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Radiation perpendicular to the symmetry axis of prolate and oblate cavities
Author(s) -
Fitzgerald Sean P.,
Strieder William
Publication year - 1998
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690441103
Subject(s) - anisotropy , perpendicular , thermal conductivity , principal axis theorem , oblate spheroid , symmetry (geometry) , transverse plane , physics , axial symmetry , rotational symmetry , thermal conduction , thermal , geometry , mechanics , classical mechanics , optics , thermodynamics , quantum mechanics , mathematics , structural engineering , engineering
Thermal radiation heat transport within prolate and oblate ellipsoidal cavities was examined. The axisymmetric anisotropy of the cavity shape gives rise to a thermal radiation conductivity tensor with principal axes components parallel (λ r , ‖ ) and perpendicular (λ r , ⊥ ) to the symmetry axis. The prolate (λ r , ⊥ ) and oblate (λ r , ⊥ ) transverse components are calculated and compared with well‐known results from the kinetic theory of transport across cylindrical and within slit void geometries. The use of λ r , ⊥ and λ r , ⊥ , along with earlier results for λ r , ‖ and λ r , ‖ , in well‐known effective conductivity equations for spheroidal inclusions within a solid matrix, provides a means to rigorously treat cavity orientation and shape in high‐temperature heat transport across porous materials. To facilitate the calculations and produce readily usable equations, a variational principle is used.