basics:thermal_bridges:tbcalculation:examples:unheatedb [2019/01/24 08:47] – [Calculation of the conductance] cblagojevic | basics:building_physics_-_basics:thermal_bridges:tbcalculation:examples:unheatedb [2019/01/24 09:40] – [See also] cblagojevic | ||
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<WRAP centeralign> | <WRAP centeralign> | ||
< | < | ||
- | $$\frac{1}{U} = \frac{1}{U_f} + \frac{A}{(A \cdot U_{bf}) + (z \cdot P \cdot U_{bw}) + (h \cdot P \cdot U_w) + (0{.}33 \cdot n \cdot V)} | + | \large{\dfrac{1}{U} = \dfrac{1}{U_f} + \dfrac{A}{(A \cdot U_{bf}) + (z \cdot P \cdot U_{bw}) + (h \cdot P \cdot U_W) + (0{,}33 \cdot n \cdot V)}} |
</ | </ | ||
\\ | \\ | ||
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<WRAP centeralign> | <WRAP centeralign> | ||
< | < | ||
- | $$\Phi = L_{iu} \cdot (\theta_i - \theta_u) + L_{ie} \cdot (\theta_i - \theta_e)$$ | + | \large{\Phi = L_{iu} \cdot (\theta_i - \theta_u) + L_{ie} \cdot (\theta_i - \theta_e)} |
</ | </ | ||
</ | </ | ||
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<WRAP centeralign> | <WRAP centeralign> | ||
< | < | ||
- | $$\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)$$ | + | \large{\Phi = \left(\frac{L_{iu} \cdot L_{ue}}{L_{iu} + L_{ue}}\right) \cdot (\theta_i - \theta_e) \quad \Rightarrow \quad L_{2d} = \left(\frac{L_{iu} \cdot L_{ue}}{L_{iu} + L_{ue}} + L_{ie}\right)} |
</ | </ | ||
</ | </ | ||
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**Determining the conductance** | **Determining the conductance** | ||
< | < | ||
- | $L_{2d}$ | + | \Large{_{2d}} |
</ | </ | ||
</ | </ | ||
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<WRAP centeralign> | <WRAP centeralign> | ||
< | < | ||
+ | \large{ | ||
$$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}}}$$} |
</ | </ | ||
</ | </ | ||
+ | |||
<WRAP centeralign> | <WRAP centeralign> | ||
< | < | ||
- | $$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}}}$$ | + | \large{L_{2d} = \left(\frac{L_{iu} \cdot L_{ue}}{L_{iu} + L_{ue}} + L_{ie}\right) = 0{.}6886 \, \frac{\text{W}}{\text{m} \cdot \text{K}}}} |
</ | </ | ||
</ | </ | ||
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Therefore: | Therefore: | ||
- | |||
<WRAP centeralign> | <WRAP centeralign> | ||
< | < | ||
- | $$\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}}}$$ |
</ | </ | ||
</ | </ | ||
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<WRAP centeralign> | <WRAP centeralign> | ||
< | < | ||
- | $$\Psi_g = L_{2d}-l_{EW} \cdot U_{EW}-0{.}5 \cdot B' \cdot U$$ | + | $$\Psi_g = L_{2d}-l_{AW} \cdot U_{AW}-0{.}5 \cdot B' \cdot U$$ |
</ | </ | ||
</ | </ | ||
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<WRAP centeralign> | <WRAP centeralign> | ||
< | < | ||
- | $$\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}}}$$ | + | $$\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}}}$$ |
</ | </ | ||
</ | </ | ||
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**Determining the conductance** | **Determining the conductance** | ||
< | < | ||
- | $L_{2d}$ | + | \Large{L_{2d}} |
</ | </ | ||
</ | </ | ||
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**Ψ-value (proportion of exterior wall)** | **Ψ-value (proportion of exterior wall)** | ||
</ | </ | ||
- | |||
<WRAP centeralign> | <WRAP centeralign> | ||
< | < | ||
- | $$\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$$ | + | </ |
+ | </ | ||
+ | |||
+ | <WRAP centeralign> | ||
+ | < | ||
+ | \large{\Psi_{exterior wall} = 0{.}231-1{.}830 \cdot 0{.}120 = 0{.}0114} | ||
</ | </ | ||
</ | </ | ||
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<WRAP centeralign> | <WRAP centeralign> | ||
< | < | ||
- | $$\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$$ | + | </ |
+ | </ | ||
+ | |||
+ | <WRAP centeralign> | ||
+ | < | ||
+ | \large{\Psi_{basement ceiling} = 0{.}5543-0{.}5 \cdot 8 \cdot 0{.}148 = -0{.}0377} | ||
</ | </ | ||
</ | </ | ||
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<WRAP centeralign> | <WRAP centeralign> | ||
< | < | ||
- | $$U_{f, | + | \large{U_{f, |
</ | </ | ||
</ | </ | ||
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<WRAP centeralign> | <WRAP centeralign> | ||
< | < | ||
- | $$\theta_{Keller} = \theta_i-f_x \cdot (\theta_i - \theta_e) = 20 \, ^\circ C - 0{.}6 \cdot (20 \, ^\circ C - (-10 \, ^\circ C)) = 2 \, ^\circ C$$ | + | \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} |
</ | </ | ||
</ | </ | ||
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**Determining the minimum surface temperature and** | **Determining the minimum surface temperature and** | ||
< | < | ||
- | $f_{Rsi}$ | + | \Large{f_{Rsi}} |
</ | </ | ||
</ | </ | ||
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<WRAP centeralign> | <WRAP centeralign> | ||
< | < | ||
- | $$f_{Rsi} = \frac{17{.}6 - (-10)}{20-(-10)}=0{.}92$$ | + | \large{f_{Rsi} = \dfrac{17{.}6 - (-10)}{20-(-10)}=0{.}92} |
</ | </ | ||
</ | </ | ||
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===== See also ===== | ===== See also ===== | ||
- | * [[basics: | + | * [[basics: |
- | * [[basics: | + | * [[basics: |
- | * [[basics: | + | * [[basics: |
+ | |||
basics/building_physics_-_basics/thermal_bridges/tbcalculation/examples/unheatedb.txt · Last modified: 2022/02/15 18:58 by admin