Source: https://guthlabs.ai/docs/instruments/overall-heat-transfer-coefficient-u-calculator/mechanism/

instrument mechanism / verified-with-binding-errata

# Overall Heat Transfer Coefficient (U) Calculator mechanism

The inspectable method record for Overall Heat Transfer Coefficient (U) Calculator, kept separate from implementation and qualification.

Status: **VERIFIED_WITH_ERRATA**Lifecycle: **verified-with-binding-errata**

## Model scope

The written resistance equation has the correct convection and cylindrical-wall terms, but the fouling term and U area basis are insufficiently defined. The honest label should state whether fouling inputs are total K/W or area-specific m²·K/W, identify inside versus outside fouling surfaces, expose whether the result is Ui or Uo, and disclose the required positivity and unit constraints. The TEMA fouling table also requires a defined source, applicability range, and temperature/fluid assumptions.

- The formula is valid only when Rfouling is a total thermal resistance in K/W. Standard fouling factors are area-specific in m²·K/W and must appear as Rf,i/Ai and/or Rf,o/Ao; the specification does not define which surface or area basis applies.

- The specification says fouling factors (plural), but the formula provides only one undefined Rfouling term.

- The formula computes UA first, so the implementation must explicitly calculate Ui=(UA)/Ai and/or Uo=(UA)/Ao. The output statement does not specify the default area basis.

## Units and conventions

- hi and ho are in W/(m²·K).

- k is in W/(m·K), ri and ro are in m, and L is in m; all geometric quantities must use a consistent length unit before calculation.

- Ai=2πriL and Ao=2πroL for a cylindrical tube.

- The test vectors interpret Rfouling as a total resistance in K/W solely to evaluate the written formula. Conventional area-specific fouling factors would require division by the applicable area.

- UA is in W/K; Ui and Uo are in W/(m²·K).

- A valid tube requires ro>ri>0 and L>0.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "hi": 1000,
    "ho": 50,
    "k": 16,
    "ri": 0.01,
    "ro": 0.012,
    "L": 1,
    "Rfouling": 0,
    "units": "hi,ho W/(m²·K); k W/(m·K); dimensions m; Rfouling K/W"
  },
  "expected_outputs": {
    "UA_W_per_K": 3.534,
    "Ui_W_per_m2K": 56.241,
    "Uo_W_per_m2K": 46.868
  },
  "working": "Ai=2π(0.01)(1)=0.0628319 m²; Ao=2π(0.012)(1)=0.0753982 m². Ri=1/(1000×0.0628319)=0.0159155 K/W. Rwall=ln(0.012/0.01)/(2π×16×1)=ln(1.2)/100.531=0.0018136 K/W. Ro=1/(50×0.0753982)=0.2652582 K/W. Rtotal=0.0159155+0+0.0018136+0.2652582=0.2829873 K/W. UA=1/0.2829873=3.5337 W/K. Ui=3.5337/0.0628319=56.241 W/(m²·K). Uo=3.5337/0.0753982=46.868 W/(m²·K)."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The calculator should reject k=0 because the wall-resistance term divides by zero. The convention probe also exposes a substantial unit and radius-versus-diameter interpretation hazard if geometry metadata are not enforced.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/overall-heat-transfer-coefficient-u-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/overall-heat-transfer-coefficient-u-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/overall-heat-transfer-coefficient-u-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`