Natural convection flows in a cubical air-filled cavity that has one pair of opposing faces isothermal at different temperatures, $T_h;and;T_c$, respectively, the remaining four faces having a linear variation from $T_c;to;T_h$ are numerically simulated by a solution code(PowerCFD) using unstructured cell-centered method. Special attention is paid to three-dimensional flow and thermal characteristics according to the variation of inclination angle $ heta$ of the isothermal faces from horizontal: namely $ heta=0^{circ},;15^{circ},;30^{circ},;45^{circ},;50^{circ},;60^{circ},;75^{circ};and;90^{circ}$. Comparisons of the average Nusselt number at the cold face are made with experimental benchmark results found in the literature. It is demonstrated that the average Nusselt number at the cold face has a maximum value around the inclination angle of $50^{circ}$. It is also found that the code is capable of producing accurately the nature of the laminar convection in a cubical air-filled cavity with differentially heated walls.