Radiation Shielding of a Spherical Black Body

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This Demonstration shows how a radiation shield affects radiative heat transfer to a ball. The ball, in the center of an enclosure, is the object that is shielded; you can remove the shield by unchecking "shield". The enclosure around the shield and ball is assumed to be a black body at a temperature of 600 K. The radiation shield diameter is 0.2 m larger than the ball diameter, and the shield is thin enough that conductive heat transfer can be ignored. Use buttons to view a radiation network or a plot of the radiative heat transfer from the enclosure to the ball as a function of the emissivity of the shield. The plot is available only when "shield" is checked and a 3D physical representation of the ball and shield is shown on the plot.

Contributed by: Mathew L. Williams (June 2014)
Additional contributions by: Rachael L. Baumann
University of Colorado Boulder, Department of Chemical and Biological Engineering
Open content licensed under CC BY-NC-SA


Snapshots


Details

The radiative heat transfer is calculated using a relation between the temperatures of the ball and enclosure over the sum of the resistances:

,

,

where is in , is the Stefan–Boltzmann constant (), and are the wall and ball temperatures (K) and is thermal resistance ().

The resistance from enclosure to shield is:

,

where .

The resistances associated with shield emissivity are:

,

.

The resistance between the shield and ball is:

,

where .

The resistance associated with the ball emissivity is:

,

where is surface area (), is diameter (m) and is emissivity.

Reference

[1] T. L. Bergman, A. S. Lavine, F. P. Incropera and D. P. DeWitt, Introduction to Heat Transfer, 6th ed., Hoboken, NJ: John Wiley and Sons, 2011.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send