English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We present a reduced order model for three dimensional unsteadypressure-driven flows in micro-channels of variable cross-section. This fastand accurate model is valid for long channels, but allows for large variationsin the channel's cross-section along the axis. It is based on an asymptoticexpansion of the governing equations in the aspect ratio of the channel. Afinite Fourier transform in the plane normal to the flow direction is used tosolve for the leading order axial velocity. The corresponding pressure andtransverse velocity are obtained via a hybrid analytic-numerical scheme basedon recursion. The channel geometry is such that one of the transverse velocitycomponents is negligible, and the other component, in the plane of variation ofchannel height, is obtained from combination of the corresponding momentumequation and the continuity equations, assuming a low degree polynomial Ansatzof the pressure forcing. A key feature of the model is that it puts norestriction on the time dependence of the pressure forcing, in terms of shapeand frequency, as long as the advective component of the inertia term is small.This is a major departure from many previous expositions which assume harmonicforcing. The model reveals to be accurate for a wide range of parameters and istwo orders of magnitude faster than conventional three dimensional CFDsimulations.

Simplified models for unsteady three-dimensional flows in slowly varying microchannels