The effect of vertical eccentricity on natural convection in a rhombic annulus is studied numerically for enclosure gap values (ER) of 0.5 and 0.75, eccentricity (ϵ) values from -0.25 lo 0.25, and Rayteigh numbers (Ra) from I04to 108Negative values of t (inner rhombus displaced downward) lead to an increase in heat transfer. At low Ra there is a critical positive e for which the flow strength is a maximum. At high Ra, increasing positive e results in a decrease in the flow strength and heat transfer. For any ϵ > 0 there is a critical Ra, beyond which there is a decrease in the total heat transfer. This critical Ra increases with decreasing ERvalues.