Study of Soret and Dufour effects and secondary instabilities on Rayleigh-Benard convection in a couple stress fluid

.The effects of Soret and Dufour parameters on the thermosolutal convection in a horizontal couple stress fluid layer with constant temperature and solutal concentration are investigated analytically under the assumption of Boussinesq approximation. In linear stability analysis, using the normal mode Fourier truncated representation, we arrived at the expressions for stationary and oscillatory Rayleigh numbers. The effects of solutal Rayleigh number, Lewis number, and couple stress, Soret and Dufour parameters on stationary and oscillatory Rayleigh numbers are presented graphically. The method of multiscales is used to derive the Newell-Whitehead-Segel equation. The possibility of occurrence of Eckhaus and zigzag secondary instabilities is discussed. The influence of the Dufour parameter on the region of secondary instabilities is demonstrated. The nondimensional parameters, Nusselt and Sherwood numbers are used to quantify the heat and mass transports. From the study it is found that the effect of Soret and couple stress parameters is to enhance the heat and mass transports. Further, the effect of a negative value of the Dufour parameter is to enhance the heat and mass transports and that of a positive value of the Dufour parameter is to diminish the same.