Source: https://guthlabs.ai/docs/instruments/fin-effectiveness-efficiency-calculator/mechanism/

instrument mechanism / verified-clean

# Fin Effectiveness/Efficiency Calculator mechanism

The inspectable method record for Fin Effectiveness/Efficiency Calculator, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## 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

[01**Overview**](<https://guthlabs.ai/docs/instruments/fin-effectiveness-efficiency-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/fin-effectiveness-efficiency-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/fin-effectiveness-efficiency-calculator/qualification/>)

## 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`