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# Validation Case: Convective Heat Transfer of a Sphere

This case belongs to thermodynamics. The aim of this test case is to validate the following parameter during a convective heat transfer in a sphere for different time steps:

• Temperature at the center of the sphere (M).
• Temperature on the outer surface of the sphere (ABCD).

The simulation results of SimScale were compared to the results presented by VPCS in [TTLV01]$$^1$$ .

## Geometry

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

## Analysis type and Domain

Tool type: Code_Aster

Analysis type: Heat transfer, linear

Time dependency: Transient

Mesh and element types: Two meshes, used in cases (A) and (B), were created with the standard meshing algorithm on the SimScale platform.

The mesh for case A was created using 1st order tetrahedral elements:

For case B, a similar mesh with 2nd order tetrahedral elements was used.

## Simulation Setup

Be Aware

All temperature dependent data in this cases is given as a function of °C (although it says °K in the Workbench)!
This is because of the equivalency between $$\frac {W}{°K}$$ and $$\frac {W}{°C}$$.

Material/Solid:

• Isotropic
• Density ($$ρ$$) = 7200 $$kg \over \ m³$$ ,
• Thermal conductivity ($$\kappa$$) = 48.822 $$W \over \ (m \times \ K\ )$$,
• Specific heat = 669 $$J \over \ kg \times \ K$$

Initial Conditions:

• Initial Temperature $$T_{initial}$$ = 20 $$K$$

• Convective heat flux on face ABCD
• Reference Temperature $$T_{0}$$ = 1000 $$K$$
• Heat transfer coefficient = 232.5 $$W \over \ (K \times \ m² \ )$$

## Results Comparison

In the table below are the temperature values at different time steps at the center of the sphere. The SimScale results are compared against the results from VPCS$$^1$$

And at the outer surface the following comparison stats for the temperature were obtained:

Both cases are in a good agreement with the reference results with maximum error < 3%, which showcases the ability of SimScale to successfully analyze the heat transfer of a sphere. Figure 3: The temperature distribution across the sphere for case A, during the final timestep (2400s)

Last updated: August 20th, 2020