Semi-infinite solid — transient

Thermal conductionPASS · 0.32%

Transient conduction, error-function solution

Tolerance:: 5%

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Problem statement

Geometry: Semi-infinite solid (half-space), x ≥ 0, uniform initial temperature.
Material: Isotropic conductivity k and thermal diffusivity α = k/(ρc).
Boundary conditions: Surface temperature suddenly stepped to T_s at t = 0.
Measured quantity: Transient profile (T−T_s)/(T_i−T_s) = erf(x/2√(αt)) at chosen depths/times.

WebCAE Terminal

Paste these commands into the Terminal panel inside WebCAE. They use the same text DSL as the application; run one command per line:

units mm
material E=2e11 nu=0.3 density=7800 kappa=40 specific_heat=460
primitive box dx=100 dy=4 dz=4
mesh tet size=1.5 order=2
thermal surface number 1 temperature=120
solve thermal transient dt=0.1 tend=16 theta=0.5 t0=20 frames=4
probe temperature x=10 time=16 id="e10"
probe temperature x=20 time=16 id="e20"

Results comparison

Reference value	T(10 mm) = 79.650 °CT(20 mm) = 48.965 °C
Our result	T(10 mm) = 79.902 °CT(20 mm) = 48.928 °C
Deviation	0.32%
Tolerance	5%
Status	PASS · 0.32%
Mesh details	tet10, size 1.5 mm (5300 nodes); 160 steps of Δt = 0.1 с, θ = 0.5, balance residual 3.49e-14

Updated: 2026-10-27 · version not recorded