Convection instability of non-Newtonian Walter's nanofluid along a vertical layer

The linear stability of viscoelastic nanofluid layer is investigated. The rheological behavior of the viscoelastic fluid is described through the Walter's model. The normal modes analysis is utilized to treat the equations of motion for stationary and oscillatory convection. The stability analysis resulted in a third-degree dispersion equation with complex coefficients. The Routh-Hurwitz theory is employed to investigate the dispersion relation. The stability criteria divide the plane into several parts of stable/unstable regions. This shows some analogy with the nonlinear stability theory. The relation between the elasticity and the longitudinal wave number is graphically analyzed. The numerical calculations show that viscoelastic flows are more stable than those of the Newtonian ones.