Abstract
In this paper, the effect of throughflow and gravity modulation on thermal convection in a couple stress fluids saturating a porous medium with an internal heating source is investigated. A weakly nonlinear stability analysis is proposed to study the stationary mode of convection. The amplitude of gravity modulation is assumed to be very small and the disturbances are extended in terms of the power series of the amplitude of convection. Using a non-autonomous Ginzburg- Landau amplitude equation, heat transport is evaluated in terms of the Nusselt number. The finite-amplitude of convection has been derived in the third order. The amplitude and frequency of modulation have the effects of increasing or diminishing heat transport. The presence of a couple-stress parameter with internal heat source throughflow and modulation effects has been discussed. The effect of the internal heat source increases or decreases heat transfer in the system. For suitable ranges of Ω the throughflow and internal heating have both destabilizing and stabilizing effects. Finally flow patterns are presented in terms of streamlines and isotherms.
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