Double Convection of a Binary Viscoelastic Fluid under Helical Force Effect: Linear and Weakly Nonlinear Analysis

We used linear stability theory based on the normal mode decomposition technique to study the criterion of appearance of the stationary convection and the oscillatory convection in a binary viscoelastic fluid mixture in a porous medium under the e ff ect of helical force. Nonlinear stability theory based on the minimum representation of double Fourier series is used to study the rate of heat and mass transfer. We have determined the analytical expression of the Rayleigh number of the system as a function of the dimensionless parameters. Expressions for heat and mass transfer rates are determined as a function of Nusselt and Sherwood number, respectively. The transient behaviors of the Nusselt number and the Sherwood number are studied by solving the finite amplitude equations using the Runge - Kutta method. Then, the e ff ect of each dimensionless parameter on the system is studied pointed out interesting results.