NAFEMS T3

Thermal conductionPASS · 0.04%

1D transient conduction with a time-dependent boundary

Tolerance:: 5%

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Problem statement

Geometry: Slender bar, 0.01 × 0.01 m cross-section, meshed along its length.
Material: k = 35 W/(m·°C), c = 440.5 J/(kg·°C), ρ = 7200 kg/m³.
Boundary conditions: One end held at 0 °C; the other driven by a time-varying (sinusoidal) temperature; uniform initial temperature.
Measured quantity: Temperature at a reference point along the bar at a specified time.

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units mm
material E=2e11 nu=0.3 density=7200 kappa=35 specific_heat=440.5
primitive box dx=100 dy=4 dz=4
mesh tet size=1.5 order=2
thermal surface number 1 temperature=0
thermal surface number 2 temperature=100
solve thermal transient dt=0.25 tend=32 theta=0.5 t0=0 amp_temperature="0:0,0.25:0.0196336924606,0.5:0.0392598157591,0.75:0.0588708036512,1:0.0784590957278,1.25:0.0980171403296,1.5:0.117537397458,1.75:0.137012341682,2:0.15643446504,2.25:0.175796279934,2.5:0.195090322016,2.75:0.214309153065,3:0.233445363856,3.25:0.252491577015,3.5:0.271440449865,3.75:0.290284677254,4:0.309016994375,4.25:0.327630179562,4.5:0.346117057077,4.75:0.364470499879,5:0.382683432365,5.25:0.400748833103,5.5:0.418659737537,5.75:0.436409240673,6:0.45399049974,6.25:0.471396736826,6.5:0.488621241497,6.75:0.505657373378,7:0.522498564716,7.25:0.539138322911,7.5:0.55557023302,7.75:0.571787960228,8:0.587785252292,8.25:0.603555941954,8.5:0.61909394931,8.75:0.634393284164,9:0.64944804833,9.25:0.664252437911,9.5:0.678800745533,9.75:0.693087362546,10:0.707106781187,10.25:0.720853596703,10.5:0.734322509436,10.75:0.747508326863,11:0.7604059656,11.25:0.773010453363,11.5:0.785316930881,11.75:0.797320653773,12:0.809016994375,12.25:0.820401443526,12.5:0.831469612303,12.75:0.842217233716,13:0.852640164354,13.25:0.862734385978,13.5:0.872496007073,13.75:0.881921264348,14:0.891006524188,14.25:0.899748284052,14.5:0.908143173825,14.75:0.916187957117,15:0.923879532511,15.25:0.931214934759,15.5:0.938191335922,15.75:0.944806046467,16:0.951056516295,16.25:0.956940335732,16.5:0.962455236454,16.75:0.96759909236,17:0.972369920398,17.25:0.976765881321,17.5:0.980785280403,17.75:0.98442656809,18:0.987688340595,18.25:0.990569340444,18.5:0.993068456955,18.75:0.995184726672,19:0.996917333733,19.25:0.998265610185,19.5:0.999229036241,19.75:0.999807240482,20:1,20.25:0.999807240482,20.5:0.999229036241,20.75:0.998265610185,21:0.996917333733,21.25:0.995184726672,21.5:0.993068456955,21.75:0.990569340444,22:0.987688340595,22.25:0.98442656809,22.5:0.980785280403,22.75:0.976765881321,23:0.972369920398,23.25:0.96759909236,23.5:0.962455236454,23.75:0.956940335732,24:0.951056516295,24.25:0.944806046467,24.5:0.938191335922,24.75:0.931214934759,25:0.923879532511,25.25:0.916187957117,25.5:0.908143173825,25.75:0.899748284052,26:0.891006524188,26.25:0.881921264348,26.5:0.872496007073,26.75:0.862734385978,27:0.852640164354,27.25:0.842217233716,27.5:0.831469612303,27.75:0.820401443526,28:0.809016994375,28.25:0.797320653773,28.5:0.785316930881,28.75:0.773010453363,29:0.7604059656,29.25:0.747508326863,29.5:0.734322509436,29.75:0.720853596703,30:0.707106781187,30.25:0.693087362546,30.5:0.678800745533,30.75:0.664252437911,31:0.64944804833,31.25:0.634393284164,31.5:0.61909394931,31.75:0.603555941954,32:0.587785252292" probes="80,2,2" frames=9
probe temperature x=80 time=32 id="T3"

Results comparison

Reference value	T(80 mm, 32 с) = 36.60 °Cbalance residual ≤ 1e-9
Our result	T(80 mm, 32 с) = 36.584 °Cresidual 1.40e-14
Deviation	0.04%
Tolerance	5%
Status	PASS · 0.04%
Mesh details	tet10, size 1.5 mm (5300 nodes); 128 steps of Δt = 0.25 с, θ = 0.5, 9 frames

Updated: 2026-10-27 · version not recorded