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# Validation Case: Thermal Bridge Case 4 – Iron Bar

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.

## Geometry

The 3D geometry for this project is a thermal bridge consisting of an iron bar penetrating an insulation layer, as seen in Figure 1: Figure 1: Side and isometric view of the thermal bridge geometry of an iron bar from EN ISO 10211 case 4

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.

## Analysis Type and Mesh

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:

In the image below, it’s possible to see the standard mesh in detail: Figure 2: The standard meshing algorithm generates a second order mesh, with a combination of tetrahedral and hexahedral elements.

## Simulation Setup

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

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 $$\frac{W}{m^2.K}$$
• Exterior wall: Convective heat flux boundary condition:
• ($$T_0$$) Reference temperature: 0 $$ºC$$
• Heat transfer coefficient: 10 $$\frac{W}{m^2.K}$$
• Side walls: Adiabatic in nature.

## Result Comparison

The results obtained with SimScale were compared to those presented in . 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:

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: Figure 3: The cutting plane normal to the x-axis provides a visual representation of the temperature distribution across the beam and the insulation layer.

Additionally, the heat flux magnitude can be visualized on the cutting plane normal to the X axis too: Figure 4: For the calculation of the heat flow, the Heat Flux magnitude can be integrated on the end side of the beam.

Last updated: August 30th, 2022