This study conducts numerical analyses and experiments on natural convection heat transfer in an eccentric horizontal annuli between a heated outer tube and a cooled inner tube with different orientation. The outer tube is an elliptical tube, and the inner tube is a cylindrical tube. Experiments are conducted with the outer tube oriented to the vertical side, and horizontal side, respectively. The numerical analyses were performed by changing the oriented angle and eccentricity parameters. Results obtained for different conditions are presented as temperature profiles, flow patterns, local Nusselt number, and total heat transfer. It is found that the heat transfer enhancement effect or heat transfer obstruction effect for the total heat transfer is changed by eccentricity and oriented angle.