2.8. Analytical Formulation

The net radiation exchange between two surfaces can be expressed analytically for some cases, depending on the radiation view factor and the surfaces areas ratio. For the case of two concentric spheres, the net radiation may be expressed as follows:

(2–4)

where:

  • is the radiation heat transfer rate between the spheres.

  • , which is the Stefan-Boltzmann constant.

  • Ti is the inner sphere's surface temperature.

  • To is the outer sphere's surface temperature.

  • is the thermal emissivity of the inner sphere.

  • is the thermal emissivity of the outer sphere.

  • Ai is the area of the inner sphere.

  • Ao is the area of the outer sphere.