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Radiative heat transfer (heat transfer by electromagnetic radiation) is proportional to

e*(T1^4 - T2^4)

where T1 is the absolute temperature of the material, T2 is the absolute temperature of the surroundings, and e is the emissivity coefficient.

A black material has a high emissivity coefficient, while a silvery material has a low emissivity coefficient.

However, the emissivity coefficient cuts both ways, so to speak. A black material in thermodynamic equilibrium with its environment absorbs more radiation, true. But it also emits more radiation (this is necessary for equilibrium to hold). Likewise, a silvery material absorbs less radiation, and also emits less radiation.

Conductive heat transfer ensures that the black material on the surface of the heat sink remains hot. The surroundings are at a lower temperature. Therefore T1 and T2 are set, and the heat transferred from the heat sink to the surroundings is simply proportional to e, the emissivity coefficient.

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