Abstract In this work, we consider a two-dimensional numerical study of conjugate natural convection in a square enclosure. The left vertical wall of the enclosure is thick with a finite thermal conductivity, while the other three walls are taken to be of zero thickness. The enclosure is subjected to horizontal temperature gradient: the vertical boundaries are isothermal at different temperatures whereas the remaining walls are adiabatic. Finite volume method is used to solve the dimensionless governing equations. The physical problem depends on five parameters: Rayleigh number (500≤Ra≤1