Soret Effect on the Instability of Double-Diffusive Convection in a Saturated Vertical Brinkman Porous Layer of Oldroyd-B Fluid

The instability of the double-diffusive convection of an Oldroyd-B fluid in a vertical Brinkman porous layer caused by temperature and solute concentration differences with the Soret effect is studied. Based on perturbation theory, an Orr–Sommerfeld eigenvalue problem is derived and numerically solved using the Chebyshev collocation method. The effects of dimensionless parameters on the neutral stability curves and the growth rate curves are examined. It is found that Lewis number Le, Darcy–Prandtl number PrD, and normalized porosity η have critical values: When below these thresholds, the parameters promote instability, whereas exceeding them leads to suppression of instability. In addition, for Le < Lec2 (a critical value of Le), Sr strengthens the instability of the flow, while for Le > Lec2, Sr suppresses it. These results highlight the complex coupling of heat and mass transfer in Oldroyd-B fluids within porous media.