V-RX-04 — thermally-thin radiative cooling (implicit exact)

Tags: radiation, radiative_bc, surface_newton, thermally_thin

References:

• partial-fraction antiderivative re-derived in exact/radiative_cooling.jl
• suite plan V-RX-04 (transient T⁴ closed form)

Problem statement

surface equilibrium

The only closed-form transient involving the T⁴ nonlinearity: a thin slab cooling purely by radiation, dT/dt = −K(T⁴−T∞⁴) with K = εσ/(ρcL), exact implicit solution t = (G(Tᵢ)−G(T))/K (exact/radiative_cooling.jl, quadrature self-tested). Verifies RadiativeBC + the surface Newton solve against something other than steady algebra.

a) transient cooling — thin-limit setup: L = 0.1 mm, k = 100 W/mK makes the internal ΔT ≈ q·L/2k ≈ 0.017 K at t = 0 (flux bias ~7e-5 relative), far below the comparison tolerance; compared on the cell-mean temperature, which is what the lumped ODE governs. b) steady companion — HeatFluxBC + RadiativeBC + ConvectiveBC vs the exact algebraic root of q_abs = εσ(Ts⁴−T∞⁴) + h(Ts−T∞): a direct check of the surface-Newton residual (Ts ≈ 732 K, cone-like). Run to 36 thermal time constants; at steady state with an adiabatic back the whole slab must be uniform at Ts.

Uses the code's own STEFAN_BOLTZMANN so the reference cannot drift from the implementation's constant.

V-RX-04a — thermally-thin radiative cooling (implicit exact)

Quantities of interest (n = 4)

Solver configuration

V-RX-04b — steady radiative–convective surface equilibrium

Quantities of interest (n = 20)

Solver configuration