Radiosity (heat Transfer) - Radiosity Method

Radiosity Method

The radiosity, for a gray, diffuse surface, is the sum of the reflected and emitted irradiances. Or,

where is the gray body radiation due to temperature, and is the incident radiation. Normally, is the unknown variable and will depend on the surrounding surfaces. So, if some surface is being hit by radiation from some other surface, then the radiation energy incident on surface is . So, the incident irradiance is the sum of radiation from all other surfaces per unit surface of area .

is the view factor, or shape factor, from surface to surface . Now, employing the reciprocity relation,

and substituting the incident irradiance into the original equation for radiosity, produces

For an surface enclosure, this summation for each surface will generate linear equations with unknown radiosities. For an enclosure with only a few surfaces, this can be done by hand. But, for a room with many surfaces, linear algebra and a computer are necessary.

Once the radiosities have been calculated, the net heat transfer at a surface can be determined by finding the difference between the incoming and outgoing energy.

Using the equation for radiosity, the incident radiation, can be eliminated from the above to obtain