Source: https://guthlabs.ai/docs/instruments/radiation-heat-transfer-calculator/mechanism/

instrument mechanism / verified-with-binding-errata

# Radiation Heat Transfer Calculator mechanism

The inspectable method record for Radiation Heat Transfer Calculator, kept separate from implementation and qualification.

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

## Model scope

The instrument can be correct for blackbody or gray-surface-to-black-surroundings exchange with F=1, and for the restricted equal-area two-surface enclosure formula. As specified, it claims broader graybody and view-factor capability than the formulas support; add the missing geometric radiation-resistance terms or narrow the claims and inputs.

- The formula q=εσA(T1⁴−T2⁴) is valid only for a gray surface radiating to a blackbody enclosure or effective black surroundings with view factor F=1; it is not a general two-surface graybody formula.

- The two-surface enclosure formula σA(T1⁴−T2⁴)/[1/ε1+1/ε2−1] requires two diffuse-gray, opaque, isothermal surfaces with equal area and mutual view factors F12=F21=1. It is not valid for arbitrary areas or the supplied view-factor input.

- View factors are listed as inputs but are absent from both formulas. General unequal-area or partial-view configurations require geometric radiation-resistance terms involving area and view factor.

- The specification claims blackbody/graybody exchange and simple view factors, but the formulas do not distinguish the blackbody-surroundings case from the two-gray-surface case.

## Units and conventions

- Temperatures must be absolute temperatures in kelvin; Celsius or Fahrenheit values must be converted before taking the fourth power.

- Area A is in square metres and the resulting heat rate q is in watts.

- Emissivities ε, ε1, and ε2 are dimensionless and must satisfy 0≤ε≤1; physical opaque-surface calculations normally require positive emissivity.

- The Stefan-Boltzmann constant is σ=5.670374419×10^-8 W·m^-2·K^-4.

- The positive sign convention is net heat transfer from surface 1 to surface 2 or the surroundings.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "formula": "q=εσA(T1^4−T2^4)",
    "epsilon": 1,
    "area_m2": 2,
    "T1_K": 500,
    "T2_K": 300,
    "view_factor": 1
  },
  "expected_outputs": {
    "q_net_W": 616.9367368
  },
  "working": "T1^4=500^4=62,500,000,000 K^4. T2^4=300^4=8,100,000,000 K^4. Difference=54,400,000,000 K^4. q=1×(5.670374419×10^-8)×2×54,400,000,000. q=616.9367368 W."
}
````

## Failure boundary

- Division by zero or nonphysical results occur if ε1 or ε2 is zero in the two-surface denominator.

- The denominator formula becomes invalid when the surfaces do not have equal area and mutual view factor one.

- Missing view-factor usage can cause large errors for partial visibility, separated surfaces, or enclosure geometries.

- Negative, zero, or non-absolute temperatures are invalid for this radiation formula; temperatures must be positive kelvin.

- Emissivities outside the interval 0 to 1 are nonphysical.

- The result can be negative when T1<T2; the interface must clearly label this as heat transfer from surface 2 toward surface 1.

- An emissivity table needs material, wavelength, temperature, and surface-condition assumptions; tabulated emissivity is not universally a single constant.

- The honest label is incomplete because it does not explicitly state the equal-area, F=1, diffuse-gray, opaque, isothermal assumptions behind the two-surface formula.

## Other records

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