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

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-Boltzman 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).