(a) Show that for an incident radiation intensity of Iph, i (energy per unit area irradiated...

  

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(a) Show that for an incident radiation intensity of Iph, i (energy per unit area irradiated is π Iph, i) in a medium with an absorption coefficient Oph, the divergence (in one dimension, along x) of radiation heat flux aph is equal to - Iph, ph expl-phx). In the positive direction, the radiation heat flux at x = 0 is from (7.32) as 4ph (x = 0) = 2 5² Iph.i cos 9 sin 9d9 — ñIph.i. Assume there is no emission and scattering. The divergence of aph appears in the macroscopic energy equation given (b) Comment on how this term becomes a heat source in the macroscopic energy equation when radiation is absorbed. (a) Show that for an incident radiation intensity of Iph, i (energy per unit area irradiated is π Iph, i) in a medium with an absorption coefficient Oph, the divergence (in one dimension, along x) of radiation heat flux aph is equal to - Iph, ph expl-phx). In the positive direction, the radiation heat flux at x = 0 is from (7.32) as 4ph (x = 0) = 2 5² Iph.i cos 9 sin 9d9 — ñIph.i. Assume there is no emission and scattering. The divergence of aph appears in the macroscopic energy equation given (b) Comment on how this term becomes a heat source in the macroscopic energy equation when radiation is absorbed.

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ANSWER a To show that the divergence of radiation heat flux qph is equal to piph sigmaphexpsigmaphx we can start with the definition of divergence divqph qphx We know that qph is given by qph DphIph w... View the full answer