Natural convection in square-cross-sectional inclined enclosures bounded by two attached solid walls (composite wall) was simulated by a numerical technique in this study. Conduction heat transfer through each part of a composite wall was examined for different solid wall thicknesses and thermal conductivities. The opposite wall was accepted as thin and it was isothermal at a lower temperature than that of the outside of the composite wall, while the remaining walls were adiabatic. The governing equations were solved by finite-difference technique for the governing parameters for different Rayleigh numbers, ranging from 103 to 106, with the thickness ratio of solid walls greater than 0.05 (for left vertical wall) and less than 0.2 (for right vertical wall), and thermal conductivity ratios for first and second materials to the fluid ranging from 1 to 5 and inclination angle ranging from 0 degrees to 180 degrees. The written code was tested with similar numerical and experimental studies in earlier literature and a good agreement was found. It was proved that lower heat transfer occurred when the wall with lower thermal conductivity ratio was located at the outside of the composite wall and it affected the flow strength in the enclosure. Inclination angle and other governing parameters were also used as control parameters for heat and fluid flow.