Radiant Heat Exchange (Stefan-Boltzmann)

q = eps F sigma A (T_s^4 - T_surr^4), sigma = 0.1714e-8 BTU/(hr ft^2 R^4), temperatures in absolute Rankine (F + 459.67). The Stefan-Boltzmann law is buried inside the insulation and ampacity models; this exposes it as its own tool for radiant-panel sizing, hot-surface heat loss, and freeze protection. A 10 ft^2 flat-painted surface (eps 0.9) at 200 F in a 70 F room sheds about 1,707 BTU/hr; the same surface bright and shiny (eps 0.05) sheds only 95 BTU/hr, and a cold 40 F surface GAINS heat from a 70 F room. Because it goes as the fourth power of absolute temperature, a hot surface radiates far more than a warm one, and emissivity multiplies it directly. View factor F = 1 for a small object fully surrounded by a large room. Radiation only (add convection and conduction for the total); first-principles (NIST). The real emissivity, geometry, and full heat balance govern.

q = eps F sigma A (T_s^4 - T_surr^4); sigma = 0.1714e-8 BTU/(hr ft^2 R^4); T in absolute Rankine (F + 459.67); q in BTU/hr, W = BTU/hr / 3.412142. Positive = net loss from the surface.

The Stefan-Boltzmann law of thermal radiation (sigma from NIST/CODATA); first-principles physics, cited by name.

The Stefan-Boltzmann law and its constant are public first-principles physics; emissivity, area, view factor, and the two temperatures are the user's inputs.

Estimate. AHJ and licensed professional govern.

Field names used by the API: area_ft2, emissivity, surface_temp_f, surroundings_temp_f, view_factor, heat_rate_btu_hr, heat_rate_w

• Stefan-Boltzmann q = eps F sigma A (T_s^4 - T_surr^4); sigma = 0.1714e-8 BTU/(hr ft^2 R^4); T in RankineStefan-Boltzmann law (NIST constant)
• Emissivity and view factor eps ~ 0.05 bright metal, ~0.9 paint/nonmetals; F = 1 for a small object in a large roomradiation heat-transfer texts
• Scope radiation only (add convection + conduction for the total); net between two temperaturesscope of this tile