Radiative-conductive multi-layer

Canonical RHS excerpt from the registered callable used for this benchmark cell. Expand it to verify the state equations; it is not a standalone runnable fixture.

def rhs(t: float, temp: np.ndarray) -> np.ndarray:
    temp = np.clip(np.asarray(temp, dtype=float), 200.0, 3500.0)
    d = np.zeros(n)
    q_solar = solar_amp * max(0.0, np.sin(2.0 * np.pi * t / 86400.0))
    for i in range(n):
        t_left = temp[i - 1] if i > 0 else temp[i]
        t_right = temp[i + 1] if i < n - 1 else temp[i]
        cond = alphas[i] * (t_left - 2.0 * temp[i] + t_right) / dx2
        rad = emiss[i] * _STEFAN_BOLTZMANN * (t_air**4 - temp[i] ** 4) / (rho_c[i] * dx)
        d[i] = cond + rad
    d[0] += q_solar / (rho_c[0] * dx)
    return d

Parameters

• _STEFAN_BOLTZMANN = 5.67037e-08
• alphas = [8e-05, 8e-05, 8e-05, 8e-05, 8e-05, 8e-05, …] [shape=(24,), min=2.5e-08, max=8e-05]
• dx = 0.00416666666667
• dx2 = 1.73611e-05
• emiss = [0.3, 0.3, 0.3, 0.3, 0.3, 0.3, …] [shape=(24,), min=0.3, max=0.95]
• n = 24
• rho_c = [3.5e+06, 3.5e+06, 3.5e+06, 3.5e+06, 3.5e+06, 3.5e+06, …] [shape=(24,), min=1.2e+06, max=3.5e+06]
• solar_amp = 900
• t_air = 290

Initial condition

y(0) = [340, 337.391304348, 334.782608696, 332.173913043, 329.565217391, 326.956521739, …] [shape=(24,), min=280, max=340]

Horizon

t ∈ [0, 2000]

Canonical RHS excerpt captured from the same registered callable used for the published benchmark. Frozen closure values are summarized below; helper imports and solver settings are intentionally omitted.