A numerical study is presented for the laminar natural convection in a differentially heated horizontal bare and finned rhombic annulus filled with air. An adaptive finite-element method is adopted to predict the complex recirculating buoyancy driven flows. Simulations were conducted for cavity widths Eg ranging from 0.25 to 0.875, for two different fin configurations with fin lengths l varying from 0.3 to 0.7 and Rayleigh numbers Ra ranging from 10(3) to 10(7). Results indicate that the heat transfer is maximized for a narrow cavity Eg = 0.25 with fin length l = 0.7 (configuration 1). In this case, conduction prevails over convection. On the other hand, when convection is dominant, the heat transfer is maximum for Eg = 0.875 and l = 0.7. The equivalent thermal conductivity k(equ) was correlated in terms of Ra for all geometries via k(equ) = CRan.