Linear and Nonlinear Stability Analysis of Nano-Fluid Flow through a Low-Permeable Porous Channel

The stability of thermal convection in a nanofluid-saturated porous layer with impermeable boundaries is investigated by considering the unsteady Darcy’s model along with the horizontal pressure gradient. The analysis employs linear stability theory, with water as the base fluid in thermal equilibrium with the porous matrix under a single thermal phase. The governing stability equations are formulated as an eigenvalue problem and solved using one-term and higher-order Weighted Residual Galerkin Methods (WRGM). Critical values of the Darcy-Rayleigh number, wave number and wave speed are examined for varying horizontal pressure gradients, Prandtl numbers, nanoparticle volume fractions and thermal diffusivity ratios. The findings indicate that higher thermal diffusivity ratios and pressure gradients stabilize the system, while increased nanoparticle volume fractions and higher Prandtl numbers promote instability. The time evolution of streamlines and isotherms is simulated by solving a nonlinear system of PDEs using the method of lines, combined with regularization and finite difference techniques. Nonlinear stability analysis reveals that nanofluids demonstrate enhanced stability compared to the base fluid. Notably, the analysis identifies a subcritical region between the convection onsets predicted by linear and nonlinear methods, showing that convection begins earlier in the nonlinear regime. These insights are crucial for optimizing nanoparticle concentrations in thermally driven systems, ultimately enhancing heat transfer efficiency.