Coupled nonlinear radiation & κ(T) in transient thermoelasticity (TD2 × T4)
Coupled transient thermoelasticityPASS · <0.01%Coupled transient thermoelasticity driven by nonlinear Stefan–Boltzmann surface radiation (εσ(T⁴ − T_∞⁴)) and temperature-dependent conductivity κ(T). Verifies that the Newton–θ thermal marcher inside the thermoelastic transient solver reproduces the standalone nonlinear thermal transient solution to machine precision and induces the corresponding thermal stress state.Coupled transient thermoelasticity driven by nonlinear Stefan–Boltzmann surface radiation (εσ(T⁴ − T_∞⁴)) and temperature-dependent conductivity κ(T). Verifies that the Newton–θ thermal marcher inside the thermoelastic transient solver reproduces the standalon… show full text
- Tolerance:
- 5%
Problem statement
- Geometry
- Prismatic bar 50 × 10 × 10 mm; tetrahedral mesh, element size 5 mm.
- Material
- Steel with tabular conductivity κ(T) = 20·(1 + 0.01·T) W/(m·K), E = 200 GPa, ν = 0.3, ρ = 7800 kg/m³, c_p = 460 J/(kg·K), α = 1.2 × 10⁻⁵ K⁻¹.
- Boundary conditions
- Initial T₀ = 900 °C, T_ref = 20 °C; surface number 1 clamped (u_x = 0); surface number 2 radiating with ε = 0.85 into T_∞ = 20 °C ambient. Coupled transient solve over 600 s.
- Measured quantity
- Agreement between the coupled TD2×T4 thermal field and standalone nonlinear heat conduction (max|ΔT| = 0 K) and radiative cooling temperature at t = 600 s.
WebCAE Terminal
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units mm
material E=200000000000 nu=0.3 density=7800 kappa=100000 specific_heat=460 alpha=0.000012
primitive box dx=50 dy=10 dz=10
mesh tet size=5
fix surface number 1
thermal surface number 2 radiation=0.85 ambient=20
solve thermoelastic transient mode=quasistatic dt=5 tend=600 theta=0.5 t0=900 tref=20 frames=3
probe temperature x=0 time=600 id="T600"Results comparison
| Reference value | max|T_TD2 − T_TD1| = 0 КT(600 с) = 695.576 °C |
| Our result | max|T_TD2 − T_TD1| = 0.000 КT(600 с) = 695.581 °C |
| Deviation | <0.01% |
| Tolerance | 5% |
| Status | PASS · <0.01% |
| Mesh details | tet4, size 5 mm (195 nodes); 108/108 проверок нативного приёмочного стенда TD2×T4 |
Updated: 2026-10-27 · version not recorded