Revisiting the optimal thickness profile of cooling fins: A one-dimensional analytical study using optimality conditions

Joe Alexandersen, Ole Sigmund

    Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

    Abstract

    This paper revisits the optimal thickness profile problem of a single cooling fin using a one-dimensional heat conduction equation with a convection boundary condition. Firstly, in contrast to previous works, we apply an approach using optimality conditions based on requiring stationarity of the Lagrangian functional of the optimisation problem. This yields an optimality condition basis for the commonly touted constant temperature gradient condition. Secondly, we seek to minimise the base temperature for a prescribed thermal power, rather than maximising the heat transfer rate for a constant base temperature as previous works. The optimal solution is shown to be fully equivalent for the two, which may seem obvious but to our knowledge has not been shown directly before. Lastly, it is shown that optimal cooling fins have a Biot number of 1, exhibiting perfect balance between conductive and convective resistances.
    Original languageEnglish
    Title of host publicationProceedings of the Twentieth InterSociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm 2021)
    PublisherIEEE
    Publication date2021
    Pages24-30
    ISBN (Electronic)978-1-7281-8539-2
    DOIs
    Publication statusPublished - 2021
    Event20th InterSociety Conference on Thermal and Thermomechanical
    Phenomena in Electronic Systems
    - San Diego, United States
    Duration: 1 Jun 20214 Jun 2021
    Conference number: 20

    Conference

    Conference20th InterSociety Conference on Thermal and Thermomechanical
    Phenomena in Electronic Systems
    Number20
    Country/TerritoryUnited States
    CitySan Diego
    Period01/06/202104/06/2021

    Keywords

    • Cooling fin
    • Optimality conditions
    • Optimal design

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