Hopf bifurcation in thermal convection of viscoelastic fluids within finite domains

Hopf bifurcation in thermal convection is an interesting phenomenon peculia r to the viscoelastic fluids. Employing a general constitutive relation whi ch encompasses Maxwell model, Jeffreys model, Oldroyd-B model and Phan-Thie n-Tanner model, the range of viscoelastic parameters where the Hopf bifurca tion arises is determined when the viscoelastic fluid is confined in finite domains, which are compatible with the experimental situations. Employing the power series method, Landau equation is derived which determines the te mporal evolution of the convection intensity in finite domains with nonslip sidewalls when the Hopf bifurcation occurs. The comparison of these result s with the experimental data may be used to guide the selection of constitu tive equations and to estimate viscoelastic parameter values. (C) 2001 Else vier Science B.V. All rights reserved.