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Modest, M. F., "Modified Differential Approximation for Radiative Transfer in General Three-Dimensional Media," Journal of Thermophysics and Heat Transfer, Vol. 3, No. 3, July, 1989, pp. 283-288.

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Nonequilibrium Radiative Heating Prediction Method for Aeroassist .. - Hartung (1991)   (Correct)

....moment methods, discrete ordinate methods, or spherical harmonics methods, obtain solutions by approximating the radiative intensity with a series of functions of increasing order [21, Sec. 9. 8] Multi dimensional solutions to the transport problem have been developed by Truelove [26] and Modest [27], but these assume equilibrium flow and the validity of Kirchhoff s law. In addition, Truelove assumes a gray gas, in which the absorption does not vary with wavelength. Cheng and Ozisik [28] have developed a threedimensional algorithm for stagnation flows, but it uses the diffusion approximation ....

....be of reasonable accuracy for all values of optical thickness. Modest has modified the differential approximation to make it even more accurate for small optical depths and generalized it for the three dimensional case. His method gives results of excellent accuracy for all optical conditions [27]. It is adapted below for the current non gray, nonscattering, and nonequilibrium flow. As previously mentioned, the source function in a nonequilibrium, nonscattering medium is S = j e 0 (4:12) The definitions of the incident intensity and flux are repeated here for convenience: G ....

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Michael F. Modest. Modified Differential Approximation for Radiative Transfer in General Three-Dimensional Media. Journal of Thermophysics and Heat Transfer, 3(3), July 1989.


Radiation Transport Around Axisymmetric Blunt Body Vehicles.. - Hartung, Hassan   (1 citation)  (Correct)

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Modest, M. F., "Modified Differential Approximation for Radiative Transfer in General Three-Dimensional Media," Journal of Thermophysics and Heat Transfer, Vol. 3, No. 3, July, 1989, pp. 283-288.

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