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The Rayleigh-Bénard instability phenomenon corresponds to the unstable state in which there is a horizontal layer of an expandable fluid subjected to a temperature gradient. The present work investigates the development of laminar convection flow at different Rayleigh numbers (10³ ≤ Ra ≤ 10⁵) in a rectangular Rayleigh-Bénard cell. The enclosure is differentially or partially heated, and it is filled with air or nanofluid. The aspect ratio is changed between 1 and 6. A mathematical model based on the stream function and vorticity approach (ψ-ω) is used. The study is performed numerically by using the finite difference method and a program created by Python. The obtained results revealed the formation of different structures of rotating flows. In the Rayleigh-Bénard configuration, the increase in the Rayleigh number intensifies the velocity and temperature fields, resulting in a transition from the conduction mode to a …