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A numerical simulation of natural convection in a horizontal porous annulus with an internal wavy surface has been carried out. Governing equations include the heat equation and the hydrodynamics equations under Darcy law and Boussinesq approximation. The mathematical model formulated with the temperature-stream function is solved numerically using the finite difference method with the alternating direction implicit scheme. Results show that the heat transfer and the convective instability depend strongly on the waviness of the inner cylinder. Last, streamlines and isotherms are presented for different waviness parameters of the internal wall for better understanding of the influence of amplitude and number of undulations on the thermo-convective instabilities. [ABSTRACT FROM AUTHOR]