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This thermal bridge validation case belongs to heat transfer. The aim of this test case is to validate the following parameters:

- Temperature distribution
- Heat flow

The simulation results of SimScale were compared to the results presented in EN ISO 10211 Standard, case 4.

The 3D geometry for this project is a thermal bridge consisting of an iron bar penetrating an insulation layer, as seen in Figure 1:

The insulated wall consists of a block with a rectangular cross-section of 1×1 \(m\) and a width of 0.2** **\(m\). The bar is placed vertically in the center of the wall and goes through the whole layer. It has a rectangular cross-section of 0.1×0.05 \(m\) and a total length of 0.6** **\(m\), including its penetrated part.

**Tool Type**: Code_Aster

**Analysis Type**: Linear, steady-state heat transfer analysis

**Mesh and Element Types**: For this case, SimScale’s standard meshing algorithm was used, which generates a combination of tetrahedral and hexahedral cells. The characteristics of the resulting mesh can be seen below:

Case | Mesh Type | Nodes | Cells | Element Type |

EN ISO 10211 Case 4 | Second-order standard | 769105 | 553835 | Standard |

In the image below, it’s possible to see the standard mesh in detail:

**Material**:

Each body is assigned to a different material:

- Insulation layer
- (\(\rho\))
*Density*: 2240 \(\frac{kg}{m^3}\) *Thermal conductivity*: 0.1 \(\frac{W}{m.K}\)*Specific heat*: 750 \(\frac{J}{kg.K}\)

- (\(\rho\))
- Iron bar
- (\(\rho\))
*Density*: 7870 \(\frac{kg}{m^3}\) *Thermal conductivity*: 50 \(\frac{W}{m.K}\)*Specific heat*: 480 \(\frac{J}{kg.K}\)

- (\(\rho\))

**Boundary Conditions**:

As shown in Figure, the following boundary conditions are defined:

- Interior wall: Convective heat flux boundary condition:
- (\(T_0\))
*Reference temperature*: 1 \(ºC\) *Heat transfer coefficient*: 10 \(\frac{W}{m^2.K}\)

- (\(T_0\))
- Exterior wall: Convective heat flux boundary condition:
- (\(T_0\))
*Reference temperature*: 0 \(ºC\) *Heat transfer coefficient*: 10 \(\frac{W}{m^2.K}\)

- (\(T_0\))
- Side walls: Adiabatic in nature.

The results obtained with SimScale were compared to those presented in [1]. The two criteria that must be satisfied are:

- The difference in heat flow between the hot and cold sides should not deviate more than 1 % from the reference value of 0.540 \(W\).

- The highest temperature measured in the exterior wall should not deviate more than 0.005 \(°C\) from the reference value of 0.805 \(°C\).

The bulk calculator feature provided in SimScale’s integrated post-processor was used to extract the maximum temperature of the beam’s end cross-section, which is coincident with the insulation layer. The Heat Flux was measured using the *Heat Flow* result control Item. The table below provides an overview of the results:

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

Maximum temperature on exterior | 0.805\(°C\) | 0.803\(°C\) | 0.002\(°C\) |

Heat Flow | 0.540\(W\) | 0.542\(W\) | -0.37% |

Table 4 indicates a good agreement of the SimScale results with the reference paper, with a permitted difference between the extracted values and the standard.

Below you can see the results of the simulation, created in the online post-processor:

Additionally, the heat flux magnitude can be visualized on the cutting plane normal to the X axis too:

Last updated: August 30th, 2022

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