The Onset of Ferromagnetic Convection in a Micropolar Ferromagnetic Fluid Layer Heated from Below

Abstract

<p class="MsoNormal"> <span lang="EN-US">The onset of ferromagnetic convection in a micropolar ferromagnetic fluid layer heated from below in the presence of a uniform applied vertical magnetic field has been investigated. The rigid-isothermal boundaries of the fluid layer are considered to be either paramagnetic or ferromagnetic and the eigenvalue problem is solved numerically using the Galerkin method. It is noted that the paramagnetic boundaries with large magnetic susceptibility</span><span lang="EN-US"> </span><a name="OLE_LINK7"></a><a name="OLE_LINK6"></a><span><i><span lang="EN-US">χ</span></i></span><span></span><span></span><span lang="EN-US"> </span><span lang="EN-US">delays the onset of ferromagnetic convection the most when compared to very low magnetic susceptibility as well as ferromagnetic boundaries. Increase in the value of magnetic parameter</span><span lang="EN-US"> </span><i><span lang="EN-US">M</span></i>_{<span lang="EN-US">1</span>}<span lang="EN-US"> </span><span lang="EN-US">and spin diffusion (couple stress) parameter </span><i><span lang="EN-US">N</span></i>_{<span lang="EN-US">3</span>}<span lang="EN-US"> is to hasten, while increase in the value of coupling parameter</span><span lang="EN-US"> </span><i><span lang="EN-US">N</span></i>_{<span lang="EN-US">1</span>}<span lang="EN-US"> and micropolar heat conduction parameter </span><i><span lang="EN-US">N</span></i>_{<span lang="EN-US">5</span>}<span lang="EN-US"> is to delay the onset of ferromagnetic convection. Further, increase in the value of</span><span lang="EN-US"> </span><i><span lang="EN-US">M</span></i>_{<span lang="EN-US">1</span>}<span lang="EN-US">, <i>N</i>₁,</span><span lang="EN-US"> </span><a name="OLE_LINK8"></a><i><span lang="EN-US">N</span></i><span>_{<span lang="EN-US">5</span>}</span><span lang="EN-US"> and</span><span lang="EN-US"> </span><i><span lang="EN-US">χ</span></i><i><span lang="EN-US"> </span></i><span lang="EN-US">as well as decrease in </span><i><span lang="EN-US">N</span></i>_{<span lang="EN-US">3</span>}<span lang="EN-US"> is to diminish the size of convection cells.</span><span lang="EN-US"><o:p></o:p></span> </p

Penetrative B&#233;nard-Marangoni Convection in a Micropolar Ferrofluid Layer via Internal Heating and Submitted to a Robin Thermal Boundary Conditions

“…Thermal instability problem in a rotating micropolar ferrofluid has also been considered by Sunil et al [11]. Nanjundappa et al [12] have investigated the onset of ferromagnetic convection in a micropolar ferromagnetic fluid layer heated from below in the presence of a uniform applied vertical magnetic field.…”

Classical Linear Stability Analysis of Energy Based Internally Heated Distributions on B&#233;nard Porous Convection in a Micropolar Fluid Layer

“…The critical magnetic thermal Rayleigh number for the onset of instability is also determined numerically by Raleigh Ritz method. Nanjundappa et al [12] have investigated the onset of ferromagnetic convection in a micropolar ferromagnetic fluid layer heated from below in the presence of a uniform applied vertical magnetic field. The rigid-isothermal boundaries of the fluid layer are considered to be either paramagnetic or ferromagnetic and the eigenvalue problem is solved numerically using the higher order-Galerkin method.…”