THROUGHFLOW EFFECT ON WEAKLY NONLINEAR OSCILLATORY CONVECTION IN A VISCOELASTIC FLUID SATURATING POROUS MEDIUM UNDER TEMPERATURE MODULATION

The effect of vertical throughflow and temperature modulation on a viscoelastic fluid-saturated porous medium has been investigated. A sinusoidal profile is taken to modulate the walls' temperature. The amplitudes of temperature modulation at the lower and upper surfaces are considered to be very small, and the disturbances are expanded in terms of power series of amplitude of convection. A weak nonlinear stability analysis has been performed for the oscillatory mode of convection, and heat transport in terms of Nusselt number, which is governed by the nonautonomous complex Ginzburg-Landau equation, is calculated. The effect of vertical throughflow is found to stabilize the system irrespective of the direction of throughflow in the case of permeable boundary conditions. The time relaxation. has a destabilizing effect, whereas the time retardation parameter epsilon has stabilizing effect on the system. The effects of amplitude and frequency of modulation on heat transport have been analyzed and depicted graphically. The study establishes that the heat transport can be controlled effectively by a mechanism that is external to the system. Furthermore, it is also found that heat transfer is more in the oscillatory mode of convection than in the stationary mode of convection.