Some isoperimetric results concerning undirectional flows in microchannels
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 prescrib...
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| creator | Keady, Grant Wiwatanapataphee, Benchawan |
| description | 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 |
| doi_str_mv | 10.48550/arxiv.1604.03394 |
| format | Article |
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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
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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
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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</abstract><doi>10.48550/arxiv.1604.03394</doi><oa>free_for_read</oa></addata></record> |
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| title | Some isoperimetric results concerning undirectional flows in microchannels |
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