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This page calculates the net radiant heat exchange for two isothermal (constant temperature) parallel flat black disks. 

The heat flow (q) from the plate is calculated as:

q = 56.69x10^-9 x VF_(1-2) x A₁ x (T₁⁴ - T₂⁴)

Where 56.69x10^-9 is the average Stefan-Bolzmann constant, A₁ is the area of disk 1, T₁ is the disk 1 temperature and T₂ is the disk 2 temperature. The view factor VF_(1-2) (also known as radiation shape factor, angle factor, and configuration factor) is defined as:

Where r₁, r₂ and X are defined as:

r₁ = rad₁ / D
r₂ = rad₂ / D
X = 1 + ( (1 + r₂²) / r₁² )

Where rad₁ is the disk 1 radius, rad₂ is the disk 2 radius, and D is the distance between the disks.

References

Rosenow, W. M., J. P. Hartnett, Y. I. Young, Handbook of Heat Transfer, 3rd Ed., McGraw-Hill Handbooks, New York, 1998. p. 7.3 - 7.19, 7.82.