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A new fractional step method in conjunction with the finite element method is proposed for the analysis of the thermal convection and conduction in a fluid region expressed by the momentum equations, the equation of continuity and the energy equation. This paper focuses on the features of the present finite element method which gives a simple way of treating the Neumann boundary condition for the pressure Poisson equation. The applicability and effectiveness of the proposed scheme are illustrated through the numerical examples of the two‐dimensional natural convection flow in enclosures with several Rayleigh numbers.