Critical assessment of numerical algorithms for convective-radiative heat transfer in enclosures with different geometries

The present work elucidates a comparative analysis to investigate the discrepancies between the incompressible and low Mach number approximations for numerically solving combined natural convection with radiative heat transfer in participating medium. The motivation behind the study is to quantify the physical differences concerning fluid flow and heat transfer characteristics between low Mach number and incompressible approximation and to examine the validity of the later for convective-radiative problems in an enclosure. A series of numerical experiments are performed considering natural convection with radiative heat transfer at large temperature difference in a square enclosure with a heated cylinder at its center using both approaches. The heated cylinder of three different geometric configurations viz circular, square and triangular shapes are considered in the present analysis to study the combined effects of various geometric form and influence of surface to surface along with gas radiation on flow and heat transfer characteristics in the cavity. Significant discrepancies are observed between the results of incompressible and low Mach number approximations, particularly for gas radiation, especially at high optical thickness. The local Nusselt number distribution also highlights the inaccuracies arising from the use of incompressible approximation demonstrating that it remains invalid for such scenarios. The results from the present low Mach number formulation are also found to be in good agreement with the compressible flow results of OpenFoam demonstrating the need for low-Mach number approximation in such scenarios. Entropy generation analysis shows that square geometry is the optimum design among the three geometries of heated cylinder as it has the maximum heat transfer and minimum entropy generation.