Energetic effects on the stability of viscoelastic Dean flow

The influence of energetics on the linear stability of viscoelastic Dean fl ew of an Oldroyd-B liquid has been investigated. Our analyses show that whe n the temperatures of inner and outer walls are maintained at constant equa l values, viscous heating does not influence the mode selection, i.e. the m ost dangerous disturbance is axisymmetric and stationary as in the case of isothermal Dean flow. The critical Deborah number increases with increasing Brinkman number indicating that viscous heating stabilizes the flow in thi s case. When the outer cylinder is kept at a higher temperature than the in ner one, the most dangerous eigenmode corresponds to a non-axisymmetric dis turbance with azimuthal wave number of one. For Pe < O(10(4)), the critical axial and temporal wave numbers for the non-isothermal flow sire similar t o those predicted for the isothermal case. This indicates that the critical eigenfamily is an extension of the isothermal family. For Pe > O(10(5)), a new axisymmetric and time-dependent eigenmode with significantly different critical parameters becomes the most dangerous one. Influence of solvent v iscosity and gap width on the critical parameters is also investigated. Fin ally, the thermoelastic mechanisms that influence the flow stability are di scussed. (C) 2000 Elsevier Science B.V. All rights reserved.