Source: https://guthlabs.ai/docs/instruments/fourier-conduction-plane-wall-calculator/mechanism/

instrument mechanism / verified-clean

# Fourier Conduction (Plane Wall) Calculator mechanism

The inspectable method record for Fourier Conduction (Plane Wall) Calculator, kept separate from implementation and qualification.

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

## Model scope

The core formula is standard and correct under the stated steady-state 1D plane-wall idealization. The specification needs an explicit heat-flux formula, SI-unit requirements or documented unit conversion, a ΔT sign convention, and input constraints before release.

- The heat-rate formula q = k·A·ΔT/L is correct for steady, one-dimensional conduction through a plane wall with constant thermal conductivity and no internal heat generation.

- The advertised heat-flux output has no explicit formula; it should be q'' = q/A = k·ΔT/L.

- The sign convention for ΔT is unspecified. For signed heat rate, define ΔT = T_hot − T_cold; otherwise the calculator should state that it reports heat-rate magnitude.

## Units and conventions

- Use SI units: k in W/(m·K), area A in m², thickness L in m, and ΔT in K or °C temperature difference; the result q is in W.

- Heat flux q'' is in W/m².

- If non-SI inputs are accepted, the calculator must explicitly convert area and thickness before applying the formula; the current specification does not state whether unit conversion is supported.

- Thermal-conductivity table entries must be in W/(m·K) or be converted to those units.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "k_W_per_mK": 0.6,
    "area_m2": 2.5,
    "thickness_m": 0.1,
    "delta_T_K": 20
  },
  "expected_outputs": {
    "heat_rate_q_W": 300,
    "heat_flux_W_per_m2": 120
  },
  "working": "q = k·A·ΔT/L = 0.6·2.5·20/0.1 = 30/0.1 = 300 W. q'' = q/A = 300/2.5 = 120 W/m²."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The zero-thickness input produces an undefined division-by-zero result and must be rejected. The specification also leaves the sign convention for ΔT and heat-flow direction unstated, allowing results that differ by sign.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/fourier-conduction-plane-wall-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/fourier-conduction-plane-wall-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/fourier-conduction-plane-wall-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`