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This page calculates the net radiant heat exchange for two isothermal (constant temperature) parallel square flat black plates of different edge lengths.

The heat flow q from the plate is calculated as:

q = 56.69x10^-9 x VF_(1-2) x L₁² x (T₁⁴ - T₂⁴)

Where 56.69x10^-9 is the average Stefan-Bolzmann constant, L₁ is the length of plate 1, T₁ is the plate 1 temperature and T₂ is the plate 2 temperature. The view factor VF_(1-2) (also known as radiation shape factor, angle factor, and configuration factor) is defined as:

Length of plate 1 divided by the distance between the plates (L₁ / D) must be greater than 0.2 for this calculation.

VF_(1-2) =

Where:

Where X and Y are defined as:

X = (C) x ( 1 +E )
Y = (C) x ( 1 - E )
C = L₁ / D
D = L₂ / L₁

Where L₁ is the plate 1 length, L₂ is the plate 2 length, and D is the distance between the plates.

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, 7.81.