Linear instability in viscoelastic fluid convection

The onset of convection in a viscoelastic fluid that obeys the Jeffreys model is investigated. Two boundary conditions have been considered separately: free-free and rigid-rigid. The role played by the retardation time, characteristic of the Jeffreys model, is emphasised. The threshold values of the parameters (critical Rayleigh number, critical wavenumber, onset frequency, etc.) for stationary and oscillatory convection are obtained. The frontier between oscillatory and stationary convection is calculated and the possibility to obtain a codimension-two point is discussed.