NAFEMS P18 T4: two-dimensional heat transfer with convection

1 Objective

Verify two-dimensional steady conduction with convection boundaries using Test T4 of The Standard NAFEMS Benchmarks [1]. The study compares a body-fitted Coreform/Abaqus IGA solution with the published target.

2 Geometry

The domain is \(0.6\ \text{m}\) wide, \(1.0\ \text{m}\) high, and \(0.05\ \text{m}\) thick. Point E is located at \((x,y)=(0.6,0.2)\ \text{m}\). Insulated front and back faces preserve the two-dimensional response.

Figure 1: Geometry and thermal boundary conditions for NAFEMS P18 T4.

3 Material

The isotropic thermal conductivity is \(k=52\ \text{W}/(\text{m K})\).

4 Loading & boundary conditions

The bottom edge AB is held at \(100\ ^\circ\text{C}\), and the left edge AD is insulated. The top and right edges exchange heat with a \(0\ ^\circ\text{C}\) environment using \(h=750\ \text{W}/(\text{m}^2\text{K})\).

5 Mesh & discretization

The Coreform/Abaqus model uses a body-fitted \(12\times20\times1\) mesh with linear, \(C^0\) splines.

Figure 2: Exact body-fitted mesh used by the Coreform T4 simulation.

6 Reference & accepted solutions

The accepted temperature at E is \(18.3\ ^\circ\text{C}\) [1]. The automated Coreform/Abaqus test enforces a 3% relative-error limit.

7 Results

7.1 Temperature at point E

Table 1: NAFEMS P18 T4 verification results.
Discretization \(T_E\) (\(^\circ\)C) Relative error Limit
Body-fitted Coreform/Abaqus IGA 18.08995 1.148% 3%
Figure 3: Coreform temperature field for NAFEMS P18 T4.

8 Discussion

The result satisfies the published target and verifies steady two-dimensional conduction and convection on a body-fitted spline discretization.

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 16:03:33
Operating system Ubuntu 22.04.4 LTS
Coreform IGA version 2026.9+69838
Source revision d88163e59ac0
Abaqus version Abaqus 6.26-4