Boundary Conditions of Radiation Gasdynamics

  • Shih-I Pai


For every particular problem of radiation gasdynamics, we have certain initial and boundary conditions. Our problem is to find solutions of the fundamental equations which satisfy these initial and boundary conditions. By initial conditions we mean the velocity distributions and the states of the gas as well as the specific intensity of radiation at certain initial time t = 0. Customarily in radiation gasdynamics, we do not give the spatial distribution of these initial conditions but we only require that the initial values be consistent with the boundary conditions for t = 0 and the fundamental equations. Hence we need to examine the boundary conditions only. In the case of dynamical system with a finite number of degrees of freedom, the motion is determined by the initial position and velocity. For a continuous medium, which has an infinite number of degrees of freedom, the motion is determined not only by the initial conditions but also by the boundary conditions, such as, for example, conditions on the velocity on the boundary of a domain considered at all the time t ≧ 0.


Free Path Specific Intensity Radiative Transfer Radiative Flux Local Thermodynamic Equilibrium 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Born, M., and E. Wolf: Principle of Optics. Pergamon Press, New York.Google Scholar
  2. 2.
    Chandrasekhar, S.: An Introduction to the Study of Stellar Structure. Dover Publications, New York, 1957.MATHGoogle Scholar
  3. 3.
    Garden, R.: Calculation of temperature distribution in glass plates undergoing heat treatment. J. Am. Ceramic Soc. vol. 41, No. 6, pp. 200–209, 1958.CrossRefGoogle Scholar
  4. 4.
    Goulard, R.: Fundamental Equations of Radiation Gasdynamics. Purdue Univ. School of Aero. & Eng. Scien, report A & ES 62–4, 1962.Google Scholar
  5. 5.
    Goulard, R. & M.: One dimensional energy transfer in radiant media. Int. J. Heat & Mass Transfer vol. 1, pp. 81–91, 1960.CrossRefGoogle Scholar
  6. 6.
    Johnson, J. C.: Physical Meteorology. John Wiley & Sons, Inc., New York, 1954.Google Scholar
  7. 7.
    Kivel, B., and K. Bailey: Tables of radiation from high temperature air. AVCO Res. Lab. research report 21, 1957.Google Scholar
  8. 8.
    Kourganoff, V.: Basic methods in transfer problem. Oxford Univ. Press, 1952.Google Scholar
  9. 9.
    Pai, S. L: Introduction of the theory of Compressible Flow. D. Van Nostrand Co., 1959.Google Scholar
  10. 10.
    Pai, S. I.: Some consideration of radiation magnetogasdynamics. Proc. Non-linear Problem. Univ. of Wisc. Press, pp. 47–67, 1963.Google Scholar
  11. 11.
    Penner, S. S.: Quantitative molecular spectroscopy and gas emissivities. Addison Wesley, 1960.Google Scholar
  12. 12.
    Planck, M.: The Theory of Heat Radiation. Dover Publications, New York, 1959.MATHGoogle Scholar
  13. 13.
    Probstein, R. F.: Radiation slip. M. I. T. Fluid Mechanics Lab. Dept. of Mech. Eng. report No. 63–2, 1963.Google Scholar
  14. 14.
    Scala, S. M., and D. H. Sampson: Heat Transfer in hypersonic flow with radiation and chemical reaction. Tech. Inf. series R 630 SD 46, Space Sci. Lab. General Electric Co., Phil. Pa., 1963. Also Supersonic Flow, chemical processes and radiative transfer, Pergamon Press, pp. 319 – 354, 1964.Google Scholar
  15. 15.
    Tellep, D.M., and D. K. Edwards: Radiant energy transfer in gaseous flows Tech. report Lockheed Missile & Space Div. LMSD-288139, 1960.Google Scholar
  16. 16.
    Rosseland, S.: Theoretical Astrophysics. Oxford Univ. Press, 1936.Google 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

Personalised recommendations