Abaqus Benchmarks Manual  


4.3.2 T2: One-dimensional heat transfer with radiation

Products: Abaqus/Standard  Abaqus/Explicit  

Elements tested

DC1D2    DC1D3   

DC2D3    DC2D4    DC2D6    DC2D8   

DCAX3    DCAX4    DCAX6    DCAX8   

CAX3T    CAX4RHT    CAX4RT    CAX4T   

CPE3T    CPE4RHT    CPE4RT    CPE4T    CPE6MHT    CPE6MT   

CPS3T    CPS4RT    CPS4T    CPS6MT   

C3D4T    C3D6T    C3D8RHT    C3D8RT    C3D8T    SC6RT    SC8RT   

EC3D8RT   

Problem description

Model:

The geometry is shown above. A uniform mesh with 10 elements along the length of the bar is used. The thickness and width of the bar are each 0.01 m. In Abaqus/Standard a steady-state simulation is performed, while in Abaqus/Explicit a transient simulation is performed. The total simulation time in the latter case is 2500 seconds. This provides enough time for the transient solution to reach steady-state conditions in this problem.

Material:

Conductivity = 55.6 W/m°C, specific heat = 460.0 J/kg°C, density = 7850 kg/m3. At end B emissivity = 0.98, Stefan-Boltzmann constant = 5.67 × 10–8 W m2/ K4.

For the coupled temperature-displacement elements dummy mechanical properties are used to complete the material definition.

Boundary conditions:

Prescribed temperature of 1000 K at end A. Radiation to ambient temperature of 300 K at end B. No heat flux perpendicular to AB.

Loading:

Zero internal heat generation.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test T2 from NAFEMS publication TNSB, Rev. 3, “The Standard NAFEMS Benchmarks,” October 1990.

Target solution: Temperature at B=927 K (653.85°C).

Results and discussion

All elements yield the exact solution.

Input files