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Thermal Bridges in Building Construction — 2D Composite Structure
Introduction
The European standard EN ISO 10211:2017 for thermal bridges in building constructions provides four test cases — two 2D and two 3D — for validating a numerical method (Ref. 1). If the values obtained by a method conform to the results of all these four cases, the method is classified as a three-dimensional steady-state high precision method.
COMSOL Multiphysics successfully passes all the test cases described by the standard. This document presents an implementation of the second 2D model (Case 2).
The example studies the temperature distribution and heat flux through a two-dimensional cross-section of an insulating wall. Table 1 and Table 2 compare the numerical results with the target solution provided by the standard.
Figure 1: Geometry and material distribution of ISO 10211:2017 test case 2.
Model Definition
Figure 1 shows the geometry and material distribution. Four materials with distinct thermal conductivities are used in the structure: a concrete layer on the top side, an aluminum layer on the left and bottom sides, an insulation material layer occupying the largest space in the structure, and a wooden batten between the aluminum and concrete layers.
The left and right boundaries are thermally insulated. The top and bottom boundaries, corresponding to cold exterior and hot interior sides, are subject to convective heat flux. The exterior temperature is 0°C while interior temperature is 20°C. The ISO 10211:2017 standard specifies the values of the thermal resistance, R, which is related to the heat transfer coefficient, h, according to
Results and Discussion
The temperature profile in Figure 2 shows the effects of the highly conductive aluminum layer on the left side.
Figure 2: Temperature distribution of ISO 10211:2017 test case 2.
The numerical results of the COMSOL Multiphysics simulation are compared with the expected values provided by EN ISO 10211:2017 (Ref. 1). Table 1 shows the comparison for the total heat flux and Table 2 compares temperature at nine particular points.
Table 1: Comparison between expected values and computed values (total heat flux).
Expected value
COMputed value
difference
9.5 W/m
9.49 W/m
0.08%
Table 2: Comparison between expected values and computed values (temperature).
(x,y) coord. (mm)
Expected value (°c)
Computed value (°C)
diff. (°C)
(x,y) coord. (mm)
Expected value (°c)
Computed value (°C)
diff. (°C)
(0, 47.5)
7.1
7.07
0.03
(15, 41.5)
6.3
6.27
0.03
(0, 41.5)
7.9
7.90
0.00
(15, 36.5)
16.3
16.33
0.03
(0, 36.5)
16.4
16.41
0.01
(500, 47.5)
0.8
0.76
0.04
(0, 0)
16.8
16.77
0.03
(500, 41.5)
0.8
0.83
0.03
 
 
 
 
(500, 0)
18.3
18.33
0.03
The maximum permissible differences to pass this case validation, 0.1°C for temperature and 0.1% for total heat flux, are respected.
Reference
1. European Committee for Standardization, EN ISO 10211, Thermal bridges in building construction – Heat flows and surface temperatures – Detailed calculations (ISO 10211:2017), Appendix A, pp. 54–60, 2017.
Application Library path: Heat_Transfer_Module/Buildings_and_Constructions/thermal_bridge_2d_composite_structure
Modeling Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  2D.
2
In the Select Physics tree, select Heat Transfer > Heat Transfer in Solids (ht).
3
Click Add.
4
Click  Study.
5
In the Select Study tree, select General Studies > Stationary.
6
Click  Done.
Global Definitions
Parameters 1
Define the parameters necessary to build the geometry.
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, locate the Parameters section.
3
In the table, enter the following settings:
Name
Expression
Value
Description
W
0.5[m]
0.5 m
Structure width
w
15[mm]
0.015 m
Short width for wood and aluminum domains
h1
6[mm]
0.006 m
Concrete domain height
h2
5[mm]
0.005 m
Wood domain height
h3
41.5[mm]
0.0415 m
Insulation domain height
h4
h3-h2
0.0365 m
Aluminum domain height
t4
1.5[mm]
0.0015 m
Aluminum domain thickness
Geometry 1
Rectangle 1 (r1)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type W.
4
In the Height text field, type h3+h1.
5
Click to expand the Layers section. In the table, enter the following settings:
Layer name
Thickness (m)
Layer 1
h3
6
Click  Build Selected.
This two-layered rectangle corresponds to the insulation and concrete layers. Continue with the aluminum layer, which consists of three rectangles.
Rectangle 2 (r2)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type W.
4
In the Height text field, type t4.
5
Click  Build Selected.
Rectangle 3 (r3)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type t4.
4
In the Height text field, type h4.
5
Click  Build Selected.
Rectangle 4 (r4)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type w.
4
In the Height text field, type t4.
5
Locate the Position section. In the y text field, type h4-t4.
6
Click  Build Selected.
Union 1 (uni1)
1
In the Geometry toolbar, click  Booleans and Partitions and choose Union.
2
In the Settings window for Union, locate the Union section.
3
Clear the Keep interior boundaries checkbox.
4
In the Model Builder window, click Union 1 (uni1).
5
Click the  Clear Selection button for Input objects.
6
Select the objects r2, r3, and r4 only.
7
Click  Build Selected.
Add a rectangle for the wooden batten.
Rectangle 5 (r5)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type w.
4
In the Height text field, type h2.
5
Locate the Position section. In the y text field, type h4.
6
Click  Build All Objects.
Materials
Concrete
1
In the Materials toolbar, click  Blank Material.
2
In the Settings window for Material, type Concrete in the Label text field.
3
Select Domain 3 only.
4
Locate the Material Contents section. In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Thermal conductivity
k_iso ; kii = k_iso, kij = 0
1.15[W/(m*K)]
W/(m·K)
Basic
Density
rho
2300[kg/m^3]
kg/m³
Basic
Heat capacity at constant pressure
Cp
880[J/(kg*K)]
J/(kg·K)
Basic
Wood
1
In the Materials toolbar, click  Blank Material.
2
In the Settings window for Material, type Wood in the Label text field.
3
Select Domain 2 only.
4
Locate the Material Contents section. In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Thermal conductivity
k_iso ; kii = k_iso, kij = 0
0.12[W/(m*K)]
W/(m·K)
Basic
Density
rho
500[kg/m^3]
kg/m³
Basic
Heat capacity at constant pressure
Cp
2500[J/(kg*K)]
J/(kg·K)
Basic
Insulation
1
In the Materials toolbar, click  Blank Material.
2
In the Settings window for Material, type Insulation in the Label text field.
3
Select Domain 4 only.
4
Locate the Material Contents section. In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Thermal conductivity
k_iso ; kii = k_iso, kij = 0
0.029[W/(m*K)]
W/(m·K)
Basic
Density
rho
150[kg/m^3]
kg/m³
Basic
Heat capacity at constant pressure
Cp
1000[J/(kg*K)]
J/(kg·K)
Basic
Aluminum
1
In the Materials toolbar, click  Blank Material.
2
In the Settings window for Material, type Aluminum in the Label text field.
3
Select Domain 1 only.
4
Locate the Material Contents section. In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Thermal conductivity
k_iso ; kii = k_iso, kij = 0
230[W/(m*K)]
W/(m·K)
Basic
Density
rho
2700[kg/m^3]
kg/m³
Basic
Heat capacity at constant pressure
Cp
900[J/(kg*K)]
J/(kg·K)
Basic
Heat Transfer in Solids (ht)
Heat Flux 1
1
In the Physics toolbar, click  Boundaries and choose Heat Flux.
2
Select Boundaries 2 and 10 only.
3
In the Settings window for Heat Flux, locate the Heat Flux section.
4
From the Flux type list, choose Convective heat flux.
5
In the h text field, type 1[W/(m^2*K)]/0.11.
6
In the Text text field, type 20[degC].
Heat Flux 2
1
In the Physics toolbar, click  Boundaries and choose Heat Flux.
2
Select Boundary 9 only.
3
In the Settings window for Heat Flux, locate the Heat Flux section.
4
From the Flux type list, choose Convective heat flux.
5
In the h text field, type 1[W/(m^2*K)]/0.06.
6
In the Text text field, type 0[degC].
Study 1
In the Study toolbar, click  Compute.
Results
Change the unit of the temperature results to degrees Celsius.
Preferred Units 1
1
In the Results toolbar, click  Configurations and choose Preferred Units.
2
In the Settings window for Preferred Units, locate the Units section.
3
Click  Add Physical Quantity.
4
In the Physical Quantity dialog, select General > Temperature (K) in the tree.
5
Click OK.
6
In the Settings window for Preferred Units, locate the Units section.
7
In the table, enter the following settings:
Quantity
Unit
Preferred unit
Temperature
K
°C
8
Click  Apply.
The default plot shows the temperature distribution (Figure 2).
Result Templates
1
In the Results toolbar, click  Result Templates to open the Result Templates window.
2
Go to the Result Templates window.
3
In the tree, select Study 1/Solution 1 (sol1) > Heat Transfer in Solids > Isothermal Contours (ht).
4
Click the Add Result Template button in the window toolbar.
5
In the Results toolbar, click  Result Templates to close the Result Templates window.
The second plot shows isothermal contours in the structure.
Results
Follow the steps below to compute the heat flux given in Table 1.
Line Integration 1
1
In the Results toolbar, click  More Derived Values and choose Integration > Line Integration.
2
Select Boundaries 2 and 10 only.
3
In the Settings window for Line Integration, click Replace Expression in the upper-right corner of the Expressions section. From the menu, choose Component 1 (comp1) > Heat Transfer in Solids > Boundary fluxes > ht.q0 - Inward heat flux - W/m².
4
Click  Evaluate.
Finally, export the temperature values at the points given in Table 2 to compare the results with the expected values.
Data 1
1
In the Results toolbar, click  Data and choose Data.
2
In the Settings window for Data, locate the Expressions section.
3
In the table, enter the following settings:
Expression
Unit
Description
T
°C
Temperature
4
Locate the Output section. Click  Browse.
5
Browse to a suitable folder, enter the filename thermal_bridge_2d_composite_structure_result.txt, and then click Save.
6
From the Points to evaluate in list, choose Grid.
7
In the X text field, type 0,w,W.
8
In the Y text field, type 0,h4,h4+h2,h4+h2+h1.
9
Click Export.