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A numerical simulation was conducted to study the free convection of Ag/H2O nanofluid between a square cavity with cold walls and an egg shaped cylinder with a hot wall. Utilizing the egg equation, dimensionless governing equations were solved using the Galerkin Finite Element Method (GFEM). In this work, several parameters were studied, i.e. Rayleigh number (10³ ≤ Ra ≤ 106), volume fraction (0 ≤ φ ≤ 0.05), position (-0.2 ≤ Y ≤ 0.2), and orientation angle (-90° ≤ γ ≤ 90°). The numerical results are presented as streamline contours, isotherm contours, and local and average Nusselt numbers. Moreover, the results were used to analyze the fluids' structure, temperature distribution, and heat transfer rate. The numerical results confirmed that the stream intensity value increased with an increase of the Rayleigh number as well as the movement of the cylinder towards the bottom wall for all values of the orientation angle. Variation of the vertical position of the cylinder inside the cavity had a noticeable effect on 𝑁𝑢𝐿, which increased by 50% at γ = -90°, and by 58% at γ = -45°. However, at Y = -0.2, 𝑁𝑢𝐿 increased by 58% at γ = -45° and decreased by 7% at γ = -90°. The highest heat transfer rate was obtained at high Rayleigh number (Ra = 106), volume fraction (φ = 0.05), negative position (Y = -0.2), and the highest positive orientation angle (γ = 90°). [ABSTRACT FROM AUTHOR]