Fin Effectiveness/Efficiency Calculator mechanism

Model scope

The m, corrected-length efficiency, and corrected-length heat-rate calculations are standard under the stated assumptions, and the numerical vectors verify them. The instrument cannot receive a PASS because effectiveness is claimed but undefined, and the specification does not unambiguously distinguish exact adiabatic-tip formulas from corrected-length approximations or define L_c.

• The effectiveness formula is missing, so the claimed effectiveness output cannot be computed or verified. A standard definition is ε_fin=q_fin/(h A_b θ_b), but the reference base area A_b is not specified.
• The formula η_fin=tanh(mL_c)/(mL_c) is the corrected-length approximation, not the exact adiabatic-tip expression unless L_c is explicitly defined as L+A_c/P.
• The heat-rate expression using tanh(mL_c) is likewise a corrected-length approximation. For an exact adiabatic-tip model it should use tanh(mL), with the corresponding fin-area convention for efficiency.
• The geometry-to-parameter definitions are absent: rectangular and pin-fin formulas for A_c and P must be specified, as must whether L is physical fin length or corrected length.
• The limiting case mL_c=0 is not defined; efficiency should use the limit η_fin=1 rather than direct division by zero.

Units and conventions

• Use SI units consistently: h in W/(m²·K), k in W/(m·K), lengths in m, A_c in m², P in m, and θ_b in K or °C temperature difference.
• m has units of 1/m, so mL_c is dimensionless.
• For these vectors, L_c is assumed to mean L+A_c/P, the standard corrected-length approximation for a convecting fin tip.
• Temperature differences in kelvins and degrees Celsius are numerically interchangeable.
• The heat-rate output q_fin is in watts.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "geometry": "rectangular",
    "t_m": 0.002,
    "w_m": 0.048,
    "L_m": 0.04904,
    "k_W_per_mK": 200,
    "h_W_per_m2K": 19.2,
    "theta_b_K": 80,
    "A_c_m2": 0.000096,
    "P_m": 0.1,
    "L_c_m": 0.05
  },
  "expected_outputs": {
    "m_per_m": 10,
    "eta_fin": 0.92423431,
    "q_fin_W": 7.09811954
  },
  "working": "A_c=t·w=0.002·0.048=0.000096 m²; P=2(t+w)=2(0.002+0.048)=0.1 m; L_c=L+A_c/P=0.04904+0.000096/0.1=0.05 m; m=√(hP/(kA_c))=√(19.2·0.1/(200·0.000096))=√100=10 m⁻¹; mL_c=10·0.05=0.5; tanh(0.5)=0.46211716; η_fin=0.46211716/0.5=0.92423431; √(hPkA_c)=√(19.2·0.1·200·0.000096)=√0.036864=0.192; q_fin=0.192·80·0.46211716=7.09811954 W."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The raw formulas expose undefined behavior for k = 0, and the zero-length limiting case produces a 0/0 effectiveness unless the calculator explicitly applies the limiting value or rejects the effectiveness output.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json