Stability of the Cattaneo–Christov–Jordan–Mariano Model for Thermal Convection in a Porous Medium with Variable Gravity
摘要
This study examines thermally induced convective flow in a fluid-saturated porous medium, where momentum transport follows extended Darcy’s law and thermal transport is governed by the Cattaneo–Christov–Jordan–Mariano (CCJM) model, allowing for variations in the gravitational field. The CCJM framework generalizes the classical Fourier heat conduction model to include thermal diffusion, finite thermal relaxation, and inertial effects, while the momentum equation accounts for the presence of a spatially varying gravitational field. Collectively, these effects provide a more physically consistent depiction of heat transport and convective behavior in porous media. The onset of convection is examined through a combined linear analysis, encompassing stationary and oscillatory modes, together with a nonlinear stability framework. Linear stability is evaluated using the normal-mode technique, while the nonlinear stability equations are obtained through the energy method. Numerical simulations are performed using MATLAB to determine the critical stability parameters, and the corresponding plots depict the resulting stability characteristics. The Galerkin single-term approach is used to measure the critical Rayleigh number and the corresponding wavenumber. Four distinct gravity-variation profiles are examined, revealing that the gravity-modulation parameter