In this article, the analyses of heat transfer and free convective motion have been carried out numerically for various structures. The solution is based on a finite element method with the frontal solver to examine the flow parameters and heat transfer characteristics. Several dome configurations--such as flat, inclined, and dome shapes--are considered for the top of the enclosure. A general conic equation is considered to represent the dome as circular, elliptical, parabolic, or hyperbolic shape. The findings from this study indicate that the convective phenomenon is greatly influenced by the shape of the top cover dome and tends to form a secondary core even at a moderate Rayleigh number when compared with an equivalent rectangular enclosure. In addition, the circular and elliptical shapes of the dome give higher heat transfer rate. The effect of various "offset" of the dome and inclined roof on convective heat transfer is also found to be quite significant. However, beyond 0.3 of offset of the top cover for the dome and inclined roof, the change in overall heat transfer rate is minimal. The heat transfer coefficients of dome shaped and inclined roof enclosures are given and discussed.