engineering fundamentals Radiation Exchange Between 2 Bodies
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Calculator Introduction
Two bodies at differing temperatures (and within sight of each other) will exchange heat energy via thermal radiation.

To calculate the radiation heat transfer between 2 bodies, enter the parameters below. The two bodies are assumed to be fully enclosed by a third nonconducting body, such that all radiation energy hitting this third surface will immediately re-radiate back into the cavity.

To simulate a single hot object fully surrounded by a large cavity (such as a hot brick sitting in a room), enter a View Factor of 1, and make sure that the second body has a much larger surface area than the first.

The default calculation is for a situation experienced by many living in cold winter climes. Ever wonder why a cloudless night sky feels so much colder than a cloudy night? The reason is that more body heat is lost to the cold clear sky; a cloud layer acts as a radiation barrier. Default values are for a hatless head at 95 deg F radiating to a cold clear sky at -150 deg F, with answers rounded to 3 significant figures.

Inputs
  Temperature of Object 1, T1:    
  Surface Area of Object 1, A1:    
  Surface Emissivity of Object 1, e1:    
  Temperature of Object 2, T2:    
  Surface Area of Object 2, A2:    
  Surface Emissivity of Object 2, e2:    
  View Factor of Object 1 to 2, F12:    
Answers
  Heat Flow from 1 to 2, Q:  11.6  W
 
Equations Behind the Calculator
This calculator assumes that both bodies are graybodies, whereas the third surface is needed for conservation of energy reasons. The heat transfered from Object 1 to Object 2 in this case is described by,
This equation is subject to the reciprocity condition for the 3-body problem,
which guards against non-physical problems. Reciprocity requires that, if Object 1 is larger than Object 2, the surface area of Object 2 seen by Object 1 must be less than unity. This means that the view factor must be less than 1 (or more exactly, less than A2/A1).
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