Radiation Heat Transfer Calculator mechanism

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

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