NAFEMS P18 T3: one-dimensional transient heat transfer

1 Objective

Verify transient thermal capacity and implicit time integration using Test T3 of The Standard NAFEMS Benchmarks [1]. This verifies the Coreform IGA thermal UEL through the Abaqus heat-transfer procedure.

2 Geometry

The rod has length \(L=0.1\ \text{m}\), and point C is located at \(x=0.08\ \text{m}\) from end A. Insulated lateral surfaces make the response one-dimensional.

Figure 1: Geometry and time-dependent boundary condition for NAFEMS P18 T3.

3 Material

The material properties are \(k=35\ \text{W}/(\text{m K})\), \(\rho=7200\ \text{kg}/\text{m}^3\), and \(c=440.5\ \text{J}/(\text{kg K})\).

4 Loading & boundary conditions

The initial temperature is \(0\ ^\circ\text{C}\). End A remains at \(0\ ^\circ\text{C}\), and end B follows

\[ T_B(t)=100\sin\left(\frac{\pi t}{40}\right)\ ^\circ\text{C}. \]

All lateral surfaces are insulated.

5 Mesh & discretization

The Coreform/Abaqus model uses the same body-fitted \(10\times1\times1\) linear, \(C^0\) mesh as T2. The Abaqus transient heat-transfer step starts with a \(0.1\ \text{s}\) increment, permits increments up to \(0.5\ \text{s}\), and ends at \(t=32\ \text{s}\).

Figure 2: Exact body-fitted mesh used by the Coreform T3 simulation.

6 Reference & accepted solutions

The accepted temperature at C and \(t=32\ \text{s}\) is \(36.60\ ^\circ\text{C}\) [1]. The automated test enforces a 2% relative-error limit.

7 Results

7.1 Temperature at point C

Table 1: NAFEMS P18 T3 verification result at 32 s.
Discretization \(T_C\) (\(^\circ\)C) Relative error Limit
Body-fitted Coreform/Abaqus IGA 37.25446 1.79% 2%
Figure 3: Coreform temperature field at 32 s for NAFEMS P18 T3.

8 Discussion

The result satisfies the published benchmark and directly exercises the volumetric capacity term and Abaqus transient thermal integration.

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