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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:

  • Heat flow
  • Temperature distribution

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:

thermal bridge geometry iso 10211 case 4 validation front and isometric view
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:

CaseMesh TypeNodesCellsElement Type
EN ISO 10211 Case 4Second-order standard769105553835Standard
Table 2: Mesh details for this validation case

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

standard mesher used for meshing the thermal bridge case
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 [1]. The two criteria that must be satisfied are:

  • Difference in heat flow between the hot and cold sides should not exceed 1 % of the analytical solution of 0.540 \(W\).
  • The highest temperature at the measured point should not exceed 0.005 \(°C\) than the analytical temperature 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, as well as the integrated heat flux magnitude. The table below provides an overview of the results:

PointHeat Flow \([W]\)Maximum Exterior Temperature \([º C]\)
ISO 102110.540.805
SimScale0.5420.803
Deviation \(%\)-0.370.002
Table 4: Overview of the temperature results, based on the points from Figure 1

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

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

temperature distribution across thermal bridge validation case
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:

heat flux magnitude distribution across thermal bridge validation case
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: June 8th, 2021

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