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This study explores the linear and nonlinear stability of double-diffusive convection in a couple-stress fluid-saturated porous layer, with explicit consideration of viscous dissipation effects. The governing equations are formulated using the Darcy model under a horizontal basic state maintained by constant temperature and concentration differences across the boundaries. Linear stability is analyzed by introducing infinitesimal disturbances and solving the associated eigenvalue problem using the Chebyshev–Tau spectral method, while nonlinear stability thresholds are determined through the Runge–Kutta method coupled with a shooting method. Motivated by the limited work on nonlinear stability analysis of convective systems influenced by viscous dissipation, the present work provides a detailed parametric investigation by treating the thermal Rayleigh number $R_z$ as the eigenvalue. The critical stability characteristics, including critical wave numbers, are examined over wide ranges of the Lewis number ($Le$), Gebhart number ($Ge$), and solutal Rayleigh number ($S_{z}$). The results show that viscous dissipation generates a nonlinear base temperature profile and exerts a pronounced destabilizing influence on the onset of convection. In contrast, the couple-stress parameter significantly enhances stability, effectively suppressing the destabilizing effects associated with viscous heating. Furthermore, a negative solutal Rayleigh number ($S_{z}$ < 0) is found to stabilize the system, whereas a positive solutal Rayleigh number ($S_{z}$ > 0) promotes instability.
Overall, this study provides the combined influence of double diffusion, viscous dissipation, and couple-stress effects on both linear and nonlinear stability thresholds, offering new physical insight into stability transitions in porous media relevant to thermal engineering, geophysical flows, and porous material systems.
| References | Straughan, B.: The Energy Method, Stability, and Nonlinear Convection, 2nd edn. Springer, New York (2013). • Dubey, R. and Murthy, P. V. S. N.: The onset of convective instability of horizontal throughflow in a porous layer with inclined thermal and solutal gradients. Physics of Fluids. 30, 074104 (2018). DOI: 10.1063/1.5040901 • Straughan, B.: Nonlinear stability for thermal convection in a Brinkman porous material with viscous dissipation. Transport in Porous Media. 134(2), 303–314(2020). DOI: 10.1007/s11242- 020-01446-5 |
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| Country | India |
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