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

Transient heat transfer

Convective heat flux

The simulation results of SimScale were compared to the results presented in [TTLV01]. The meshes used in (A) and (B) were created with the automatic-tetrahedralization-tool on the SimScale platform.

Only a portion of a sphere with a diameter of 0.2 m is used for the analysis, as shown in the picture above. M is the center of the sphere and the face ABCD represents the outer surface.

Analysis type and Domain

Tool Type : Calculix, Code_Aster

Analysis Type : Transient heat transfer

Mesh and Element types :

Case

Mesh type

Number of nodes

Element type

(A)

linear tetrahedral

3714

3D isoparametric

(B)

quadratic tetrahedral

26494

3D isoparametric

Simulation Setup

Important

All temperature dependent data is given as a function of °C. This also applies for the data in the different simulations on the SimScale platform (although it says K)!

Material:

isotropic: ρ $\rho $

= 7200 kg/m³, κ

$\kappa $

= 48.822 W/(m °C), Specific heat c

$c$

= 669 J/°C

Initial Conditions:

Initial Temperature Tinitial ${T}_{initial}$

= 20°C

Loads:

Convective heat flux on face ABCD with a temperature Touter ${T}_{outer}$

= 1000°C and a convection coefficient h

$h$

= 232.5 W/(m² °C)

Results

Comparison of temperature at the center point M and at the outer surface obtained with SimScale with the results presented in [TTLV01]. The Error was calculated with respect to [VPCS].

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