Thermal radiation from nonisothermal spherical particles of a semitransparent material

The applicability of radiation transfer theory for calculations of the thermal radiation emitted by spherical particle of a semitransparent material, and in particular the determination of radial heat generation profiles, is analyzed. For homogeneous isothermal particles, a comparison with the exact solution based on the Mie theory shows that the radiation transfer calculations are sufficiently accurate for diffraction parameter of the particle of x ≥ 20. Numerical examples for large particles illustrate the transition from conditions of dominant radiation of the central region of the particle to conditions of the surface layer emission. A new differential approximation for radiation transfer in a refracting particle is proposed. This approximation called MDP0 (modified DP0) is much simpler than the radiation transfer equation. Using MDP0, we have a chance to consider radiation–conduction interaction in nonisothermal particles without great computational efforts.