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Hartmann number
About: Hartmann number is a research topic. Over the lifetime, 2593 publications have been published within this topic receiving 61342 citations.
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TL;DR: Seilmayer et al. as mentioned in this paper developed a fully three-dimensional numerical code, and utilized it for the simulation of the Tayler instability at typical viscosities and resistivities of liquid metals.
Abstract: The electrical current through an incompressible, viscous and resistive liquid conductor produces an azimuthal magnetic field that becomes unstable when the corresponding Hartmann number exceeds a critical value of the order of 20. This Tayler instability (TI), which is not only discussed as a key ingredient of a nonlinear stellar dynamo model (Tayler-Spruit dynamo), but also as a limiting factor for the maximum size of large liquid metal batteries, was recently observed experimentally in a column of a liquid metal (Seilmayer et al 2012 Phys. Rev. Lett. 108 244501). On the basis of an integro-differential equation approach, we have developed a fully three-dimensional numerical code, and have utilized it for the simulation of the Tayler instability at typical viscosities and resistivities of liquid metals. The resulting growth rates are in good agreement with the experimental data. We illustrate the capabilities of the code for the detailed simulation of liquid metal battery problems in realistic geometries.
71 citations
TL;DR: In this paper, the effect of magnetic field on the flow driven by the combined mechanism of buoyancy and thermocapillarity in a rectangular open cavity filled with a low Prandtl number fluid (Pr = 0.054) was studied.
Abstract: A numerical study is conducted to understand the effect of magnetic field on the flow driven by the combined mechanism of buoyancy and thermocapillarity in a rectangular open cavity filled with a low Prandtl number fluid (Pr = 0.054). The two side walls are maintained at uniform but different temperatures θh and θc (θh > θc), while the horizontal top and bottom walls are adiabatic. A finite difference scheme consisting of the ADI (Alternating Direction Implicit) method, which incorporates upwind differencing for non-linear convective terms and the SLOR (Successive Line Over Relaxation) method are used to solve the coupled non-linear governing equations. Computations are carried out for a wide range of Grashof number Gr ranging from 2 × 104 to 2 × 106, Marangoni number Ma from 0 to 105 and Hartmann number Ha from 0 to 100. The detailed flow structure and the associated heat transfer characteristics inside the cavity are presented. At large Ma, two counter-rotating cells are formed at the upper half and lower half of the enclosure. As Ha increases, the temperature field resembles that of a conduction type and the streamlines are elongated in nature in the horizontal direction. The upper cell is crowded and stretched along the free surface. The average Nusselt number increases with Ma but decreases with Ha.
71 citations
TL;DR: In this paper, the effects of magnetohydrodynamics and partial slip on blood flow of Ree-Eyring fluid through a porous medium have been investigated and the resulting equation is solved analytically and exact solution has been obtained.
71 citations
TL;DR: In this article, the effect of nanoparticle shape on thermal conductivity is taken into consideration to solve the final equations which are obtained with vorticity stream function formulation, and results demonstrate that greatest Nusselt number obtains for Platelet shaped Fe3O4 nanoparticle.
71 citations
TL;DR: In this article, the authors deal with thermosolutal Marangoni convection, which can be formed with an electrically conducting fluid along a vertical surface in the presence of a magnetic field, heat generation and a first-order chemical reaction.
71 citations