This paper reports on the effect of buoyancy ratio due to both heat and mass transfer on natural convection in a porous enclosure between two isothermal concentric cylinders of rhombic cross sections. For negative values of the buoyancy ratio, buoyancy forces due to heat and mass transfer are in opposite directions (opposing mode), while for positive values they are in the same direction (aiding mode). Numerical results demonstrate that the flow strength increases as the absolute value of the buoyancy ratio increases. In the opposing mode, the eye of the vortex flow is located in the lower half of the enclosure, while in the aiding mode it is positioned in the upper part of the annulus. The average Nusselt and Sherwood number values increase as the absolute value of the buoyancy ratio moves away from 1, with values obtained in the aiding mode being higher than corresponding values achieved in the opposing mode. A comparison is also made between the computed average Nusselt and Sherwood number values and similar ones obtained in a circular annulus having the same inner and outer perimeters as the rhombic enclosure. Predictions indicate large percent difference in values, demonstrating that circular geometries cannot be exploited to accurately predict heat and mass transfer in complex geometries.