The Stability of Viscoelastic Creeping Plane Shear Flows with Viscous Heating

− The two-dimensional linear stability of creeping plane Couette and Poiseuille flow of a viscoelastic fluid with viscous heating is investigated using a Galerkin-type Chebyshev collocation approach and a non-isothermal formulation of the FENE-P constitutive model. Viscous heating is observed to have a destabilizing/stabilizing tendency for Couette/Poiseuille flow at long to moderate disturbance wavelengths, and a stabilizing effect at short wavelengths, but no instabilities are found in the inertialess flow limit. Shear-thinning due to finite polymer extensibility reduces the base flow stresses as well as normal stress gradients at fixed Nahme number, and tends to further stabilize the flow, especially at short wavelengths. In addition to our non-isothermal results, our calculations indicate that creeping Poiseuille flow using the isothermal upper-convected Maxwell model is least-stable at high Deborah numbers to an odd mode with a wavenumber based on channel half-width of k = 1.5.