Influence of Local Thermal Nonequilibrium and Thermal Gradients on Magneto‐Darcy‐Rayleigh‐Bénard Convective Stability With Heat Generation

In this study, we employ a standard perturbation technique to analyze the onset of Rayleigh‐Bénard convection in a horizontally oriented, electrically conductive fluid layer overlying a porous substrate. The system is bounded laterally by rigid, adiabatic walls and subjected to internal heat generation, a uniform vertical magnetic field, and local thermal nonequilibrium (LTNE) conditions. The analysis is conducted within the Darcy regime and incorporates various temperature gradient (TG) profiles. We investigate how different TG configurations influence the onset of convection, particularly under thermally adiabatic boundary conditions at the upper and lower surfaces. Critical Rayleigh numbers are determined by solving the corresponding eigenvalue problem for configurations with both rigid‐bottom/free‐top boundaries, incorporating surface tension‐driven velocity boundary conditions. The study further examines the effects of parameters such as the modified porosity ratio, thermal diffusivity ratio, and heat source intensity, emphasizing their role in promoting LTNE under six distinct TG models. Perturbation analysis reveals that maximum convective activity occurs at the mid‐plane for the inverted parabolic (Model‐3) and Dirac delta (Model‐6) temperature gradients. Magneto‐convective behavior under LTNE is visualized in the presence of a vertical magnetic field and volumetric heat generation, providing insights into the thermal system's behavior under complex boundary and gradient conditions. The results align well with existing literature, supporting their relevance to thermal management in energy systems, biomedical devices, aerospace structures, electronic cooling, and geophysical processes.