CFD Study of Low Mach Number Conjugate Natural Convection & Radiation

Conjugate natural convection combined with radiation in a vertical annulus with a centrally located vertical heat generating rod is studied numerically. The governing equations are discretised on a staggered mesh and solved using a pressure-correction algorithm for both Boussinesq and Low Mach number equations. A parametric study is performed by varying the Grashof number, aspect ratio, solid-to-fluid thermal conductivity ratio and overheat ratio over wide ranges. The interaction of natural convection with surface radiation is studied using radiosity formulation. Results are obtained for the local Nusselt numbers on the inner and outer boundaries, the axial variation of the centre line and interface temperatures, maximum solid, average solid and average interface temperature variations. The results show that simplification of the conjugate problem with heat generation by the prescription of an isoflux boundary condition on the rod surface can be inaccurate at higher aspect ratios and the solution of the conjugate problems is necessary. Correlations are developed for the Nusselt number and the dimensionless temperatures of interest in terms of the parameters of the problem.