Stability analysis for viscoelastic fluid with thermorheological effects: Linear and nonlinear approaches

• Published in: International journal of non-linear mechanics 2025-01, Vol.168, p.104927, Article 104927
• Main Authors: Basavarajappa, Mahanthesh, Bhatta, Dambaru
• Format: Article
• Language: English
• Subjects: Chebyshev-τ method; Energy method; Non-Newtonian fluid; Nonlinear stability analysis; Thermosolutal convection
• ISSN: 0020-7462
• DOI: 10.1016/j.ijnonlinmec.2024.104927

This study investigates the stability analysis of Rayleigh-Bénard configuration for a viscoelastic fluid subject to thermorheological effects, using the D2-Chebyshev-τ method. The fluid is modeled as a third-order viscoelastic fluid. This study accentuates how salting the fluid layer affects the thresholds for the onset of instability in a fluid of third order encompassing physically realistic rigid boundaries. The dynamic model incorporates advection-diffusion of temperature and solute concentration and a modified Navier–Stokes equation. We determine instability thresholds for the complex non-Newtonian fluid by analyzing the linear stability of the steady-state conduction solution. Our analysis proves the strong form of the principle of exchange of stabilities, demonstrating that convective motions can only occur through stationary motion. Additionally, a nonlinear stability analysis using the energy method is performed, deriving an unconditional nonlinear stability criterion. The results provide a comprehensive understanding of how variable viscosity and viscoelasticity impact system stability. Both the viscosity parameter and the third-grade fluid parameter exhibit stabilizing effects. Notably, we observe a discrepancy between the linear and global nonlinear stability results, indicating the presence of a subcritical instability region. This study contributes to the understanding of complex fluid dynamics in non-linear mechanical systems, with potential applications in various industrial and natural processes. •A system of differential equations models the double-diffusive convection in viscoelastic fluid.•The effect of temperature-dependent viscosity on the onset of convection is examined.•The strong form of principle of exchange of stabilities is proved.•Linear analysis determines thresholds above which steady solutions become unstable.•Nonlinear analysis proves the total perturbed energy of the system decays asymptotically.