On Weakly Nonlinear Convective Instability of Soret-Driven Jeffrey Fluid Flow Through a Porous Layer

Abstract

This study examines the linear and weakly nonlinear stability of double-diffusive Bénard convection in a horizontal permeable layer saturated with a Jeffrey fluid. The momentum equation is formulated using the linear Oberbeck–Boussinesq approximation to account for thermal and solutal density variations, while the concentration equation incorporates the Soret effect to represent thermally induced mass transport. Following non-dimensionalization, small perturbations are imposed on the base state to analyze instability. Linear stability theory determines the onset of stationary convection, whereas weakly nonlinear analysis characterizes heat and mass transfer. Flow structures and transport features are illustrated using streamlines, isotherms, and isosolutes. The results reveal that increasing the Jeffrey parameter destabilizes the system, emphasizing the role of fluid elasticity. For negative values of the solutal Rayleigh number, a negative Soret number delays convection by opposing thermal buoyancy, while a positive Soret number enhances instability. Transient Nusselt number behavior shows that higher Lewis number suppresses oscillations and accelerates system relaxation. Furthermore, positive solutal Rayleigh number enhances early mass transfer, whereas negative solutal Rayleigh suppresses it, and increasing relaxation time transforms streamlines from unicellular to bi-cellular when it greatly exceeds the retardation time.