The effect of wall heat conduction on natural convection heat transfer in cavities has gained attention of many researchers in recent years due to its wide application areas in engineering such that building heating and cooling and thick enclosures , etc . 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 to fluid thickness ratio (0.5<=L1/L2<=1.5) , the ratio of (left or right) solid thickness to the height )(D=L1/H=0.5,0.6667,0.75) and the aspect ratio (H/L= 0.5,1,1.5) . The main focus of the study is on examining the effect of conduction in the wall on the natural convection flow .The results are presented to show the effect of these parameters on the heat transfer and fluid flow characteristics
