Abstract
We investigate the linear stability problem of the Rayleigh–Bénard 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 λ and the dimensionless retardation time ϵ on the critical Rayleigh number and convection cell size are examined. The range of λ and the ϵ 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.
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