Fin Effectiveness/Efficiency Calculator

Inspectable records

Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Area

Thermodynamics, Fluids & Aero

Tranche

tranche-4

Evidence ID

t4-156

Ledger rows

1

No ledger note is attached.

Review findings

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.

Formula and scope findings

• 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.

Unit assumptions

• 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.

Boundary hardening

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.

Errata and corrections

No applied erratum is attached to this unique-name record.

Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

{
  "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."
}

Related workflows

Sources and evidence

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

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