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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
  1. 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]
  2. 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]
  3. 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]

Related

References

  1. Grubka & Bobba (1985); Ishak, Nazar & Pop (2009).

    • 1.1

      JHT 107, 248–250 — −θ′(0) for the reduced steady case: 0.8086 (Pr = 0.72), 1.0000 (Pr = 1), 1.9237 (Pr = 3), 3.0723 (Pr = 7), 3.7207 (Pr = 10).

      Established
  2. Sharidan et al. (2006); Pal (2011); Kumar & Srinivas (2017).

    • 2.1

      IJAME 11, 647–654 — f″(0) = −1.261042 at A = 0.8 and −1.377722 at A = 1.2 for the reduced unsteady case.

      Established
  3. Pavlov (1974), Magnitnaya Gidrodinamika 10, 146–148.

    • 3.1

      MG 10, 146–148 — f″(0) = −√(1 + M) exactly: 1, 1.224745, 1.414214, 1.581139, 1.732051 for M = 0, 0.5, 1, 1.5, 2 — a machine-precision validation target.

      Established
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