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An exact solution of linearized flow of an emitting, absorbing and scattering grey gas

Cheng, Ping and Leonard, A. (1971) An exact solution of linearized flow of an emitting, absorbing and scattering grey gas. Journal of Fluid Mechanics, 45 (4). pp. 673-699. ISSN 0022-1120. doi:10.1017/S0022112071000272.

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The governing equations for the problem of linearized flow through a normal shock wave in an emitting, absorbing, and scattering grey gas are reduced to two linear coupled integro-differential equations. By separation of variables, these equations are further reduced to an integral equation similar to that which arises in neutron-transport theory. It is shown that this integral equation admits both regular (associated with discrete eigenfunctions) and singular (associated with continuum eigenfunctions) solutions to form a complete set. The exact closed-form solution is obtained by superposition of these eigen-functions. If the gas downstream of a strong shock is absorption–emission dominated, the discrete mode of the solution disappears downstream. The effects of isotropic scattering are discussed. Quantitative comparison between the numerical results based on the exact solution and on the differential approximation are presented.

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Additional Information:© 1971 Cambridge University Press. Reprinted with permission. (Received 7 October 1969 and in revised form 24 August 1970) The authors would like to take this opportunity to thank M.W. Rubesin for his interest. Thanks are also due to Mrs E. Williams for her capable assistance in the numerical work. For the case of the first author (P.C.), this work was performed while he was in receipt of a National Academy of Sciences-National Research Council Post-doctoral Resident Associateship.
Issue or Number:4
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ID Code:10886
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Deposited On:15 Jun 2008
Last Modified:08 Nov 2021 21:11

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