Some isoperimetric results concerning undirectional flows in microchannels
نویسنده
چکیده
At a given pressure gradient, for all channels with given area, that which maximises the steady flow Qsteady has a circular cross-section. Consider flows starting from rest developing from a constant imposed pressure gradient: for all channels with given crosssectional area, that which has the slowest approach to the steady flow is the circular disk cross-section. This arXiv preprint will supplement the short journal paper (submitted April 2016) which reports these isoperimetric results. Items additional to the journal paper include further isoperimetric results, estimates involving geometric functionals besides area such as perimeter and moment of inertia, and perturbation analysis of nearly circular domains.
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