Abstract
In this study, the integral of the radiative source function appearing in the apparent solution of the Radiative Transfer Equation (RTE) is approximated by the two-point trapezoidal rule which is different from the Taylor series expansion approximation used in the Finite Volume Method (FVM) or the discrete ordinates interpolation method. The resulting equation derived from the trapezoidal rule approximation has much simpler form than that obtained from the existing Taylor series approximation. The approximate equation of transfer by the trapezoidal rule is applied for the discrete ordinates interpolation method using nonorthogonal grid systems to predict the radiative heat transfer in 3-D enclosures filled with a gray, absorbing, emitting and scattering medium. The upstream intensity and the source function required for analyses are determined by a linear interpolation on a diagonally placed triangular plane that is reported to be very simple for radiative transfer analyses in three dimensional irregular systems. Numerical results indicate that good accuracy is obtained by using the trapezoidal rule which showed fairly good agreement with the results from the zone method or the original discrete ordinates interpolation method both of which are considered to be more accurate as compared to the conventional S-N discrete ordinate method and the FVM. The trapezoidal rule proposed in this study is successful for nonorthogonal grid systems and it can be used for analyses of the radiative transfer in three dimensional irregular enclosures.
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Kim, TK., Seo, SH., Min, DH. et al. Study on radiation in 3-D irregular systems using the trapezoidal rule approximation on the transport equation. KSME International Journal 12, 514–523 (1998). https://doi.org/10.1007/BF02946367
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DOI: https://doi.org/10.1007/BF02946367