Knowledge card
Validation Against Benchmarks
Mathematical Modelling — Fluid Dynamics & Heat TransferNumerical analysis; boundary-layer similarity theory
Symbol
✓The trust argument for the numbers: reduce the model to published limiting cases and reproduce their values — including two EXACT closed-form checks — across independent method families (finite-difference, semi-analytic, shooting).
Dimension I
Definition
What it is — and what it is not
No definition recorded yet.
Dimension II
In practice
How to deal with it
- Physical interpretation
- S1The three sweeps cross three independent method families (finite difference, semi-analytic series, shooting/RK) AND two exact solutions; consistent agreement means errors specific to any one numerical family would have been exposed. [3.1]
- Validation evidence
- S2Pr-sweep (steady, no PE/MHD/radiation limit): computed −θ′(0) = 0.8086, 1.0000, 1.9237, 3.0723, 3.7207 at Pr = 0.72, 1, 3, 7, 10 — agreeing with Ishak et al. (Keller-box), Abolbashari et al. (HAM), Das et al. (RKF shooting), and Aziz et al. (Keller-box) to 4–8 significant figures. [1.1]
- S3A-sweep (unsteady Newtonian limit): computed f″(0) = −1.261043 at A = 0.8 and −1.377724 at A = 1.2 — matching Sharidan et al., Pal, and Kumar & Srinivas to 5 decimal places. [2.1]
- S4M-sweep (steady MHD Newtonian limit): computed −f″(0) reproduces the EXACT closed form √(1 + M) — 1.000000, 1.224745, 1.414214, 1.581139, 1.732051 at M = 0, 0.5, 1, 1.5, 2 — to machine precision. [3.1]
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