Unified framework for buoyancy induced radiative-convective flow and heat transfer on hybrid unstructured meshes

The development of a non-Boussinesq flow solver for simulating combined radiative-convective heat transfer is presented on arbitrary polygonal meshes using the ideas of low-Mach number asymptotics. A segregated approach for solving the governing equations using a fractional step methodology on finite-volume method is adapted to handle the low-Mach number formulation. Simulations are carried out for two- and three-dimensional problems involving combined convective-radiative heat transfer both in the small and large temperature difference regimes. It is shown through investigations over a range of Gay-Lussac's and Planck numbers that non-Boussinesq effects could become significant due to the sole influence of large temperature difference and radiative heat transfer. Furthermore, the influence of non-Boussinesq effect on overall heat transfer is larger for the three-dimensional simulation of a given radiation-convection heat transfer problem relative to the two-dimensional assumption for the same problem. Interestingly, even at the low-temperature difference with the presence of significant radiation the Boussinesq approximation fails. This study clearly identifies the limits of validity of the Boussinesq approximation and conclusively prove that solutions to radiation-convection heat transfer problems are best acquired using a quasi-incompressible approach as described in this work.