Gravitational Modulation Effect on Double-Diffusive Oscillatory Convection in a Viscoelastic Fluid Layer

Abstract

The complex Ginzburg-Landau model has been employed to derive the temporal amplitude of convection in a viscoelastic fluid layer under gravity modulation. The finite amplitude is based on a weakly nonlinear thermal convection. The perturbation technique is applied to simplify the nonlinear system of partial differential equations into a non-autonomous amplitude equation. Heat and mass transfer obtained in terms of the Nusselt and Sherwood numbers, and the corresponding results are presented for the small amplitude of modulation. The moderate values of amplitude and frequencies of gravity modulation are considered, their effect is to enhance the heat and mass transfer in the layer. Thus, the modulation plays dual role in heat and mass transfer. The variations of Nusselt and Sherwood numbers with slow time becomes rapid on either increasing the parameters Rs, Pr, λ, δ or decreasing the parameters Γ, ε, Ω. Each parameter effect has been presented graphically with their effect on Nu and Sh. Further, it is found that an oscillatory mode of convection enhances the heat and mass transfer than a stationary mode.