The discrete ordinates method (DOM) for the solution of radiative heat transfer problems have received significant attention and development owing to their good compromise between accuracy, flexibility and moderate computational requirement. However, the DOM suffers from the ray effects related to the discretization of the angular distribution of the radiation intensity. The modified discrete ordinate method (MDOM) proved to significantly mitigate ray effects originated from discontinuities or abrupt changes of the wall temperature. This article presents blocked-off region treatment of irregular geometries using a modified discrete ordinates method in Cartesian coordinates. The Cartesian based 2D algorithm can be used to solve radiative heat transfer in irregular geometries by dividing the region into active and inactive regions. It is easier and convenient way of handling 2D irregular geometries than to write an algorithm in curvilinear coordinates. It is capable of handling participating (absorbing, emitting and isotropic or anisotropic scattering) or non participating gray media enclosed by gray diffuse walls. Both radiative and non-radiative equilibrium situations are considered. The walls of the enclosures can have either heat flux or temperature boundary conditions. Cases with curved and obstacle and radiation shield are considered. Some test problems are considered and results are validated with the available results in the literature. Results are found to be accurate for all kinds of situations.

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