Spectral Characterization of Local Thermal Non‐Equilibrium Darcy–Bénard–Brinkman Convection With Uniform Internal Heat Generation

This investigation explores the influence of a constant internal heat source on Darcy–Bénard–Brinkman convection in a porous medium under local thermal non‐equilibrium (LTNE) conditions. Both linear and nonlinear stability analyses are conducted for rigid‐rigid isothermal boundaries. This work presents a detailed analysis using a high‐accuracy Chebyshev collocation method under these boundary conditions. The Chebyshev method, with its high spectral resolution, effectively captures sharp boundary layer structures and higher‐order thermal interactions, providing a physically realistic representation of the system dynamics. The study reveals that the constant internal heat source can trigger subcritical instability. In addition, the inter‐phase heat transfer coefficient and the Darcy–Brinkman number exert stabilizing effects, whereas the porosity‐modified conductivity ratio and the internal heat source parameter promote instability. These findings highlight the intricate interplay between internal heating and LTNE conditions and emphasize the necessity of high‐fidelity numerical methods such as the Chebyshev approach for accurately capturing such behaviors.