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

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 equili...

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Bibliographic Details
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
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Summary: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.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.10177