In this article, we study the influence of the Rayleigh number on the natural convection of air between two square cavities. The internal cavity is subjected to a constant flow of heat while the external cavity is kept at a constant temperature. This temperature difference leads to a decrease in the density that represents the motor of the movement. Especially since the information on pressure is not sufficient, we have used the formalism vorticity current function to eliminate the pressure term in the equation of movement. Adimensionnals equations transfers were solved using the finite volume. In order to examine the heat transfer between the cavity and the fluid, we have used Rayleigh values ranging from 103 ≤ Ra ≤ 106 and Prandtl Pr = 0.7. The results obtained have shown from Rayleigh number Ra = 103, the isotherms line are quasicircular and bicellular current lines of high intensity on both sides of the median axis. When we increase the Rayleigh number from Ra = 104 through Ra =105 to Ra = 106, we have noticed that the isotherms tend to decrease and split. This results in the formation of small oscillations in the middle of the internal cavity. For the current lines, we have noticed the formation of secondary cells in the upper cavity and low movement in the horizontal cavity.