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The qualitative effect of nonuniform temperature gradient on thelinear stability analysis of the Rayleigh-Benard convectionproblem in a Boussinesquian, viscoelastic fluid-filled,high-porosity medium is studied numerically using the single-termGalerkin technique. The eigenvalue is obtained for free-free,free-rigid, and rigid-rigid boundary combinations with isothermaltemperature conditions. Thermodynamics and also the present stability analysis dictates the strain retardation timeto be less than the stress relaxation time for convection to setin as oscillatory motions in a high-porosity medium. Furthermore,the analysis predicts the critical eigenvalue for the viscoelasticproblem to be less than that of the corresponding Newtonian fluidproblem

Rayleigh-Benard convection in a viscoelastic fluid-filled high-porosity medium with nonuniform basic temperature gradient