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Conjugate natural convection heat transfer inside a differentially heated square cavity having a heat conducting and sinusoidal corrugated solid partition has been investigated numerically in the present study. The fluid flow and the heat transfer within the cavity are governed by two-dimensional Navier–Stokes and energy equations, and those are solved using the finite element method. Numerical simulation is carried out for a wide range of Rayleigh number (10³ ≤ Ra ≤ 10⁹) with a fixed Prandtl number (Pr = 0.71) since the working fluid in the cavity is considered as air. The variations of both corrugation amplitude and corrugation frequency of the sinusoidal partition wall on the average Nusselt number of the heated wall are observed in order to assess the influence of the roughness of the solid partition on the heat transfer characteristics of the cavity. Moreover, different types of partition material are selected …