Heat Transfer: Perforated Plate

Overview

The aim of this test case is to validate the following functions:

• Transient thermal solver
• Surface heat flux boundary condition
• Convective heat flux boundary condition

The simulation results of SimScale were compared to the results presented in case B of [TTLP301]. Four of the mesh cases were considered; linear and quadratic tetrahedrals, linear and quadratic hexahedrals.

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Geometry

Analysis type and Domain

Tool Type : CalculiX, Code-Aster

Analysis Type : Transient thermal analysis

Mesh and Element types :

Simulation Setup

Material:

• isotropic: ρ
  $\rho$

   

  = 1 kg/m³, κ

  $\kappa$

   

  = 0.1 W/(m K), Specific heat c

  $c$

   

  = 1 J/(kg K)

Initial Condition:

• Initial Temperature Tinitial
  $T_{initial}$

   

  = 273.15 K

Heat flux:

• Surface heat flux on face AFJE with a surface heat flux q
  $q$

   

  = 1 W/(m²)

• Convective heat flux on face CHID with a temperature TCHID
  $T_{CHID}$

   

  = 273.15 K and a convection coefficient h

  $h$

   

  = 1 W/(m² K)

Results

Comparison of the temperature on node N1 for 12 timesteps obtained with SimScale and the results presented in case B of [TTLP301] ¹ and [TTLP301] ². The Error was calculated with respect to [TTLP301] ¹.

References

¹ Results by Donea as mentioned in [TTLP301]: Donea, J. (1974), On the accuracy of finite element solutions to the transient heat-conduction equation. Int. J. Numer. Meth. Engng., 8: 103–110

² Code_Aster results as mentioned in case B of [TTLP301]