4.3.4 T4: Two-dimensional heat transfer with convection

Products: ABAQUS/Standard ABAQUS/Explicit

Elements tested

DC2D3 DC2D4 DC2D6 DC2D8

DC3D4 DC3D6 DC3D8 DC3D10 DC3D15 DC3D20

CPE3T CPE4RT CPE4RHT CPE6MT CPE6MHT CPS3T CPS4RT CPS6MT C3D4T C3D6T C3D8T C3D8RT C3D8RHT C3D10MT C3D10MHT

Problem description

Model:

The two-dimensional geometry is shown above. Three-dimensional elements are tested with a thickness of 1.0 in the z-direction. 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 20000 seconds, which provides enough time for the transient solution to reach steady-state conditions in this problem.

Material:

Conductivity = 52 W/m°C, surface convective coefficient = 750 W/m²/° C.

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

Boundary conditions:

Temperature = 100° C along edge AB. Zero heat flux along edge DA. Convection to ambient temperature of 0° C along edges BC and CD.

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 T4 from NAFEMS publication TNSB, Rev. 3, “The Standard NAFEMS Benchmarks,” October 1990.

Target solution: Temperature of 18.3° C at point E.

Results and discussion

The results for the ABAQUS/Standard analysis are shown in the following table. The values enclosed in parentheses are percentage differences with respect to the reference solution.

Element	T, Coarse Mesh	T, Fine Mesh
DC2D3	22.40° C (22.4%)	19.22° C (5.0%)
DC2D4	19.34° C (5.7%)	18.91° C (3.3%)
DC2D6	17.99° C (–1.7%)
DC2D8	17.90° C (–2.2%)
DC3D4	18.81° C (2.8%)
DC3D8	19.34° C (5.7%)	18.91° C (3.3%)
DC3D6	22.40° C (22.4%)	18.94° C (3.5%)
DC3D10	19.00° C (3.8%)
DC3D15	17.99° C (–1.7%)
DC3D20	17.89° C (–2.2%)
CPE4RT	19.34° C (5.7%)	18.91° C (3.3%)
CPE4RHT	19.34° C (5.7%)	18.91° C (3.3%)
CPE6MT	17.22° C (5.8%)
CPE6MHT	17.22° C (5.8%)
CPS4RT	19.34° C (5.7%)	18.91° C (3.3%)
CPS6MT	17.22° C (5.8%)
C3D8T	19.34° C (5.7%)	18.91° C (3.3%)
C3D8RT	19.34° C (5.7%)	18.91° C (3.3%)
C3D8RHT	19.34° C (5.7%)	18.91° C (3.3%)
C3D10MT	21.51°C (17.5%)
C3D10MHT	21.51°C (17.5%)

The results for the ABAQUS/Explicit analysis are shown in the following table. The values enclosed in parentheses are percentage differences with respect to the reference solution.

Element	T, Coarse Mesh	T, Fine Mesh
CPE3T	22.26° C (21.6%)	18.90° C (3.3%)
CPE4RT	19.29° C (5.4%)	18.87° C (3.1%)
CPS3T	22.36° C (22.2%)	18.90° C (3.3%)
CPS4RT	19.29° C (5.4%)	18.87° C (3.1%)
C3D4T	19.21° C (5.0%)
C3D6T	22.36° C (22.2%)	18.90° C (3.3%)
C3D8RT	19.29° C (5.4%)	18.87° C (3.1%)