# Xie-EGM-RPI-2011.pdf

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Xie-EGM-RPI-2011.pdf
```E. Gutierrez-Miravete and X. Xie
Department of Engineering and Science
Rensselaer at Hartford
A Study of Fluid Flow and Heat Transfer in a
Liquid Metal in a Backward-Facing Step under
Combined Electric and Magnetic Fields
• Reliable, easy to use, multi-physics analytical methods for
the prediction of the effects of EM fields on fluid flow and
heat transfer phenomena in electrically conducting fluids are
needed.
• Some common industrial applications include EM braking in
continuous casting, levitation melting, EM shaping and EM
pumping.
• Electromagnetic fields can and are used to influence the
fluid flow behavior of electrically conducting fluids.
• Electromagnetic body forces affect and modify the fluid flow.
• Applied electromagnetic (EM) fields produce body forces in
electrically conducting fluids.
Motivation and Background
Example: Induction Melting
Example: Induction Melting
Example: Induction Melting
(Ampere’s Law)
(Ohm’s Law – No Hall effect)
ϱ Cp ∂T/ ∂t + v · ∇ T = k ∇2 T (Energy Equation)
ϱ ∂v/ ∂t + (v · ∇) v = - ∇ p + J x B + η ∇2 v (Navier-Stokes)
∇ · v = 0 (Continuity)
J = σ (E + v x B)
∇ · J = 0 (Kirchoff’s First Law)
∇ ·B=0
∇xB = µJ
∇ x E = - ∂B/∂t
Governing Equations
• The working fluid was NaK.
• Steady Laminar Flow around a Backward Facing Step. A
conducting fluid flows between two large parallel plates and it
comes into a backward facing step where a magnetic field is
applied perpendicular to the plane of the plates. Electric field (if
any) applied perpendicular to the plane formed by the fluid velocity
and the magnetic field. The presence of the step, in general leads
to flow separation and the formation of vortex structures.
• Steady Laminar Hartmann Flow. A conducting fluid flows between
two large parallel plates. Magnetic field applied perpendicular to the
plane of the plates. Electric field (if any) applied perpendicular to
the plane formed by the fluid velocity and the magnetic field.
• To gain confidence in the approach and validate modeling work two
simple configurations were selected for analysis.
Model Description
Flow Geometries
Hartmann Flow Results
Step Flow Results
(no EM field)
Step Flow Results
(EM field applied)
Step Flow Results
(Pressure Profiles)
Step Flow Results
(Temperature Profile)
• The obtained results are encouraging and suggest that COMSOL
Multi-physics could be used to investigate more complex
magnetohydrodynamic flows.
• The COMSOL results predict the expected flattening of velocity
profiles as well as the vortex elimination in the backward facing step
flow.
• The COMSOL results are in excellent agreement with the available
exact solution for the Hartmann problem.
• COMSOL Multi-physics has been used to model the steady laminar
flow and convective heat transfer of an electrically conducting fluid
subjected to an applied electromagnetic field in two simple flow
configurations, namely, flow between parallel plates (Hartmann flow)
and flow around a backward facing step.
Summary
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