T4: Two-dimensional heat transfer with convection

This problem provides evidence that Abaqus can reproduce the result from the benchmark defined by NAFEMS and cited as the reference solution.

This page discusses:

ProductsAbaqus/StandardAbaqus/Explicit

Elements tested

  • DC2D3
  • DC2D4
  • DC2D6
  • DC2D8
  • DC3D4
  • DC3D6
  • DC3D8
  • DC3D10
  • DC3D15
  • DC3D20
  • CPE3T
  • CPE4RHT
  • CPE4RT
  • CPE6MHT
  • CPE6MT
  • CPS3T
  • CPS4RT
  • CPS6MT
  • C3D4T
  • C3D6PHT
  • C3D6PT
  • C3D6T
  • C3D8RHT
  • C3D8RT
  • C3D8T
  • C3D10MHT
  • C3D10MT
  • EC3D8RT
  • SC6RT
  • SC8RT

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.

ElementT, Coarse MeshT, 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%)  
CPE3T 22.40°C (22.4%) 18.94°C (3.5%)
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%)  
CPS3T 22.40°C (22.4%) 18.94°C (3.5%)
CPS4RT 19.34°C (5.7%) 18.91°C (3.3%)
CPS6MT 17.22°C (5.8%)  
C3D4T 19.26°C (5.2%)  
C3D6T 22.40°C (22.4%) 18.94°C (3.5%)
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 19.79°C (8.1%)  
C3D10MHT 19.79°C (8.1%)  

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.

ElementT, Coarse MeshT, 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%)
C3D8T 19.29°C (5.4%) 18.87°C (3.1%)
SC6RT 22.36°C (22.2%) 18.90°C (3.3%)
SC8RT 19.29°C (5.4%) 18.87°C (3.1%)
EC3D8RT 19.29°C (5.4%) 18.87°C (3.1%)

Input files

Abaqus/Standard input files

Coarse mesh tests:
nt4xx23c.inp

DC2D3 elements.

nt4xx24c.inp

DC2D4 elements.

nt4xx26c.inp

DC2D6 elements.

nt4xx28c.inp

DC2D8 elements.

nt4xx34c.inp

DC3D4 elements.

nt4xx36c.inp

DC3D6 elements.

nt4xx38c.inp

DC3D8 elements.

nt4xx3ac.inp

DC3D10 elements.

nt4xx3fc.inp

DC3D15 elements.

nt4xx3kc.inp

DC3D20 elements.

twodheattrconvecc_std_cpe3t.inp

CPE3T elements.

twodheattrconvecc_std_cpe4rt.inp

CPE4RT elements.

twodheattrconvecc_std_cpe4rht.inp

CPE4RHT elements.

twodheattrconvecc_std_cpe6mt.inp

CPE6MT elements.

twodheattrconvecc_std_cpe6mht.inp

CPE6MHT elements.

twodheattrconvecc_std_cps3t.inp

CPS3T elements.

twodheattrconvecc_std_cps4rt.inp

CPS4RT elements.

twodheattrconvecc_std_cps6mt.inp

CPS6MT elements.

twodheattrconvecc_std_c3d4t.inp

C3D4T elements.

twodheattrconvecc_std_c3d6pht.inp

C3D6PHT elements.

twodheattrconvecc_std_c3d6pt.inp

C3D6PT elements.

twodheattrconvecc_std_c3d6t.inp

C3D6T elements.

twodheattrconvecc_std_c3d8t.inp

C3D8T elements.

twodheattrconvecc_std_c3d8rt.inp

C3D8RT elements.

twodheattrconvecc_std_c3d8rht.inp

C3D8RHT elements.

twodheattrconvecc_std_c3d10mt.inp

C3D10MT elements.

twodheattrconvecc_std_c3d10mht.inp

C3D10MHT elements.

Fine mesh tests:
nt4xx23f.inp

DC2D3 elements.

nt4xx24f.inp

DC2D4 elements.

nt4xx36f.inp

DC3D6 elements.

nt4xx38f.inp

DC3D8 elements.

twodheattrconvecf_std_cpe3t.inp

CPE3T elements.

twodheattrconvecf_std_cpe4rt.inp

CPE4RT elements.

twodheattrconvecf_std_cpe4rht.inp

CPE4RHT elements.

twodheattrconvecf_std_cps3t.inp

CPS3T elements.

twodheattrconvecf_std_cps4rt.inp

CPS4RT elements.

twodheattrconvecf_std_c3d6t.inp

C3D6T elements.

twodheattrconvecf_std_c3d8t.inp

C3D8T elements.

twodheattrconvecf_std_c3d8rt.inp

C3D8RT elements.

twodheattrconvecf_std_c3d8rht.inp

C3D8RHT elements.