Energy Transfer between Two Blackbodies

This Demonstration calculates radiative heat transfer from the green surface to the black surface as a function of the temperature of the green surface. Both surfaces are blackbodies which lose energy by emission, but absorb all incident radiation. The blackbodies are maintained at constant temperatures by internal heaters. You can select "parallel plates", "perpendicular walls" or "parallel cylinders". The view factor is shown. The rate that heat transfers from the green surface and is intercepted by the black surface is plotted as a function of the temperature of the green surface. The magenta point on the plot represents the green surface temperature (select with a slider). You can change distances between surfaces and dimensions of the plates, walls or cylinders.

SNAPSHOTS

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DETAILS

The view factor is defined as the fraction of the radiation leaving the green surface i that is intercepted by the black surface j. The view factors for each situation are shown below.
Parallel plates:
,
,
,
where is the plate length, is the plate width and is the distance between the plates.
Perpendicular walls:
,
where and are the lengths of the walls.
Parallel cylinders:
,
,
,
,
where is the cylinder radius and is the space between the cylinders.
The rate of heat transfer from surface to is:
,
where is the area of surface , is the Stefan–Boltzmann constant and is surface temperature.
Reference
[1] T. L. Bergman, A. S. Lavine, F. P. Incropera and D. P. DeWitt, Introduction to Heat Transfer, 6th ed., Hoboken: John Wiley and Sons, 2011 pp. 832–833, 839.
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