Stefan's law for radiation between body and surroundings

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SUMMARY

Stefan's law for radiation between bodies is fundamentally governed by Kirchhoff's law of thermal radiation, which states that a single value of emissivity (ε) applies for heat transfer in both directions. This principle holds true when the body in question is significantly smaller than its surroundings, allowing for simplified calculations of net energy exchange. The discussion emphasizes the importance of geometry when considering heat transfer between two bodies rather than a body and its surroundings. The use of imperial units such as ft² and °R is criticized as outdated and impractical.

PREREQUISITES
  • Understanding of Kirchhoff's law of thermal radiation
  • Familiarity with emissivity (ε) in thermal systems
  • Basic principles of heat transfer and radiation
  • Knowledge of geometric considerations in thermal analysis
NEXT STEPS
  • Study the derivation and applications of Kirchhoff's law in thermal radiation
  • Explore the implications of emissivity in various materials and conditions
  • Investigate geometric factors affecting heat transfer between multiple bodies
  • Learn about modern units of measurement in thermal analysis, focusing on SI units
USEFUL FOR

Thermal engineers, physicists, and students studying heat transfer principles, particularly those interested in radiation heat exchange and thermal system design.

Remusco
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My PE handbook describes how to calculate the "Net Energy Exchange by Radiation Between Two Bodies", as shown below:

1733092199642.png




How can a single value of epsilon be used for heat transfer in both directions? Why does the body need to be small compared to the surroundings?
 
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Remusco said:
My PE handbook describes how to calculate the "Net Energy Exchange by Radiation Between Two Bodies", as shown below:

View attachment 354010



How can a single value of epsilon be used for heat transfer in both directions? Why does the body need to be small compared to the surroundings?
There is one ##\varepsilon## because the absorptivity of the body is the same as its emissivity per Kirchhoff's law of thermal radiation. You are calculating the heat on the body due to surroundings. If the surroundings are instead another body then you have to take into account the geometry of the second body.

Edit: not important, but who in their sane minds uses ft2 and °R?
 
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