Impact of Maxwell–Cattaneo effect on thermal convection instability in vertical porous layer saturated with an Oldroyd-B fluid

Abstract The investigation focuses on the Maxwell–Cattaneo (MC) effect on the thermal convection instability in a vertical porous layer saturated with an Oldroyd-B fluid. The MC effect modifies the conventional Fourier’s law for temperature by incorporating the upper convective Oldroyd derivative. The flow through the porous layer is modeled by the Darcy‒Oldroyd model. Using the Chebyshev collocation method addresses an Orr-Sommerfeld eigenvalue problem. Analysis of temporal growth rates reveals that the MC effect causes the originally stable flow to become unstable. Furthermore, the study finds double impacts of the MC effect on convection instability depending on whether it is primarily influenced by the fluid or the solid phase. Neutral stability curves highlight a critical threshold for the averaged Cattaneo number ( C a ) of both solid and fluid. When C a falls below this critical value, instability is suppressed, but when it exceeds this value, instability is magnified. The analysis also reveals that viscoelasticity parameters can impact the system by either stabilizing or destabilizing it. A rise in the retardation time parameter ( λ 2 ) exerts a stabilizing influence, whereas an increase in the relaxation time parameter ( λ 1 ) exhibits a destabilizing effect.