Nonlinear Stability Analysis of Oldroyd‐B Non‐Newtonian Fluid in a Reactive Saturated Porous Medium

ABSTRACT This study examines double‐diffusive convection in a reactive porous layer saturated with an Oldroyd‐B viscoelastic fluid, a configuration relevant to catalytic porous reactors, geothermal systems, polymeric filtration, and biochemical transport. The combined effects of viscoelastic relaxation–retardation, chemical reactions, and heat‐mass diffusion significantly alter flow stability, yet a unified analysis of these mechanisms is largely lacking. The objective of this work is to determine how a first‐order chemical reaction and Oldroyd‐B rheology influence the onset of stationary and oscillatory convection, as well as the resulting heat and mass transfer. The governing Darcy–Brinkman equations are formulated using the Boussinesq approximation, and linear stability analysis with a Galerkin approach is employed to determine critical Rayleigh–Darcy numbers. A weakly nonlinear analysis is further used to evaluate the Nusselt and Sherwood numbers.