Korean Journal of Chemical Engineering

The Korean Institute of Chemical Engineers (한국화학공학회)
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Magnetic field effect on the onset of Soret-driven convection of a nanofluid confined within a Hele-Shaw cell

  • Kim, Min Chan (Department of Chemical Engineering, Jeju National University)
  • Received : 2016.04.23
  • Accepted : 2016.07.23
  • Published : 2017.01.01
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Abstract

The effect of a magnetic field on the early stages of Soret-driven convection of a nanoparticle suspension with large negative separation ratio ${\chi}$ confined within a Hele-Shaw cell, heated from above, was analyzed. Taking the Lorentz force into account, new stability equations were formulated in a similar (${\tau}$, ${\zeta}$)-domain as well as in a global (${\tau}$, z)-domain by introducing the Hele-Shaw Rayleigh number based on the Soret flux ($Rs_H$) and the Hele-Shaw Hartmann number ($Ha_H$). With and without the quasi-steadiness assumptions, the resulting stability equations were solved analytically by expanding the disturbances as a series of orthogonal functions, and also the numerical shooting method was used. The critical time of the onset of convection and the corresponding wave number were obtained as a function of $Rs_H$ and $Ha_H$. It was found that the magnetic field plays a critical role in the onset of convective instability. The onset time increases with increasing $Ha_H$ and decreasing $Rs_H$. The linear stability limits are independent of the solution methods, if the trial functions for the disturbance quantities are properly chosen. Based on the results of the linear stability analysis, a non-linear analysis was conducted using direct numerical simulations. The non-linear analysis revealed that the convective motion can be apparent far after the linear stability limit.

Keywords

Acknowledgement

Supported by : Jeju National University.

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