Role of the Maxwell–Cattaneo effect on convection instability in a vertical Brinkman porous layer

This study investigates the influence of the Maxwell–Cattaneo (MC) effect on convection instability in a vertical Brinkman porous layer. The MC effect modifies the classical Fourier's law for temperature by incorporating the upper convective Oldroyd derivative. The Chebyshev collocation method is used to solve the Orr–Sommerfeld eigenvalue problem, yielding the temporal growth rates and neutral stability curve. The results demonstrate that the MC effect influences convection instability in two distinct ways, depending on whether the fluid or solid phase dominates. When the MC effect is primarily in the solid phase, the temporal growth rate decreases due to its stabilizing influence. Conversely, when the MC effect is more prominent in the fluid phase, the temporal growth rate increases, indicating an amplification of instability. The neutral stability curves show a critical threshold for the Cattaneo number of fluids (Cf): instability is suppressed when Cf is below this threshold, while it is enhanced when Cf exceeds this value. Moreover, the averaged Cattaneo number (Ca), representing the combined effects of the solid and fluid phases, induces oscillations in the neutral stability curves, with the amplitude of these oscillations increasing as Ca increases. Specifically, for small Cf, increasing Ca promotes instability, whereas for larger Cf, instability is suppressed.