Stability of the Cattaneo–Christov–Jordan–Mariano Model for Thermal Convection in Porous Media

This study investigates the problem of thermal convection in a porous medium saturated with fluid, governed by extended Darcy’s law and analyzed within the framework of the Cattaneo–Christov–Jordan–Mariano (CCJM) model. The CCJM framework extends Fourier’s law by incorporating finite thermal relaxation, thermal diffusion, and inertial effects, thereby providing a more realistic description of heat transfer in porous systems. A combined linear (stationary and oscillatory) and nonlinear stability analysis is employed to determine the onset of convection. Linear instability, developed through normal mode decomposition, provides the critical Rayleigh number and wavenumber marking the instability threshold, while nonlinear stability, based on the energy method, evaluates finite-amplitude disturbances and identifies subcritical regimes. This work investigates the effects of three dimensionless parameters: the thermal diffusion (Mariano) parameter \(ζ \) , which characterizes the diffusion of heat flux, the Vadasz number Va , which represents inertial effects in porous media, and the Straughan number Sg , which accounts for thermal relaxation. All critical thresholds are computed numerically, and the results demonstrate that increasing \(ζ \) generally stabilizes the system by postponing the onset of convection, whereas inertial and thermal relaxation effects can destabilize the flow by promoting oscillatory modes and triggering convection at lower Rayleigh numbers. These findings provide new insights into thermal convection in porous media by establishing a stricter stability criterion and clarifying how material parameters control the onset of convection, thereby deepening our understanding of thermal stability within the Cattaneo–Christov–Jordan–Mariano (CCJM) model.