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Radiation of an Isothermal Plane-Parallel Layer

Leonid A. Dombrovsky

Following from: P1 approximation of the spherical harmonics method, The simplest approximations of double spherical harmonics, Solutions for one-dimensional radiative transfer problems

Leading to: An estimate of P1 approximation error for optically inhomogeneous media, Radiation of a nonisothermal layer of scattering medium, Diffusion approximation in multi-dimensional problems

The radiative transfer equation (RTE) for a homogeneous plane-parallel layer of an emitting, absorbing, and scattering isothermal medium with an azimuthally symmetric radiation field can be written in the following dimensionless form:

(1a)

where

(1b)
(1c)

Dimensionless quantity ω is called the albedo of a medium, or Schuster number. For brevity, subscript λ is omitted in designations of I, τ, ξ, and ω. The boundary conditions in s ...

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References

  1. Abramowitz, M. and Stegun, I. A., eds., Handbook of Mathematical Functions, New York: Dover, 1965.
  2. Bohren, C. F. and Huffman, D. R., Absorption and Scattering of Light by Small Particles, New York: Wiley, 1983.
  3. Case, K. M. and Zweifel, P. F., Linear Transport Theory, Reading, MA: Addison-Wesley, 1967.
  4. Dombrovsky, L. A., Calculation of radiation heat transfer in a plane-parallel layer of absorbing and scattering medium, Fluid Dyn., vol. 7, no. 4, pp. 691–695, 1972.
  5. Dombrovsky, L. A., Radiation Heat Transfer in Disperse Systems, New York: Begell House, 1996.
  6. Korn, G. A. and Korn, T. M., Mathematical Handbook for Scientists and Engineers, 2nd ed., New York: McGraw-Hill, 1968.
  7. Korn, G. A. and Korn, T. M., Mathematical Handbook for Scientists and Engineers, 2nd ed., New York: Dover, 2000.
  8. Love, T. J. and Grosh, R. J., Radiative heat transfer in absorbing, emitting and scattering media, ASME J. Heat Transfer, vol. 87, no. 2, pp. 161–166, 1965.
  9. van de Hulst, H. C., Light Scattering by Small Particles, New York: Wiley, 1957.
  10. van de Hulst, H. C., Light Scattering by Small Particles, New York: Dover, 1981.
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