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Conjugate natural convection-conduction heat transfer in a square enclosure with a finite wall thickness is studied numerically in the present paper. The governing parameters considered are the Rayleigh number 5×103≤Ra≤106, the wall-to-fluid thermal conductivity ratio 0.5≤Kr≤10, and the ratio of wall thickness to its height 0.2≤D≤0.4. The staggered grid arrangement together with MAC method was employed to solve the governing equations. It is found that the fluid flow and the heat transfer can be controlled by the thickness of the bottom wall, the thermal conductivity ratio, and the Rayleigh number.