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7.2.1 Equation of Phonon Radiative Transfer

7.2.1 Equation of Phonon Radiative Transfer. Dongwoo , Shin. Contents. Equation of Radiative Transfer (ERT) Equation of Phonon Radiative Transfer. Equation of Radiative Transfer.

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7.2.1 Equation of Phonon Radiative Transfer

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  1. 7.2.1 Equation of Phonon Radiative Transfer Dongwoo, Shin

  2. Contents Equation of Radiative Transfer(ERT) Equation of Phonon Radiative Transfer

  3. Equation of Radiative Transfer Radiative transfer is the physical phenomenon of energy transfer in the form of electromagnetic radiation. Theequation of radiative transfer describes the radiation intensity of microscopic point of view.

  4. Equation of Radiative Transfer : intensity in a participating medium : velocity of light. ( : absorption coefficient : scattering coefficient : scattering phase function.

  5. Equation of Phonon Radiative Transfer Problems exist using ERT at thin film or superlattice because local equilibrium breaks down in the acoustically thin limit. EPRT can describe Heat conduction across layered structures.

  6. Equation of Phonon Radiative Transfer The phonon BTE under the relaxation time approximation. Make simple : 1-D , without internal source

  7. Equation of Phonon Radiative Transfer is for equilibrium distribution. ERT :: corresponds to the inverse of the absorption coefficient of ERT.

  8. Equation of Phonon RadiativeTransfer • Acoustically thick limit / macroscale regime. • Most phonons will collide with phonons or defects inside the medium Local equilibrium situation. • Fourier’s law is applicable without at a very short time. • Acoustically thin limit / microscale regime • Most phonons will collide with the boundaries. The walls are different T even in steady states. • BTE is applicable.

  9. Equation of Phonon RadiativeTransfer Using Bose-Einstein statistics, Integrating over all frequencies The total intensity

  10. Equation of Phonon RadiativeTransfer When upper limit with Derive heat capacity from energy flux High T : Low T :

  11. Equation of Phonon Radiative Transfer Kinetic expression of thermal conductivity When ,C is the volumetric heat capacity of all phonon modes. Near the Debye temperature, C is the fraction of the volumetric specific heat. Also , we must use the appropriate upper limit in the integral when applying the EPRT.

  12. Equation of Phonon Radiative Transfer The heat flux per unit frequency The Criterion for radiative equilibrium Based on the energy density Local equilibrium condition

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