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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. Definitions. Constriction resistance – heat flows from a larger to a smaller area

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Constriction and spreading resistance l.jpg

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.


Definitions l.jpg
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


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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.


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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


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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 Ψ, 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-case+Rcontact+Rspreading+Rheatsink

  • The larger the area ratio, the more important the constriction/spreading resistance is. For example


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Terminology

Other important researchers in this area: M.M. Yovanovich (1969, 76, 77, 79, 87,

92, 93) and D. P. Kennedy (1960)


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