The outset of convection in a thin layer of couple stress fluid is analyzed using the linear stability analysis when the fluid is heated from below. In order to assimilate the inertial effects Maxwell-Cattaneo law is used in lieu of the classical Fourier's heat conduction law. The normal mode analysis is used to arrive at the eigenvalues of the perturbed state and a regular perturbation method to find the analytical solutions. The effect of Cattaneo number, couple stress parameter and Prandtl number is discussed and it is concluded that gravity modulation can delay or advance the onset of convection.
The Rayleigh-B´enard convection in a couple stress liquid with rotational modulation is studied using the linear analysis based on normal mode technique. The stability of a horizontal layer of fluid heated from below is examined when, in addition to a steady rotation, a time-periodic sinusoidal perturbation is applied. The expression for Rayleigh number and correction Rayleigh number are obtained using regular perturbation method. The expression for correction Rayleigh number is obtained as a function of frequency of modulation, Taylor number, Couple Stress parameter and Prandtl number. It is observed that rotational modulation leads to delay in onset of convection. Rotation modulation is an example of external control of internal convection.
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