Jayalatha Gopal

The linear and weakly nonlinear stability analysis of the quiescent state in a viscoelastic fluid subject to vertical solute concentration and temperature gradients is investigated. The non-Newtonian behavior of the viscoelastic fluid is characterized using the Oldroyd model. Analytical expressions for the critical Rayleigh numbers and corresponding wave numbers for the onset of stationary or oscillatory convection subject to cross diffusion effects is determined. A stability diagram clearly demarcates non-overlapping regions of finger and diffusive instabilities. A Lorenz system is obtained in the case of the weakly nonlinear stability analysis. The effect of Dufour and Soret parameters on the heat and mass transports are determined and discussed. Due to consideration of dilute concentrations of the second diffusing component the route to chaos in binary viscoelastic fluid systems is similar to that of single-component (thermal) viscoelastic fluid systems. � 2013 Elsevier Inc..

Oscillatory onset of convection is studied numerically for Rivlin-Ericksen, Maxwell and Jeffreys liquids by considering free-free and rigid-free isothermal/adiabatic boundaries. The effect of variable viscosity parameter is shown to destabilize the system. The problem reveals the stabilizing nature of strain retardation parameter and the destabilizing nature of stress relaxation parameter, on the onset of convection. The Maxwell liquids are found to be more unstable than the one subscribing to the Jeffreys description whereas the Rivlin-Ericksen liquids are comparatively more stable. Rigid-free adiabatic boundary combination is found to give rise to a most stable system, whereas the free isothermal free adiabatic combination gives rise to a most unstable system. � 2010 Elsevier Ltd.

A study of heat transport in Rayleigh-B�nard convection in viscoelastic liquids with/without gravity modulation is made using a most minimal representation of Fourier series and a representation with higher modes. The Oldroyd-B constitutive relation is considered. The resulting non-autonomous Lorenz model (generalized Khayat-Lorenz model of four modes and seven modes) is solved numerically using the adaptive-grid Runge-Kutta-Fehlberg45 method to quantify the heat transport. The effect of gravity modulation is shown to be stabilizing there by leading to a situation of reduced heat transfer. The Deborah number is shown to have an antagonistic influence on convection compared to the stabilizing effect of modulation amplitude and elastic ratio. The results in respect of Maxwell, Rivlin-Ericksen and Newtonian liquids are obtained as particular cases of the present study. A transformation of the momentum equations illustrates the equivalence of present approach and the one due to Khayat that uses normal stresses explicitly. � 2010 Elsevier B.V.