CHEMICAL ENGINEERING TRANSACTIONS
VOL. 71, 2018
A publication of
The Italian Association
of Chemical Engineering
Online at www.aidic.it/cet
Guest Editors: Xiantang Zhang, Songrong Qian, Jianmin Xu
Copyright © 2018, AIDIC Servizi S.r.l.
ISBN 978-88-95608-68-6; ISSN 2283-9216
Numerical Simulation of Magneto Hydrodynamic Natural
Convection in a Vertical Cylindrical Crucible
Vahid Ahmadpour*, Iraj Mirzaei, Sajad Rezazadeh
Urmia University of technology, Mechanical Engineering Department, P.O. Box 57155-419, Urmia, Iran
V.ahmadpour@yahoo.com
The purpose of this paper is a numerical study to investigate the effects of external horizontal magnetic field
on heat transfer characters within a pure molten metal filled a vertical 3D cylindrical crucible. The inner and
outer walls of annulus are kept at constant temperature and the upper and lower walls are thermally insulated.
The model is based on magneto hydrodynamic natural-convection theory and low Reynolds number
approximation. Finite volume approach and fully implicit scheme is adopted to discrete corresponding
equations. Results have been conducted for three different geometrical sizes, Rayleigh and Hartman
Numbers. The 3D simulation results indicate a strong relation between heat transfer, the magnetic field
strength and the aspect ratio of the crucible. In addition, this model shows that the azimuthal distribution of
velocity and temperature fields affected greatly in crucible in presence of external magnetic field. The model
has been validated availiable results. The findings of this study are expected to be useful for enhancing the
design of solidification systems.
1. Introduction
Solidification processing has been used extensively in metallic alloys and semiconductors industry for many
years. From the view of production, the final product quality is dependent upon many parameters including
composition, cooling rate, boundary conditions, body and external forces and the temperature field of the melt
region. In fact, these parameters could affect the flow patterns in the melt by producing convection flows. In
addition, the nature of these flows is so that plays significant role on melt/solid front morphology and solidified
structure. Also, experimental evidences proved that during solidification process such fluid motions in molten
metal affect performance of final product. Hence, controlling unwanted convection flows in melt is crucial. In
practice, it is possible to overcome these limitations partially by several methods. An interesting solution is
applying an external magnetic field to suppress the buoyancy driven flows which referred to Magneto
hydrodynamics (MHD) problems in the literature.
Whatever we recognize as main figures of MHD theory refers to Hartmann, Alfvén, and other’s experiments in
the first half of the twentieth century (Davidson 2001). (Sarris et al., 2010) carried out numerical investigations
about the problem of transient and turbulent natural convection of the electrically conductive low-Prandtl
number fluid that driven by horizontal temperature gradients in a vertical cylinder in the presence of a vertical
magnetic field. An investigation of solidification and melting of gallium in presence of constant magnetic field in
a rectangular cavity was performed (Charmchi et.al, 2004). (Sankar et al., 2008) studied the effect of magnetic
field on the driven convection in combination of buoyancy and surface tension forces in a cylindrical annular
enclosure. (Afrand et al., 2017) investigated a 3D numerical method to analyse the natural convection in a
cylindrical annulus containing molten potassium under a magnetic field. An experimental study for free
convection in a vertical annulus was presented by Ejaz and Manzoor (2018). Effects of a bottom heated
rotating cylinder in a vertical annulus have been experimentally studied with respect to heat transfer
parameters. (Vasanthakumari and Pondy, 2018) presented a numerical investigation of steady two
dimensional laminar, boundary layer flow of incompressible, viscous nanofluid with MHD along with heat
generation and suction effect is considered. (Wang et al., 2017) examined the natural convection heat transfer
of Al2O3-water nanofluid in a differentially-heated three-dimensional cubic enclosure. The study focuses on the
DOI: 10.3303/CET1871230
Please cite this article as: Ahmadpour V., Mirzaei I., Rezazadeh S., 2018, Numerical simulation of magneto hydrodynamic natural convection
in a vertical cylindrical crucible, Chemical Engineering Transactions, 71, 1375-1380 DOI:10.3303/CET1871230
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