Constriction and Spreading Resistance

1
Constriction and Spreading Resistance

• Reference S. Lee, S. Song, K. Moran,
  Constriction/Spreading Resistance Model for
  Electronics Packaging, ASME/JSME Thermal
  Engineering Conference Vol. 4, 1995.

2
Definitions

• Constriction resistance heat flows from a
  larger to a smaller area
• Spreading resistance heat flows from a smaller
  to a larger area
• Equations are the same for both

3
Geometry Considerations

• Different shapes (squares, circles) have
  basically the same resistance for the same square
  root of contact area and same area ratio (a/b)
• As the area ratio gets large, the geometry starts
  to matter more. However, at that point the
  constriction and spreading resistances are
  usually much smaller than other resistances in
  the system.

4
Analytical problem/solution
Ave average resistance, based on average
temperature of contact region this is what we
almost always want Max resistance based on
maximum temperature of contact region
5
Easier Approximation

• Including 100 terms of the infinite series
  results in near perfect agreement with two
  different numerical simulations.
• Approximate solutions shown below agree with
  infinite series solutions within 10.

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Easier Approximation, cont.

• Using the definition of ?, solve for Rave, which
  will be your constriction or spreading
  resistance..
• Add this resistance to your 1-D thermal
  resistance network.
• For example, here is a typical resistance
  network
• Rjunction-caseRcontactRspreadingRheatsink
• The larger the area ratio, the more important the
  constriction/spreading resistance is. For example

7
Terminology
Other important researchers in this area M.M.
Yovanovich (1969, 76, 77, 79, 87, 92, 93) and D.
P. Kennedy (1960)