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A parametric study of heat spreading through multiple layer substrates

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Thermal Management of Electronic Systems

Abstract

A double Fourier series technique is used to develop an analytical expression for the three-dimensional temperature field within a thin multiple layer substrate cooled by convection and heated by sources mounted on one side. The temperature distribution, in a dimensionless form, is a function of nondimensional parameters: the Biot number, aspect ratios and conductivity ratios of each layer, and the ratios of Fourier coefficients which describe the sources. A parametric study is presented to illustrate the influences of these parameters for a practical electronics cooling problem. Equivalent series and parallel orthotropic conductivity components are derived which can be used to model multiple layer structures as single layers.

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References

  • Bergquist company, 1991, “The Thermal Clad Design Guide,” available from Bergquist, 5300 Edina Industrial Boulevard Mpls., MN 55435, p. 6.

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  • Carslaw, H.S., and Jaeger, J.C., 1959, Conduction of Heat in Solids, Clarendon, Oxford, pp. 180–182.

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  • Punch, J., and Davies, M., 1993, “Three-Dimensional Heat Conduction Through Rectangular Multiple Layer Plane Substrates,” accepted for presentation at the ASME National Heat Transfer Conference, August.

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Limerick, Limerick, Ireland

    J. Punch & M. Davies

Authors
  1. J. Punch
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  2. M. Davies
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Editor information

Editors and Affiliations

  1. J. M. Burgers Centre for Fluid Mechanics, Delft University of Technology, Delft, The Netherlands

    C. J. Hoogendoorn  & R. A. W. M. Henkes  & 

  2. Philips B.V., Eindhoven, The Netherlands

    C. J. M. Lasance

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© 1994 Springer Science+Business Media Dordrecht

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Punch, J., Davies, M. (1994). A parametric study of heat spreading through multiple layer substrates. In: Hoogendoorn, C.J., Henkes, R.A.W.M., Lasance, C.J.M. (eds) Thermal Management of Electronic Systems. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1082-2_14

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  • DOI: https://doi.org/10.1007/978-94-011-1082-2_14

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4472-1

  • Online ISBN: 978-94-011-1082-2

  • eBook Packages: Springer Book Archive

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