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This validation case belongs to heat transfer, with the case of a three-dimensional corner where two walls and one floor element meet. The aim of this project is to demonstrate the validity of SimScale’s Heat Transfer solver by replicating the standard test case and comparing the following parameters:

- Temperature distribution

The simulation results from SimScale were compared to the reference results presented in the standard EN-ISO 10211, “Thermal Bridges in Building Construction”, validation case 3 (Annex C)\(^1\).

The structural corner geometry is shown in figure 1:

The model is composed of the following parts:

- Floor
- Horizontal structure (which acts as the thermal bridge)
- Internal wall – upper
- Internal wall – lower
- External wall
- Insulation

For the application of boundary conditions and measurement of result quantities, the surfaces of the structure are classified according to the spaces they belong to:

- Lower internal (\(\alpha\))
- Upper internal (\(\beta\))
- External (\(\gamma\))
- Structure cuts (\(\delta\))

**Tool Type**: Code_Aster

**Analysis Type**: Heat Transfer

**Mesh and Element Types**:

The mesh was computed using SimScale’s standard meshing algorithm, with the fineness parameter maxed up to 10. Statistics of the resulting mesh are presented in Table 1, and illustration shown in Figure 2:

Mesh # | Mesh Type | Element Type | Number of Nodes | Number of Elements |
---|---|---|---|---|

1 | Standard | 1st order tetrahedrals | 741457 | 483998 |

**Materials**:

- Interior Wall
- \((\rho)\)
*Density*: 1700 \(kg/m^3\) *Conductivity*: Isotropic- \( (\kappa)\) )
*Thermal conductivity*: 0.7 \( W/(m.K) \) *Specific Heat*: 800 \( J/(kg.K) \)

- \((\rho)\)
- Isolation
- \((\rho)\)
*Density*: 200 \(kg/m^3\) *Conductivity*: Isotropic- \( (\kappa)\) )
*Thermal conductivity*: 0.04 \( W/(m.K) \) *Specific Heat*: 1000 \( J/(kg.K) \)

- \((\rho)\)
- Exterior Wall
- \((\rho)\)
*Density*: 2000 \(kg/m^3\) *Conductivity*: Isotropic- \( (\kappa)\) )
*Thermal conductivity*: 1 \( W/(m.K) \) *Specific Heat*: 1000 \( J/(kg.K) \)

- \((\rho)\)
- Horizontal Structure
- \((\rho)\)
*Density*: 5000 \(kg/m^3\) *Conductivity*: Isotropic- \( (\kappa)\) )
*Thermal conductivity*: 2.5 \( W/(m.K) \) *Specific Heat*: 600 \( J/(kg.K) \)

- \((\rho)\)
- Floor
- \((\rho)\)
*Density*: 1000 \(kg/m^3\) *Conductivity*: Isotropic- \( (\kappa)\) )
*Thermal conductivity*: 1 \( W/(m.K) \) *Specific Heat*: 800 \( J/(kg.K) \)

- \((\rho)\)

**Boundary Conditions**:

The model considers convective heat transfer from the surfaces of the structure to the corresponding spaces. The interior spaces are at 20\(°C\) and 15\(°C\), and the exterior is at 0\(°C\). Also, the standard specifies the heat transfer properties in terms of the thermal resistance \(R\), which must be converted to the heat transfer coefficient used in SimScale, according to:

$$ h = \frac{1}{R} $$

The following boundary conditions were used in the simulation (see Figure 2 for illustration):

- Lower internal faces \(\alpha\):
- Convective heat flux
- (\(T_0\)) Reference temperature 20\(°C\)
- Heat transfer coefficient 5 \(W/(K.m^2)\)

- Upper internal faces \(\beta\):
- Convective heat flux
- (\(T_0\)) Reference temperature 15\(°C\)
- Heat transfer coefficient 5 \(W/(K.m^2)\)

- External faces \(\gamma\):
- Convective heat flux
- (\(T_0\)) Reference temperature 0\(°C\)
- Heat transfer coefficient 20 \(W/(K.m^2)\)

- Structure cuts \(\delta\):
- Adiabatic (applied by default)

The reference solution\(^1\) for the structure is given in terms of the minimum temperatures and heat fluxes at the control surfaces.

The computed temperature values from the simulation are presented in Table 2, and compared to the expected values from the standard:

Result | Reference Value | SimScale Value | Deviation |
---|---|---|---|

Minimum temperature on \(\alpha\) | 11.32\(°C\) | 11.29\(°C\) | 0.03\(°C\) |

Minimum temperature on \(\beta\) | 11.11\(°C\) | 11.12\(°C\) | 0.01\(°C\) |

Heat Flow on \(\alpha\) | 46.09\(W\) | 45.75\(W\) | 0.74% |

Heat Flow on \(\beta\) | 13.89\(W\) | 13.76\(W\) | 0.72% |

Heat Flow on \(\gamma\) | 59.98\(W\) | 59.60\(W\) | 0.63% |

The acceptance criterion states that the difference between the computed temperatures by the method being validated and the listed temperatures shall not exceed 0.1\(°C\). For the Heat Flows, the deviation should not exceed 1%. Thus, it is found that the SimScale solver is accepted under the standard’s validation case 3.

Note

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Last updated: August 3rd, 2022

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