NAFEMS P18 T2: one-dimensional heat transfer with radiation

1 Objective

Verify steady one-dimensional conduction coupled to nonlinear radiation using Test T2 of The Standard NAFEMS Benchmarks [1]. The study compares a body-fitted Coreform/Abaqus IGA solution with the published target.

2 Geometry

The rod has length \(L=0.1\ \text{m}\). Its square cross-section is a convenient three-dimensional representation; insulated lateral surfaces make the solution one-dimensional.

Figure 1: Geometry and thermal boundary conditions for NAFEMS P18 T2.

3 Material

The thermal conductivity is \(k=55.6\ \text{W}/(\text{m K})\). The specified density and specific heat do not affect this steady solution.

4 Loading & boundary conditions

End A is held at \(T_A=1000\ \text{K}\). End B radiates to surroundings at \(T_\infty=300\ \text{K}\) according to

\[ q=\epsilon\sigma\left(T_B^4-T_\infty^4\right), \]

where \(\epsilon=0.98\) and \(\sigma=56.7\times10^{-9}\ \text{W}/(\text{m}^2\text{K}^4)\).

5 Mesh & discretization

The Coreform/Abaqus model uses a body-fitted \(10\times1\times1\) mesh with linear, \(C^0\) splines.

Figure 2: Exact body-fitted mesh used by the Coreform T2 simulation.

6 Reference & accepted solutions

The accepted temperature at B is \(927\ \text{K}\) [1]. The automated Coreform test enforces a 1% relative-error limit.

7 Results

7.1 Temperature at point B

Table 1: NAFEMS P18 T2 verification results.
Discretization \(T_B\) (K) Relative error Limit
Body-fitted Coreform/Abaqus IGA 927.00323 0.000% 1%
Figure 3: Coreform temperature field for NAFEMS P18 T2.

8 Discussion

The result agrees with the accepted endpoint temperature and verifies conduction and nonlinear radiation in the steady heat-transfer formulation.

References

[1]
The standard NAFEMS benchmarks. NAFEMS.

Appendix

8.1 Download artifacts

Download all verification artifacts (ZIP)

8.1.1 Geometry CAD files

8.1.2 Abaqus/CAE journal files

1 generated Abaqus/CAE journal is available.

Show 1 individual journal

8.2 Provenance

The record below identifies the Coreform/Abaqus verification evidence used by this page.

Parameter Value
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 10-Sep-2026 16:03:46
Operating system Ubuntu 22.04.4 LTS
Coreform IGA version 2026.9+69838
Source revision d88163e59ac0
Abaqus version Abaqus 6.26-4