Comparison of the blocked-off and embedded boundary methods in radiative heat transfer problems in 2D complex enclosures at radiative equilibrium

Abstract

Radiative heat transfer in participating media at radiative equilibrium in two-dimensional complex geometries will be investigated using two Cartesian boundary treatments, i.e. the blocked-off method and the embedded boundary method. The main advantages of Cartesian formulation are to simplify grid generation and using efficient Cartesian solvers for complicated problems. Angular and spatial discretization of the radiative transfer equation are performed using the discrete ordinates method and the finite volume method, respectively. The accuracy of both methods in solution of radiative heat transfer problems in irregular geometries are verified by comparison with benchmark solutions from literatures. Then, in order to investigate all features of the blocked-off and embedded boundary methods, two radiative problems with complex enclosures that contain gray absorbing and emitting medium at radiative equilibrium are examined. The results obtained from the two methods are compared with each other as well as with results obtained by body-fitted grid system. It has been shown that for a medium at radiative equilibrium with Cartesian formulation, the embedded boundary method is the method of choice, especially for calculations near the complex boundaries. It should be noted that for optically thick media, both blocked-off and embedded boundary methods show poor performance.