Throughflow and g-jitter effects on binary fluid saturated porous medium

Abstract

A non-autonomous complex Ginzburg-Landau equation (CGLE) for the finite amplitude of convection is derived, and a method is presented here to determine the amplitude of this convection with a weakly nonlinear thermal instability for an oscillatory mode under throughflow and gravity modulation. Only infinitesimal disturbances are considered. The disturbances in velocity, temperature, and solutal fields are treated by a perturbation expansion in powers of the amplitude of the applied gravity field. Throughflow can stabilize or destabilize the system for stress free and isothermal boundary conditions. The Nusselt and Sherwood numbers are obtained numerically to present the results of heat and mass transfer. It is found that throughflow and gravity modulation can be used alternately to heat and mass transfer. Further, oscillatory flow, rather than stationary flow, enhances heat and mass transfer.

The Complex Ginzburg Landau Model for an Oscillatory Convection in a Rotating Fluid Layer

“…Introducing a small perturbation parameter  that shows deviation from the critical state of onset of convection, the variables for a weak nonlinear state may be expanded as a power series in terms of  (as in Venezian [4], Bhadauria and Kiran [27,28,[36][37][38][39] and Malkus and Veronis [30]…”

“…Thermal instability in a rotating media is presented in the studies of [32][33][34]. The effect of gravity modulation on thermal instability in a fluid saturation porous media is given by Siddheshwar et al [35], Bhadaria et al [36] and Kiran [37,38]. They investigated g-jitter effect on chaotic convection and binary convection.…”

Throughflow and non-uniform heating effects on double diffusive oscillatory convection in a porous medium

“…According to the studies of [15,16,[47][48][49] and Kim et al [51] the fast time scale of time s and the slow time scale of time s as @ @t ¼ @ @s þ v 2 @ @s were introduced.…”

“…Now under the solvability condition for the existence of third order solution, the following complex nonautonomous Ginzburg-Landau equation (CGLE) is obtained, which describes the temporal variation of the amplitude AðsÞ of the convection cell [15,16,[47][48][49] and Vada´sz [52] dAðsÞ ds À c À1 1 FðsÞAðsÞ þ c À1 1 k 1 jAðsÞj 2 AðsÞ ¼ 0:…”

“…The objective of the present article was, therefore, to investigate weakly nonlinear stability characteristics of a porous layer with simultaneous temperature and solute concentration gradients for constant vertical throughflow. Analytic expressions for both Nusselt and Sherwood numbers were derived from the complex non-autonomous Ginzburg-Landau equation [15,16,[47][48][49] to calculate finite amplitude.…”