Radiation perpendicular to the symmetry axis of prolate and oblate cavities

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.