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The present article investigates the stability of the mixed convective flow of nanofluids through a horizontal porous channel under the influence of a constant pressure gradient, utilizing the local thermal nonequilibrium (LTNE) model. The governing equations are derived by integrating the Oberbeck-Boussinesq theory with the Darcy model for low-permeability porous media. Using linear stability theory, we formulate a generalized eigenvalue problem (GEP) in terms of non-dimensional parameters. The weighted residual Galerkin method (WRGM) is then employed to solve the GEP, and the results are compared analytically. The findings of this study reveal that a horizontal pressure gradient initiates convection in an oscillatory mode rather than a stationary one. We identify that the interphase scaled heat transfer coefficient, thermal diffusivity ratio, nanoparticle volume fraction, and horizontal pressure gradient collectively influence the onset of oscillatory convection. Notably, our investigation into Titanium Oxide (TiO2), Copper Oxide (CuO), and Aluminum Oxide (Al2O3) nanoparticles reveals that TiO2 particles enhance the onset of convection compared to Al2O3 and CuO, while CuO nanoparticles exhibit greater thermal stability. Further, the nonlinear stability analysis is performed using the method of lines in conjunction with regularization and finite difference schemes for spatial derivatives. The time evolution of all field variables is simulated through the visualization of streamlines and isotherms, providing a detailed representation of the system's dynamics. Additionally, the critical values of the Darcy-Rayleigh number are computed and compared for both linear and nonlinear stability analyses. The results demonstrate the equivalence of linear instability and nonlinear stability boundaries in the absence of a constant pressure gradient, whereas subcritical instability becomes apparent in its presence. These insights advance our understanding of mixed convective flows in porous media, with potential implications for various engineering and environmental applications. [ABSTRACT FROM AUTHOR]