Conjugate Natural Convection-Surface Radiation in a Square Cavity with an Inner Elliptic Body

In this study, the finite volume method is combined with the discrete ordinate method to study numerically the natural convection coupled to surface radiation in a square cavity with an elliptic inner cylinder maintained at a high temperature \( 299\;{\text{K}} \le T_{H} \le 341\;{\text{K}} \). The cavity is filled with air cooled by a single vertical wall maintained at a cold temperature \( T_{C} = 293\;{\text{K}} \). The hydrodynamic and thermal behaviors of the fluid and the convective and radiative heat transfer are investigated for a several geometric parameters of the elliptical cylinder. These parameters are the inclination angle \( \left| \phi \right| \) ≤ 90° of the elliptic body and the eccentricity \( 0 \le \xi \le 0.98 \). Effect of the Rayleigh number and emissivities of both the inner and the outer surfaces are also investigated. The numerical work is carried out using an in-house CFD code written in FORTRAN. It is found that the geometric parameters of the inner elliptic cylinder have remarkable effects on the streamlines, isotherms and the convective and radiative heat transfer in the enclosure. These effects are generally more dependent on the Rayleigh number for the convective heat transfer than for the radiative one.