Effects of viscous dissipation on hydrodynamic stability of viscoelastic fluids
Two constitutive equations for viscoelastic fluids are examined in linearized hydrodynamic stability analysis for the effects of viscous dissipation, in plane Couette flow heated from below. All physical properties are assumed constant except the density in the body-force term of the momentum equation. Critical and marginal Rayleigh numbers are demonstrated for a variety of flow conditions for the Newtonian fluid and for a variety of fluid and flow conditions for the non-Newtonian fluid. It has been found that inclusion of dissipation terms in the energy transport equation generally destabilizes the flow. Data was generated for Brinkman numbers from zero to ten. The difficulty of the retarded-motion constitutive equation (second-order fluid) in linearized hydrodynamic stability analysis is further documented. The superiority of the integral model in this type of analysis is made clear. Overstability is found to be a result in the Newtonian fluid case due to the inclusion of the dissipation terms. The viscoelastic fluid analysis also demonstrates overstability due to both dissipation and elasticity.
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