In this work, we consider a two-dimensional numerical study of a rectangle cavity filled with an air with two vertical conductive walls of finite thickness. The enclosure is subjected to horizontal temperature gradient, the vertical boundaries are isothermal at different temperatures whereas the remaining walls are adiabatic. The theoretical study involved the numerical solution of the Navier-stokes and energy equations by using finite difference method. The stream-vorticity formulation was used in the mathematical model. The physical problem depends on five parameters: Rayleigh number (1000˂ Ra˂ 1000000), the Prandtl number (Pr= 0.7), the wall to fluid thermal conductivity ratio (0.1≤ Kr≤ 10), solid