Couple stress effects on thermosolutal convection in Navier–Stokes–Voigt fluid

Abstract

The present study advances the theoretical understanding of thermosolutal convection in a Navier–Stokes–Voigt fluid with couple stresses, which is relevant to a range of industrial, biomedical, and geophysical processes involving fluid transport as well as heat and mass transfer. This study aims to analyze the influence of couple stresses, solute gradients, and viscoelasticity on the onset of both stationary and oscillatory convection in the Navier–Stokes–Voigt fluid. Linear and nonlinear stability analyses are performed by formulating eigenvalue problems using the normal mode technique and the energy method, respectively. These eigenvalue problems are solved via a single-term Galerkin method to determine the Rayleigh number. The identical Rayleigh numbers obtained confirm the absence of subcritical instabilities and indicate global stability within the studied parameter range. Couple stresses, solute gradients, and viscoelasticity influence the onset and characteristics of oscillatory convection, either promoting or inhibiting instabilities depending on their relative strengths. Both couple stresses and solute gradients stabilize the convective system. Additionally, viscoelasticity does not affect the onset of stationary convection but significantly enhances the stability of oscillatory convection.