Instability of the Navier-Stokes-Voigt fluid flow with couple stresses effect

This study examines the linear instability in a channel flow of the Navier-Stokes-Voigt viscoelastic fluid, influenced by couple stresses. It confirms the applicability of Squire's theorem and develops a generalized eigenvalue problem for two-dimensional modes using two Chebyshev collocation methods. This problem is then solved with the QZ algorithm. Despite the base flow maintaining characteristics of the Newtonian fluid, the instability of the fluid flow is significantly affected by the presence of the Kelvin-Voigt parameter and the couple stresses parameter. Numerical results showed the effect of increasing the couple stresses and the Kelvin-Voigt parameters on the stability of the system. As the value of these parameters increases, the critical values of the Reynolds number begin to increase, which initially indicates a stabilising effect.