Radiation heat transfer down an elongated spheroidal cavity

✍ Scribed by Sean P. Fitzgerald; William Strieder

• Publisher: American Institute of Chemical Engineers
• Year: 1997
• Tongue: English
• Weight: 982 KB
• Volume: 43
• Category: Article
• ISSN: 0001-1541
• DOI: 10.1002/aic.690430103

✦ Synopsis

Effects of elongation on the radiation heat transport down a spheroidal cavity, located in a conducting solid with a difisely reflecting cavitysolid interface, are examined. A n effective conductivity A, and a void radiation conductivity A, are obtained as a function of cavity eccentricity a and surface emissivity E . To facilitate the calculations and produce readily applicable equations, a rigorous variational principle is used.

Exact solutions are generated in the neighborhood of the spherical cavity ( a ' + 0) for any E > 0, a long needle-shaped void ( a 2 + 1) for any E > 0, and a pegect reflector ( E + 0) for arbitrary elongation (0 I a I I). Signifcant differences arising from the shape change are observed. The a ' + 0 edge demonstrates a linear increase in A, with E . A t the opposite edge a ' + 1 and positive E, A, is a horizontal line independent of E , much like the long cylinder, whose conductivity is a factor of 3 2 / ( 9 ~) ( = 1.13) latger. In the neighborhood of E + 0, A, is always zero for any 0 I a 2 I 1. The emissivity slope for E + 0 starts from unity at a ' = 0 and increases monotonically with elongation to a singularity 3 ~[ 1 6 ( 1a')]-' as a' -+ 1 for the long needle.