Buoyancy-driven natural-convection heat transfer in enclosures has been the subject of considerable research with applications to electronic packaging, solar collectors, and shipping containers for spent nuclear fuel. A numerical study has been carried out to predict combined natural-convection and radiation heat transfer in the annular region between concentric tubes. The inner tube was volumetrically heated. Both tubes were of finite conductance. The surfaces of the annular region were diffuse and gray. The gas in the annulus was assumed to be nonparticipating. A newly developed hybrid finite element finite difference method was used for the study. This method combines finite element discretization of geometries with finite difference discretized solution procedures for the governing differential equations. This study examined the effects of surface radiative properties and material conductivities on the temperature and velocity fields and on local heat transfer rates. Fluid Rayleigh numbers ranging from 101 to 107, ratios of solid to fluid region thermal conductivities ranging from 10 to 104, and surface total hemispherical emissivities ranging from 0.0 to 1.0 were examined in this study. It was found that the heat transfer across the annulus was dominated by conduction and radiation for the lower Rayleigh number flows. As the fluid Rayleigh number increased, convection became a primary mode of heat transfer. As the surface emissivity was increased in the annulus, the average Nusselt number on the inner tube surface decreased. The ratio of thermal conductivity was found to have little effect on the convective and radiative modes of heat transfer, for a fixed value of the fluid Rayleigh number, when the ratio was >100. When the conductivity ratio was <100, the inner tube was thermally coupled to the fluid region, and the conductivity ratio affected the distribution of convective and radiative flux distributions, resulting in local peaks and valleys in the temperature of the inner tube.