No definition recorded yet.

Warnings

• !S1Interpret Rd sweeps with care: in the linearised Rosseland form used here, radiation only rescales conduction — solutions at (Pr, Rd) coincide with no-radiation solutions at the effective Prandtl number Pr_eff = Pr·(φ_k/φ_Cp)/(φ_k/φ_Cp + 4Rd/3); Rd is not independent physics. Reporting both Pr and Rd sweeps double-counts one mechanism.

Observed results

• S2Report both normalisations from the converged wall gradient: the reference-temperature proxy Re_x^{−1/2}Nu~_x=(φ_k+4Rd/3)(−θ′(0)), and the standard surface value Re_x^{−1/2}Nu_{x,s}=(φ_k+4Rd/3)(−θ′(0))/θ(0). State −θ′(0), θ(0), the flux prefactor, continuation branch and tolerances; parameter trends are numerical findings, not assumptions.

Physical interpretation

• ✦S3Magnetic damping can weaken convective heat removal through the coupled velocity field, while unsteadiness can alter the instantaneous thermal thickness. Neither monotonic trend is assumed: it must be established from the converged branch, and the chosen reference or surface Nusselt normalisation must be named.