Maximum thermal spreading resistance for rectangular sources and plates with nonunity aspect ratios

An exact three-dimensional (3-D) solution is derived for the steady-state heat conduction equation with the source on an otherwise adiabatic surface and Newtonian cooling on the opposing surface. Dimensionless solutions are provided for maximum and source-averaged thermal spreading resistances. The...

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Bibliographic Details
Published in:IEEE transactions on components and packaging technologies 2003-06, Vol.26 (2), p.439-454
Main Author: Ellison, G.N.
Format: Article
Language:English
Subjects:
Aspect ratio
Cooling
Cooling effects
Fourier series
Heat transfer
Immune system
Mathematical analysis
Packaging
Planes
Plates
Resistance heating
Spreading
Steady-state
Surface resistance
Temperature
Thermal conductivity
Thermal resistance
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Summary:An exact three-dimensional (3-D) solution is derived for the steady-state heat conduction equation with the source on an otherwise adiabatic surface and Newtonian cooling on the opposing surface. Dimensionless solutions are provided for maximum and source-averaged thermal spreading resistances. The solution for unit-source contours in a plane perpendicular to the source plane is also included. Maximum thermal spreading resistance plots are provided for several source-to-plate edge length ratios and source aspect ratios (plate maintained square). The Newtonian cooling effects are incorporated via a Biot number. Examples illustrate application of the theory.
ISSN:1521-3331
1557-9972
DOI:10.1109/TCAPT.2003.815088