Abstract
AbstractIn the present paper, a weakly nonlinear stability analysis is used to analyze the effect of time-periodic concentration/gravity modulation on mass transport. We have considered an infinite horizontal fluid layer with constant appliedmagnetic flux salted from above, subjected to an imposed time-periodic boundary concentration (ITBC) or gravity modulation (ITGM). In the case of ITBC, the concentration gradient between the plates of the fluid layer consists of a steady part and a time-dependent oscillatory part. The concentration of both walls is modulated. In the case of ITGM, the gravity fleld consists of two parts: a constant part and an externally imposed time periodic part, which can be realized by oscillating the fluid layer. We have expanded the infinitesimal disturbances in terms of power series of an amplitude of modulation, which is assumed to be small. Ginzburg-Landau equation is derived for dinding the rate of mass transfer. Effect of various parameters on the mass transport is also discussed. It is found that the mass transport can be controlled by suitably adjusting the frequency and amplitude of modulation.
Highlights
The transport phenomena such as heat and mass transfer, play a vitally important role in human life
We study the combined e ect of concentration and gravity modulation on mass transport of a Newtonian uid with an applied magnetic eld
We demonstrated weakly nonlinear analysis of mass transport by perturbation technique to obtain a closed form expression for the problem of weakly nonlinear mass transport of the Newtonian uid of an incompressible and electrically conducting viscous uid within two in nite horizontal uid layer
Summary
The transport phenomena such as heat and mass transfer, play a vitally important role in human life. Abstract: In the present paper, a weakly nonlinear stability analysis is used to analyze the e ect of time-periodic concentration/gravity modulation on mass transport.
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