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Application of singular eigenfunction expansions to the propagation of periodic disturbances in a radiating grey gas

Cheng, Ping and Leonard, A. (1971) Application of singular eigenfunction expansions to the propagation of periodic disturbances in a radiating grey gas. Physics of Fluids, 14 (5). pp. 906-919. ISSN 0031-9171. doi:10.1063/1.1693547.

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The effect of thermal radiation on the propagation of small disturbances generated by the harmonic oscillation of a planar wall, either in position or temperature or both, is considered. By separation of variables, it is shown that the governing linearized equations can be reduced to a homogeneous integral equation that admits both regular and singular solutions to form a complete set; thus, the problem can be solved by the application of singular eigenfunction expansions analogous to those used in neutron-transport theory. An exact closed form solution is obtained for disturbed quantities in the flow and radiation fields. The exact solution shows that the disturbances consist of a damped continuum mode with infinite wave speed in addition to two discrete modes with finite wave speed. One of the discrete modes represents the "modified classical" wave whereas the other discrete mode plus the continuum mode corresponds to the radiation-induced wave. For sufficiently small Bouguer numbers, the discrete mode of the radiation-induced wave disappears. The newly found continuum mode damps faster than the discrete mode. Consequently, only the discrete modes persist away from the boundary. The differential approximation is found to predict the modified classical wave accurately but predicts the radiation-induced wave only approximately. The implications as well as the accuracy of the differential approximation are discussed and compared.

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Additional Information:© 1971 American Institute of Physics. Received 10 November 1969. The authors wish to thank M.W. Rubesin and B.S. Baldwin, Jr., for their interest. They also wish to thank E. Williams for her capable assistance in the numerical work. For the case of the first author (P.C.), the work was carried out while he was pursuing a National Academy of Science-National Research Council resident associateship.
Issue or Number:5
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5335
Deposited By: Tony Diaz
Deposited On:11 Oct 2006
Last Modified:08 Nov 2021 20:24

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