Source: https://guthlabs.ai/docs/instruments/biot-number-lumped-capacitance-validity-check/

instrument / verified-clean

# Biot Number / Lumped Capacitance Validity Check

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

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

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/biot-number-lumped-capacitance-validity-check/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/biot-number-lumped-capacitance-validity-check/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/biot-number-lumped-capacitance-validity-check/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/biot-number-lumped-capacitance-validity-check/qualification/>)

## 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**: t4-204

**Ledger rows**: 1

No ledger note is attached.

## Review findings

Formula and threshold are conditionally standard, but the instrument needs an explicit definition or required input convention for Lc, preferably Lc = volume/surface area for the body under analysis. The honest label should state that PASS means Bi < 0.1 under the selected geometry and property assumptions, not that lumped capacitance is universally accurate.

### Formula and scope findings

- Bi = hLc/k is the standard Biot-number formula when Lc is the appropriate characteristic length, commonly V/A for lumped-capacitance analysis.

- The validity rule is correctly stated as Bi < 0.1, but the specification does not define how Lc is obtained from body geometry; using a different length convention can change the result.

- The output flag should explicitly define that Bi = 0.1 is FAIL because the stated criterion is a strict inequality.

### Unit assumptions

- h is in W/(m^2·K).

- Lc is in m.

- k is in W/(m·K).

- Temperature units cancel, so K and °C temperature differences are equivalent in this ratio.

- h, Lc, and k must describe the same physical body and operating temperature range.

- k must be positive; material thermal conductivity may vary with temperature.

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

A zero thermal-conductivity input causes division by zero and an undefined Bi unless explicitly rejected. A separate convention ambiguity can also change the validity result from pass to fail.

## 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": {
    "h": 25,
    "Lc": 0.01,
    "k": 0.5,
    "units": "h in W/(m^2·K), Lc in m, k in W/(m·K)"
  },
  "expected_outputs": {
    "Bi": 0.5,
    "valid": "FAIL"
  },
  "working": "Bi = hLc/k = (25 × 0.01) / 0.5 = 0.25 / 0.5 = 0.5. Since 0.5 is not less than 0.1, valid = FAIL."
}
````

## Related workflows

[Heat-Transfer Pathmodel gate](<https://guthlabs.ai/docs/instrument-workflows/heat-path/>)

## 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`