Double-diffusive Rayleigh–Marangoni–Bénard instability of viscoelastic fluids in a fluid–porous channel with Soret and Dufour effects

This study investigates the instability of double-diffusive Rayleigh–Bénard and Marangoni convection of viscoelastic fluids in a coupled fluid–porous channel in the presence of Soret and Dufour effects. Linear stability analysis reduces the governing equations to generalized eigenvalue problems solved by the Chebyshev tau method, while energy budgets identify the dominant instability mechanisms. The results show that the depth ratio has opposite effects, destabilizing thermal Rayleigh–Bénard convection but stabilizing thermal Marangoni convection. A positive Dufour number exerts a non-monotonic influence only on thermal Marangoni convection, whereas a positive Soret number always destabilizes it. In addition, increasing the strain retardation time suppresses oscillatory instability, whereas increasing the stress relaxation time promotes it. Larger Biot numbers stabilize both types of convection, while the effect of the Sherwood number depends on the solutal driving. In the coupled convection, thermal Marangoni convection promotes thermal Rayleigh–Bénard instability, whereas solutal Marangoni convection suppresses it. Moreover, Rayleigh–Bénard forcing has a stronger influence on Marangoni instability than Marangoni forcing has on Rayleigh–Bénard instability.