Dissipation effects in hydrodynamic stability of viscoelastic fluids

In this paper an analysis is made of the hydrodynamic stability of a Boussinesq viscoelastic fluid undergoing plane Couette flow with a superposed temperature gradient. Of special interest is the effect of including the dissipation term in the energy equation. This term is shown to destabilize the fluid for most values of disturbance wave number and material parameters and to cause overstability for all values of the Brinkman number. At a critical Weissenberg number of 1, a rheological instability is developed which is essentially independent of the Reynolds, Prandtl, and Brinkman numbers.