M1 model for radiative heat transfer in absorbing, emitting, and scattering medium

• The radiative heat transfer in participating medium was analyzed with the M1 model.
• A radiation code based on the M1 model has been developed.
• The M1 model was applied to three different test cases.
• The M1 model was solved by the central difference technique instead of the HLLE.
• The M1 model results were considerably accurate and sensitive in the studied cases.

The M1 model has been extended to analyze the radiative heat transfer in the 1-D and 2-D enclosures containing absorbing, emitting, and scattering medium. The governing differential equations for the M1 model were solved numerically by the central difference technique instead of the Harten-Lax-van Leer-Einfeld type approximate Reimann solver used in the previous studies. The predictive accuracy of the model was tested by calculating both an infinite parallel plate and an infinite concentric cylindrical enclosure for 1-D test cases. In addition, the 2-D rectangular gray semitransparent media were also studied to test the predictive accuracy of the M1 model and then they were compared to the benchmark solutions available in the literature. The results of the M1 model were found to be in good agreement with the exact results of the studied cases.