Nonlinear stability analysis of double‐diffusive convection in Kelvin–Voigt fluid with chemical reaction

• Published in: Mathematical methods in the applied sciences 2024-11, Vol.47 (16), p.12720-12741
• Main Authors: Basavarajappa, Mahanthesh, Bhatta, Dambaru
• Format: Article
• Language: English
• Subjects: chemical reaction; Chemical reactions; Convection cooling; Convection modes; Damkohler number; double‐diffusive convection; Ekman damping; energy method; Friction; Heat transmission; Kelvin–Voigt; Navier–Stokes–Voigt fluid; Stability; Stability analysis; Systems stability; Temperature dependence; Thresholds; Traveling waves
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.10177

The influence of Rayleigh friction and chemical reaction on the onset of double‐diffusive convection in a Navier–Stokes–Voigt (NSV) fluid layer is investigated by conducting linear instability and nonlinear stability analyses. The fluid layer is subjected to isothermal conditions and chemical equilibrium at the boundaries. The solubility of the dissolved component exhibits a linear dependency on temperature. The analysis is conducted for two distinct cases: the fluid layer is heated and salted from the bottom (case‐1), and the fluid layer is heated from the bottom and salted from the top (case‐2). Analytical expressions for the thermal Rayleigh number are obtained for both linear and nonlinear theories, and these expressions depend on Kelvin–Voigt, Rayleigh friction, solutal Rayleigh, Lewis, Prandtl, and Damkohler numbers. Including the Rayleigh friction term in the NSV fluid model improves the stability of the system and hence instability occurs with less ease. For lower solutal Rayleigh numbers, convection commences in the stationary mode and subsequently transitions to the traveling wave mode occurred in case‐1. The Damkohler number plays a significant role in the linear instability thresholds. It is also found that the Kelvin–Voigt number acts as a stabilizing factor for oscillatory mode convection. The comparison between linear and nonlinear thresholds unveils the region characterized by subcritical instability.