Natural convection in air-filled, inclined enclosure is numerically studied by using Patankar’s method. The enclosure was composed of the partial horizontal cylinder limited by a plate. Calculation was carried out for a wide range of modified Grashof number (Gr*) at three aspect ratios of enclosure and the heat transfer rate and mode of natural convection were determined. The minimum heat transfer rate was found to occur at 30-45-degrees of inclination. At high Gr*, the heat transfer is affected by secondary buoyancy forces, generated by the inclination. The utilization of the bicylindrical coordinates seems well adapted for the study of this type of enclosures and must frequently applied for different practical problems. Now, we try to improve the performances of our calculation code to be used for the study of other enclosures which are limited by two planes.