Development and Application of a Two-Dimensional, Transient Numerical Model for Temperature Distribution within a Cylinder Subjected to Electromagnetically Induced Heat Generation

1
Development and Application of a Two-Dimensional,
Transient Numerical Model for Temperature
Distribution within a Cylinder Subjected to
Electromagnetically Induced Heat Generation

• Conduction Heat Transfer
• MEAE 6630

2

• Induction heating - passage of current thru a
  metallic material to cause internal heat
  generation
• Applications surface hardening of wear-intensive
  parts, purification of semiconductor materials
  (zone refining)
• Typically 60 Hz to 1 MHz range used
• As frequency increases, penetration of current
  decreases . Greater material conductivity also
  lessens penetration.
• skin depth - measure of current penetration

3

• Basic setup AC coil with material acting as
  shorted secondary
• Eddy currents induced in secondary, opposite
  direction to current in primary

4

• OBJECTIVE
• Develop electrical circuit (inductance) model to
  solve for induced eddy currents in cylinder and
  simultaneously volumetric heat generation at
  discrete locations within cylinder
• Apply discrete heat generation to nodes (sharing
  same nodes from electrical model) in thermal
  model and solve for temperature distribution

5

• Basic mutual inductance model

6

• Discretize cylinder (and coil) into several
  circuits for accurate heat generation
  determination
• Circuit mesh based on skin thickness, as
  defined by
• Apply mutual inductance model, with N amount of
  circuits,

7

• M, L, R defined from geometry of a specific,
  discretized circuit

where E(k) and K(k) are the complete elliptic
integrals of the first and second kind
8

• Solve set of equations simultaneously for current
  in each discretized circuit (using Visual Basic
  routine)
• Determine volumetric heat generation at each node
  in cylinder from the relation

9
Radial cross-section of discretized cylinder and
coil
10
(No Transcript)
11
(No Transcript)
12

• Temperature Model
• Exact 2-D equations and boundary conditions
  (insulated case, no radiation heat transfer - low
  temperature model)

and from symmetry,
13

• 2-D, explicit finite volume equations are

• for i 1, 1 lt j lt N 2, n gt 1

• for 2 lt i lt M 1, 1 lt j lt N 2, n gt 1

14

• Discretized boundary conditions

• for i M 2, 1 lt j lt N 2, n gt 1,

• for 1 lt i lt M 2 , j 1, n gt 1,

• for 1 lt i lt M 2 , j N 2, n gt 1,

• Explicit - stability criterion dependent on two
  dimensions

15
(No Transcript)
16
(No Transcript)
17
(No Transcript)