The Essential Linearity of Thermal Radiation Net Transport

Thermal radiation net transport is proportional to the difference in the fourth powers of the absolute temperatures of the radiator and the receiver. During a study of heat transfer mechanisms in the underground storage tanks for the radioactive wastes at the Hanford Site in Washington, it was discovered that the fourth power difference is approximated by a linear function of the temperature difference between the radiator and the receiver, with astounding fidelity. This linearity makes satisfying boundary conditions for analytical and numerical calculations much simpler and simplifies comparisons with other modes of heat transfer. The paper derives the relationship and illustrates its use by demonstrating that radiation transports more heat through the air space in the tank than does natural convection.