V-HC-02 — finite slab, convective BC, Bi = 0.1

Tags: heat_conduction, convective_bc, biot_sweep

References:

• Carslaw & Jaeger (1959) §3.11 (eigenfunction series)
• FDS Verification Guide heat_conduction_a–d

Problem statement

0.1 m slab initially at Tᵢ = 300 K, convective front (T∞ = 500 K), adiabatic back, Bi = hL/k ∈ {0.1, 1, 10, 100} — four regimes from one definition: Bi = 0.1 is lumped-like (BC-dominated), Bi = 100 is surface-Dirichlet-like (interior-dominated). Exact eigenfunction series with eigencondition λₙ tan λₙ = Bi (exact/slab_series.jl).

Mesh mapping: adiabatic face is z = 0, so the series coordinate is x̃ = z/L. Comparison times are Fo = αt/L² ∈ {0.05, 0.1, 0.2, 0.5}, all well above the 60-root series validity floor (Fo ≳ 1.1e-3).

Convergence spot check runs on the Bi = 10 member only (the mixed regime); the other three assert QoIs at the CI mesh.

V-HC-02a — finite slab, convective BC, Bi = 0.1

Quantities of interest (n = 320)

Comparison with other codes

The same case was solved with FDS 6.11.0 at 101 cells (Δx≈1 mm); decks, outputs, and run provenance are committed under test/verification/reference/. Each code's error against the same exact solution is drawn below on a log scale, muted gray behind this solver's series — the signed linear-scale panel above shows where the error lives, this one compares magnitudes across codes.

Wall times at every ladder rung against the reference runs. Resolutions and simulated spans differ where noted (details in reference/timings.csv), so cross-code timings are indicative rather than a controlled benchmark; rungs at a matched resolution are directly comparable.

Solution overlays including the other codes' points: Tprofilesvs_codes, surfaceThistoryvscodes, backThistoryvscodes.

Convergence

Observed order 2 (L2).

Solver configuration

V-HC-02b — finite slab, convective BC, Bi = 1.0

Quantities of interest (n = 320)

Comparison with other codes

The same case was solved with FDS 6.11.0 at 101 cells (Δx≈1 mm); decks, outputs, and run provenance are committed under test/verification/reference/. Each code's error against the same exact solution is drawn below on a log scale, muted gray behind this solver's series — the signed linear-scale panel above shows where the error lives, this one compares magnitudes across codes.

Wall times at every ladder rung against the reference runs. Resolutions and simulated spans differ where noted (details in reference/timings.csv), so cross-code timings are indicative rather than a controlled benchmark; rungs at a matched resolution are directly comparable.

Solution overlays including the other codes' points: Tprofilesvs_codes, surfaceThistoryvscodes, backThistoryvscodes.

Convergence

Observed order 2 (L2).

Solver configuration

V-HC-02c — finite slab, convective BC, Bi = 10.0

Quantities of interest (n = 320)

Comparison with other codes

The same case was solved with FDS 6.11.0 at 101 cells (Δx≈1 mm); decks, outputs, and run provenance are committed under test/verification/reference/. Each code's error against the same exact solution is drawn below on a log scale, muted gray behind this solver's series — the signed linear-scale panel above shows where the error lives, this one compares magnitudes across codes.

Wall times at every ladder rung against the reference runs. Resolutions and simulated spans differ where noted (details in reference/timings.csv), so cross-code timings are indicative rather than a controlled benchmark; rungs at a matched resolution are directly comparable.

Solution overlays including the other codes' points: Tprofilesvs_codes, surfaceThistoryvscodes, backThistoryvscodes.

Convergence

Observed order 2.001 (L2), expected 2.0.

Solver configuration

V-HC-02d — finite slab, convective BC, Bi = 100.0

Quantities of interest (n = 320)

Comparison with other codes

The same case was solved with FDS 6.11.0 at 101 cells (Δx≈1 mm); decks, outputs, and run provenance are committed under test/verification/reference/. Each code's error against the same exact solution is drawn below on a log scale, muted gray behind this solver's series — the signed linear-scale panel above shows where the error lives, this one compares magnitudes across codes.

Wall times at every ladder rung against the reference runs. Resolutions and simulated spans differ where noted (details in reference/timings.csv), so cross-code timings are indicative rather than a controlled benchmark; rungs at a matched resolution are directly comparable.

Solution overlays including the other codes' points: Tprofilesvs_codes, surfaceThistoryvscodes, backThistoryvscodes.

Convergence

Observed order 2 (L2).

Solver configuration