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    Some isoperimetric results concerning undirectional flows in microchannels

    Access Status
    Fulltext not available
    Authors
    Keady, G.
    Wiwatanapataphee, Benchawan
    Date
    2016
    Type
    Journal Article
    
    Metadata
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    Citation
    Keady, G. and Wiwatanapataphee, B. 2016. Some isoperimetric results concerning undirectional flows in microchannels. -. -.
    Source Title
    -
    School
    Department of Mathematics and Statistics
    URI
    http://hdl.handle.net/20.500.11937/57956
    Collection
    • Curtin Research Publications
    Abstract

    Three isoperimetric results are treated. (i) At a given pressure gradient, for all channels with given (cross-sectional) area that which maximises the steady flow $Q_{\rm steady}$ has a circular cross-section. (ii) Consider flows starting from prescribed initial conditions developing from a prescribed imposed pressure gradient, either periodic or steady. For such flows, amongst all channels with given area, that which generically has the slowest approach to the long-term, periodic or steady, flow is the circular disk cross-section. (iii) Similar results for polygonal, $n$-gon, channels, with the optimising shape being the regular $n$-gon are discussed

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