Thermal Transient 1D
thermal_transient_1dSolve 1-D transient conduction in a plane wall cooled or heated by convection, returning center, surface, and lumped temperatures over time.
Instructions
Analytic 1-D plane-wall transient conduction (one-term Heisler series), valid
for Fourier ≳ 0.2 — the closed-form transient the Elmer thermal_transient solve is
gated against, and the distributed (spatial-gradient) answer the lumped screen
only approximates. A wall of half-thickness L cools/heats toward ambient by surface
convection: Bi = h·L/k, Fo = α·t/L², α = k/(ρ·cₚ). Pass alpha_m2_s, or k+rho+cp,
or a material (Materials DB: thermal_conductivity/Density/specific_heat); get
h_conv from the h_estimate correlation screen rather than guessing.
As Bi→0 the body is isothermal and this collapses to the lumped exponential exp(−t/τ) (cross-checked via t_center_lumped_c / lumped_agrees). Returns {biot, fourier, eigenvalue_1, c1, t_center_c, t_surface_c, t_center_lumped_c, time_constant_s, one_term_valid, lumped_agrees}.
Input Schema
| Name | Required | Description | Default |
|---|---|---|---|
| k | No | ||
| cp | No | ||
| rho | No | ||
| h_conv | Yes | ||
| material | No | ||
| alpha_m2_s | No | ||
| duration_s | Yes | ||
| t_ambient_c | No | ||
| t_initial_c | No | ||
| half_thickness_mm | Yes |