Rayleigh-Benard convection of viscoelastic fluids in finite domains

We investigate the linear stability problem of the Rayleigh-Benard convection of viscoelastic fluids in a two-dimensional rectangular box with nonslip sidewalls, where there may exist a heat source to enhance or suppress the convection. A Chebyshev pseudospectral method is generalized to solve the hydrodynamic stability problem. We adopt a very general constitutive equation that encompasses the Maxwell model, the Oldroyd model and the Phan-Thien-Tanner model, The effects of box aspect ratio, heat source, the Deborah number lambda and the dimensionless retardation time epsilon On the critical Rayleigh number and convection cell size are examined. The range of lambda and the epsilon for the onset of overstability is also obtained for a given box aspect ratio, The results of the present paper may be used to investigate the appropriateness of a constitutive equation and its parameter values adopted for a given viscoelastic fluid. (C) 2001 Elsevier Science B.V, All rights reserved.