Thermal Bridges in Building Construction — 3D Structure Between Two Floors

The European standard EN ISO 10211:2007 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 and is hence classified as a three-dimensional steady-state high precision method. This document presents an implementation of the first 3D model (Case 3).

Figure 1: Geometry and boundary conditions of ISO 10211:2007 test case 3.

This tutorial studies the heat conduction in a building structure separating two floors from the external environment. The structure’s surfaces are divided into four parts:

•

the lower level, α;

•

the upper level, β;

•

the outside, γ;

•

and the remaining thermally insulated surfaces, δ.

The values of interest for validation are the lowest temperatures at surfaces α and β, and the heat fluxes through α, β, and γ.

Model Definition

Figure 1 illustrates the geometry. The external surface is at 0°C and the interior surface is at 20°C. Four materials with distinct thermal conductivities k are used in the structure. The horizontal block separating the two floors has the highest thermal conductivity (2.5 W/(m·K)). It crosses the wall, thereby creating a thermal bridge in the structure.

The surfaces α, β, and γ are subject to convective heat flux. The ISO 10211:2007 standard specifies the values of the thermal resistance, R, which is related to the heat transfer coefficient, h, according to

Results and Discussion

Figure 2 shows the temperature profile. The heat losses are greater near the thermal bridge formed by the horizontal block that crosses the wall.

Figure 2: Temperature distribution of ISO 10211:2007 test case 3.

The numerical results of COMSOL Multiphysics are compared with the expected values provided by ISO 10211:2007 (Ref. 1) in Table 1.

Table 1: Comparison between expected values and computed values.
measured quantity	Expected values	Computed values	difference
Minimum temperature on α	11.32°C	11.325°C	0.005°C
Minimum temperature on β	11.11°C	11.10°C	0.01°C
Heat flux through α	46.09 W	46.19 W	0.22%
Heat flux through β	13.89 W	13.92 W	0.25%
Heat flux through γ	59.98 W	60.12 W	0.23%

The maximum permissible differences to pass this test case are 0.1°C for temperature and 1% for heat flux. The measured values are completely consistent and meet the validation criteria. Note that they may change slightly depending on geometry representation and operating system.

As shown in Figure 3 and Figure 4, the minimum temperature of the surfaces α and β are located at their respective corners.

Figure 3: Minimum and maximum temperatures on surface α, ISO 10211:2007 test case 3.

Figure 4: Minimum and maximum temperatures on surface β, ISO 10211:2007 test case 3.

Reference

1. European Committee for Standardization, EN ISO 10211, Thermal bridges in building construction – Heat flows and surface temperatures – Detailed calculations (ISO 10211:2007), Appendix A, pp. 30–36, 2007.

Heat_Transfer_Module/Buildings_and_Constructions/thermal_bridge_3d_two_floors

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

Click

In the tree, select .

Click

Global Definitions

Define the geometrical parameters.

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
wall_t1	5[cm]	0.05 m	Insulation layer thickness
wall_t2	30[cm]	0.3 m	Wall thickness
rect1	1.2[m]	1.2 m	Wall first rectangle basis
rect2	1.3[m]	1.3 m	Wall second rectangle basis
rect_shift	-10[cm]	-0.1 m	Shift for the rectangles
wall_h	2.15[m]	2.15 m	Wall height
blk_w	1.15[m]	1.15 m	Rectangle horizontal block width
blk_d	1.9[m]	1.9 m	Rectangle horizontal block depth
blk_h	0.15[m]	0.15 m	Rectangle horizontal block height
blk_shiftx	5[cm]	0.05 m	Rectangle horizontal block x-shift
blk_shifty	-0.7[m]	-0.7 m	Rectangle horizontal block y-shift
blk_shiftz	1[m]	1 m	Rectangle horizontal block z-shift
sq_l	1[m]	1 m	Square horizontal block side length
sq_h	5[cm]	0.05 m	Square horizontal block height
sq_shift	0.2[m]	0.2 m	Square horizontal block shift

Geometry 1

To build the walls separating the external and internal surfaces, create the cross section geometry and extrude it.

Work Plane 1 (wp1)

In the toolbar, click

In the window for , click

Work Plane 1 (wp1)>Plane Geometry

In the window, click .

The first two rectangles below correspond to the insulation layer of the wall.

Work Plane 1 (wp1)>Rectangle 1 (r1)

In the toolbar, click

In the window for , locate the section.

In the text field, type rect1.

In the text field, type wall_t1.

Click

Work Plane 1 (wp1)>Rectangle 2 (r2)

In the toolbar, click

In the window for , locate the section.

In the text field, type wall_t1.

In the text field, type rect1.

Click

Click the

button in the toolbar.

Work Plane 1 (wp1)>Union 1 (uni1)

In the toolbar, click

and choose .

Click in the window and then press Ctrl+A to select both objects.

In the window for , locate the section.

Clear the check box.

Click

Work Plane 1 (wp1)>Plane Geometry

Build the remaining layers of the walls in a similar manner.

Work Plane 1 (wp1)>Rectangle 3 (r3)

In the toolbar, click

In the window for , locate the section.

In the text field, type rect2.

In the text field, type wall_t2.

Locate the section. In the text field, type rect_shift.

In the text field, type rect_shift.

Click

Work Plane 1 (wp1)>Rectangle 4 (r4)

In the toolbar, click

In the window for , locate the section.

In the text field, type wall_t2.

In the text field, type rect2.

Locate the section. In the text field, type rect_shift.

In the text field, type rect_shift.

Click

Work Plane 1 (wp1)>Union 2 (uni2)

In the toolbar, click

and choose .

Select the objects and only.

In the window for , locate the section.

Clear the check box.

Click

Extrude 1 (ext1)

In the window, right-click and choose .

In the window for , locate the section.

In the table, enter the following settings:


Distances (m)
wall_h

Click

Click the

button in the toolbar.

Block 1 (blk1)

In the toolbar, click

This block separates the two floors of the structure.

In the window for , locate the section.

In the text field, type blk_w.

In the text field, type blk_d.

In the text field, type blk_h.

Locate the section. In the text field, type blk_shiftx.

In the text field, type blk_shifty.

In the text field, type blk_shiftz.

Click

To remove unnecessary edges, you need to remove the parts of the walls that intersect this block. To do so, use the boolean operation to subtract a copy of the block from the walls. Begin by creating the copy.

Block 2 (blk2)

Right-click and choose .

Difference 1 (dif1)

In the toolbar, click

and choose .

Select the object only.

The object labeled ext1 is made up of the walls previously obtained by extrusion.

In the window for , locate the section.

Find the subsection. Select the

toggle button.

Select the object only.

Click

Block 3 (blk3)

In the toolbar, click

This block corresponds to the floor of the inside upper level.

In the window for , locate the section.

In the text field, type sq_l.

In the text field, type sq_h.

Locate the section. In the text field, type sq_shift.

In the text field, type sq_shift.

In the text field, type blk_shiftz+blk_h.

Click

Ignore Edges 1 (ige1)

In the toolbar, click

and choose .

In the first steps of the geometry sequence, six unused vertical edges were created on the walls. They are responsible for unnecessary constraints on the mesh and they generate extra boundaries by splitting some faces. For these reasons, follow the instructions below to remove them.

On the object , select Edges 6, 17, 33, 38, 60, and 63 only.

To reach the edges, click the button in the toolbar. Note that you can make the selection by clicking the button and typing the indices in the dialog box that opens.

In the window for , click

Materials

Interior Wall

In the toolbar, click

In the window for , type Interior Wall in the text field.

Select Domains 4 and 5 only.

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Thermal conductivity	k_iso ; kii = k_iso, kij = 0	0.7	W/(m·K)	Basic
Density	rho	1700	kg/m³	Basic
Heat capacity at constant pressure	Cp	800	J/(kg·K)	Basic

Isolation

In the toolbar, click

In the window for , type Isolation in the text field.

Select Domain 2 only.

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Thermal conductivity	k_iso ; kii = k_iso, kij = 0	0.04	W/(m·K)	Basic
Density	rho	200	kg/m³	Basic
Heat capacity at constant pressure	Cp	1000	J/(kg·K)	Basic

Exterior Wall

In the toolbar, click

In the window for , type Exterior Wall in the text field.

Select Domain 1 only.

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Thermal conductivity	k_iso ; kii = k_iso, kij = 0	1	W/(m·K)	Basic
Density	rho	2000	kg/m³	Basic
Heat capacity at constant pressure	Cp	1000	J/(kg·K)	Basic

Horizontal Structure

In the toolbar, click

In the window for , type Horizontal Structure in the text field.

Select Domain 3 only.

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Thermal conductivity	k_iso ; kii = k_iso, kij = 0	2.5	W/(m·K)	Basic
Density	rho	5000	kg/m³	Basic
Heat capacity at constant pressure	Cp	600	J/(kg·K)	Basic

Floor

In the toolbar, click

In the window for , type Floor in the text field.

Select Domain 6 only.

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Thermal conductivity	k_iso ; kii = k_iso, kij = 0	1	W/(m·K)	Basic
Density	rho	1000	kg/m³	Basic
Heat capacity at constant pressure	Cp	800	J/(kg·K)	Basic