Fundamental Equations of Radiation Gasdynamics

  • Shih-I Pai


In radiation gasdynamics, we study the interaction between the gasdynamic field and the radiation field. In the most general analysis, we should consider the distribution functions of a mixture of various types of particles of which photons may be considered as a special type of particles. In deriving the equations for these distribution functions, the relativistic character of photon must be considered. We shall discuss such an analysis in chapter X. In this general case, we may deal with both rarefied gasdynamics and continuum gasdynamics including the effects of radiation field. In order to bring some essential features of radiation effects, we shall consider only the case where the gas may be considered as a continuum in this chapter and the following four chapters. When the gas may be considered as a continuum, the gasdynamic variables are the pressure p, density ρ, temperature T, and three velocity components. In radiation gasdynamics, we have to add the specific intensity of radiation I v to these gasdynamic variables. Hence we need to find seven fundamental equations for these seven unknowns. These fundamental equations are
  1. (i)

    Equation of state which connects the pressure, density, and temperature of the gas (§ 2).

  2. (ii)

    Equation of continuity which expresses the conservation of mass of the medium (§ 3).

  3. (iii)

    Equations of motion which are generally three in number and which express the conservation of momentum. In radiation gasdynamics, the radiation stresses should be included (§ 4).

  4. (iv)

    Equation of energy which expresses the conservation of energy (§ 5).

  5. (v)

    Equation of radiative transfer, which determines the specific intensity of radiation (§ 6).



Free Path Specific Intensity Radiative Transfer Optical Thickness Fundamental Equation 
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  1. 1.
    Chandrasekhar, S.: An Introduction to the Study of Stellar Structure. Dover Publications, New York, 1957.MATHGoogle Scholar
  2. 2.
    Goulard, P.: Fundamental equations of radiation Gasdynamics. Purdue Univ. School of Aero. & Eng. Sci. report A & ES 62–4, 1962.Google Scholar
  3. 3.
    Goulabd, R. & M.: One dimensional energy transfer in radiant media. Int. Jour. Heat and Mass Transfer, vol. 1, pp. 81–91, 1960.CrossRefGoogle Scholar
  4. 4.
    Jahnke, E., and E. Emde: Tables of Functions. Dover Publications, New York, 1945.MATHGoogle Scholar
  5. 5.
    Kivel, B., and K. Bailey: Tables of Radiation from High temperature Air. AVCO Research Lab. Research Report 21, 1957.Google Scholar
  6. 6.
    Kourganoff, V.: Basic Methods in Transfer Problems. Oxford Press, 1952.Google Scholar
  7. 7.
    Pai, S. I.: Some considerations of radiation magnetogasdynamics. Proc. Non-linear Problem. University of Wisconsin Press, pp. 47–67, 1963.Google Scholar
  8. 8.
    Planck, M.: The Theory of Heat Radiation. Dover Publications, New York, 1959.MATHGoogle Scholar
  9. 9.
    Rosseland, S.: Theoretical Astrophysics. Oxford Press, 1936.Google Scholar
  10. 10.
    Scala, S. M., and D. H. Sampson: Heat Transfer in hypersonic flow with radiation and chemical reaction. Techn. Inform. Series R 63 D 46, Space Sciences Lab. General Electric Co., Phil. Pa., 1963. Also Supersonic Flow, Chemical Processes and Radiative Transfer, Pergamon Press, pp. 319–354, 1964Google Scholar
  11. 11.
    Tellep, D. M., and D. K. Edwards: Radiant energy transfer in gaseous flows. Tech. report, Lockheed Missile & Space Div. LMSD-288139, 1960.Google Scholar
  12. 12.
    Zhigulev, V. N., Ye. A. Romishevskii, and V. K. Vertushkin: Role of Radiation in Modern Gasdynamics. AIAA Journal, vol. 1, No. 6, pp. 1473–1485, June 1963.ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag / Wien 1966

Authors and Affiliations

  • Shih-I Pai
    • 1
  1. 1.Institute for Fluid Dynamics and Applied MathematicsUniversity of MarylandCollege ParkUSA

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