Preprint Article Version 1 This version is not peer-reviewed

A New Form of Velocity Distribution in Rectangular Microchannels with Finite Aspect Ratios

Version 1 : Received: 25 May 2019 / Approved: 27 May 2019 / Online: 27 May 2019 (12:32:24 CEST)

How to cite: Kashaninejad, N. A New Form of Velocity Distribution in Rectangular Microchannels with Finite Aspect Ratios. Preprints 2019, 2019050316 (doi: 10.20944/preprints201905.0316.v1). Kashaninejad, N. A New Form of Velocity Distribution in Rectangular Microchannels with Finite Aspect Ratios. Preprints 2019, 2019050316 (doi: 10.20944/preprints201905.0316.v1).

Abstract

This study presents a new form of velocity distribution in laminar liquid flow in rectangular microchannels using the eigenfunction expansion technique. Darcy friction factor and Poiseuille number are also obtained analytically. Due to the symmetry of the solutions, the effects of changing the aspect ratio from 0 to ∞ are also discussed. Using finite element method (FEM), the obtained analytical results are further compared with the 3D numerical simulations for the rectangular microchannels with different range of aspect ratio and pressure gradient, and excellent agreements were found. These findings provide additional insights in interpreting the results of the pressure-driven flows in finite aspect ratio microchannels, in which very precise comparison with the macroscale theory is crucial.

Subject Areas

aspect ratio effects; velocity profile of poiseuille flow; friction factor; eigenfunction expansion technique; finite element method; 3D microchannels

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