The Horton–Rogers–Lapwood problem for a non-Newtonian Oldroyd B nanofluid with modulated gravity effects under isothermal boundary conditions is investigated. Both linear and nonlinear stability analyses are performed, with numerical results presented graphically. The nonlinear Boussinesq approximation (NBA) is applied to the buoyancy term in the momentum equation, providing a more accurate representation of fluid behavior under high-temperature gradients, which is essential in advanced heat transfer applications. Consequently, the governing system includes the continuity equation, the Navier–Stokes momentum equation, the equation of state, the energy equation, and the nanoparticle volume fraction equation. A comprehensive stability analysis is conducted for free-free, rigid-free, and rigid-rigid boundary conditions. Additionally, a weakly nonlinear stability study employing the spectral Fourier method under isothermal, tangential stress-free boundary conditions quantifies heat and nanoparticle transport. The analysis reveals the transition from periodic convection to chaotic convection and bifurcation. A reduced Lorenz model is developed to explore the underlying dynamics further, offering deeper insights into the onset and progression of chaotic convection within the system. The NBA can be interpreted as lowering the critical Rayleigh number, thereby facilitating the onset of convection. This behavior contrasts with findings in many studies based on the linear Boussinesq approximation commonly reported in the literature. Gravity modulation enhances heat transfer and induces chaotic patterns within the nonlinear domain. The Darcy number (Da) and scaled nanoparticle Rayleigh number (Rn) promote chaos, while the modified diffusivity ratio (NA) supports periodicity.
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