Nonlinear stability analysis for double-diffusive convection when the viscosity depends on temperature

Abstract

Models of double-diffusive convection in a fluid layer with the viscosity having linear dependence on the temperature are analyzed here. The density is assumed to have a quadratic dependence on temperature and a linear dependence on the species concentration. Conditional and unconditional nonlinear energy stability criteria for two different models are derived. A comparison of linear and nonlinear theories suggests that there are significant regions where the basic state is subject to a deep subcritical instability when the value of solute Rayleigh number is high.

Nonlinear Stability and Linear Instability of Double-Diffusive Convection in a Rotating with LTNE Effects and Symmetric Properties: Brinkmann-Forchheimer Model

“…Chebyshev collocation method has been used for solving the systems of eigenproblems (11), (30) and (37). More information about these types of systems can be seen in [21][22][23][24][37][38][39]. The solutions are then presented in Tables 1-3, which comprise R L and R E which are called the critical thermal Rayleigh numbers (CTRN) for both of the linear instability theory and the non-linear stability theory, respectively.…”

“…The impact of porous medium anisotropy on double diffusive convection was explained in [20]. Further studies with many different applications such as solidify and centrifugal casting of minerals, bio-mechanics, petroleum manufacture, chemical operations and food, rotating machinery, and geophysical problem are found in [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35].…”

Stability of Darcy thermosolutal convection in bidispersive porous medium with reaction

“…Double diffusive convection is a problem that is being researched, and the scientific community is paying attention to it 9,17–32 . Stability analyses in double diffusive convection were introduced in the highly influential papers of Nield 26,27 and from an unconditional energy stability point of view by Joseph 33,34 .…”