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Validation Case: Heat Transfer in a Perforated Plate

This project belongs to the heat transfer analysis type. The aim of this test case is to validate the following parameter using a transient thermal solver, with a surface and a convective heat flux boundary condition on a perforated plate:

  • Temperature \([K]\) on a single node for 12 consecutive timesteps.

The simulation results of SimScale were compared to the results presented in case B of [TTLP301]\(^1\).


The geometry used for the analysis with the highlighted node N1 can be seen below. It is a random thick plate with straight and curved edges.

perforated plate geometry points
Figure 1: Geometry of a perforated plate with highlighted node N1 (red)

The coordinates for each vertex of the plate are displayed in the following table:

x \([m]\)0.6350.93950.93950.54270.31750.6350.93950.93950.54280.3175
y \([m]\)000.83380.94010.5499000.83380.94010.5499
z \([m]\)000000.
Table 1: The coordinates of the main geometry points

Analysis Type and Domain

Tool type : Code_Aster

Analysis type : Heat transfer, linear

Time dependency: Transient

Mesh and element types: Four mesh cases were considered for the analysis of the perforated plate; with 1st order and 2nd order tetrahedral, as well as 1st order and 2nd order hexahedral elements. The hexahedral mesh was locally computed and uploaded to the SimScale Workbench.

CaseMesh typeNumber of nodesNumber of 3D elementsElement type
(A)1st order tetrahedral534025676Standard
(B)2nd order tetrahedral1680710976Standard
(C)1st order hexahedral1210840Standard
(D)2nd order hexahedral4433840Standard
Table 2: The mesh characteristics for all the cases

Below, the 1st order tetrahedral mesh for case A is visualized:

mesh standard first order tetrahedral elements
Figure 2: The mesh used for case A, created with SimScale’s standard meshing algorithm

And the mesh that was uploaded for case C is presented below:

mesh standard first order hexahedral elements
Figure 3: The mesh used for case C, created externally with 1st order hexahedral elements

Simulation Setup


  • Isotropic:
    • Density \(ρ\) = 1 \( kg \over \ m³ \),
    • Thermal conductivity \(\kappa\) = 0.1 \( W \over \ m \ K\),
    • Specific heat = 1 \( J \over \ kg \ K\)  

Initial conditions

  • Initial Temperature = 273.15 \(K\)  

Boundary conditions

  • Surface heat flux on face AFJE:
    • Heat flux value = 1 \(W \over \ m²\)  
  • Convective heat flux on face CHID
    • Reference temperature \(T_{0}\) = 273.15 \(K\)
    • Heat transfer coefficient = 1 \(W \over \ m² \ K\)  

Results Comparison

The temperature values at node N1 for 12 time steps obtained with SimScale are compared against the results presented in case B of [TTLP301]\(^1\).

Timesteps \([s]\)[TTLP301]
Case A \([K]\)Error [%]Case B \([K]\)Error [%]Case C \([K]\)Error [%]Case D \([K]\)Error [%]
Table 3: Temperature results for all cases at different time steps

All of the cases are in a good agreement with the reference results.

You can see the temperature distribution on the plate for the last time step of Case A below:

temperature distribution perforated plate
Figure 4: Temperature distribution on the plate for Case A at time 1.2s

Last updated: January 26th, 2021

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