THREE-DIMENSIONAL NUMERICAL SIMULATION OF THE INTERACTION BETWEEN NATURAL CONVECTION AND RADIATION IN A DIFFERENTIALLY HEATED CAVITY IN THE LOW MACH NUMBER APPROXIMATION

Many studies have been devoted to the interaction between natural convection and radiation heat transfer in a differentially heated cavity. This problem has already been treated using the Boussinesq approximation. The main purpose of t his study is to extend this interaction to the low Mach number approximation (in 3D), for both tra nsparent and participating media. The NavierStokes and energy equations written for an ideal ga s are solved using a finite volume method, while the discrete ordinates method is used to solve the radiation transfer equation. The coupling between the energy equation and the radiation transfer is d one by adding an additional source term in the energy equation and via the radiation heat exchange between the surfaces bounding the computation domain. The work is first validated using the Bouss ine q approximation mainly by investigating the distribution of the heat flux on the hot isothermal wall. Then some simulations are presented highlighting the differences between the low Mach n umber and the Boussinesq approximations.