2019
DOI: 10.20944/preprints201905.0316.v1
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A New Form of Velocity Distribution in Rectangular Microchannels with Finite Aspect Ratios

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 diff… Show more

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Cited by 3 publications
(3 citation statements)
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References 34 publications
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“…The 2-dimensional velocity distribution was obtained on the plane where y = 0 in the z-axis direction as Equation (1) [28,29]. The inlet flow rate, Q in , was calculated by integrating the velocity distribution over the width as Equation (2).…”
Section: 𝑱 (đ‘„ 𝑩mentioning
confidence: 99%
“…The 2-dimensional velocity distribution was obtained on the plane where y = 0 in the z-axis direction as Equation (1) [28,29]. The inlet flow rate, Q in , was calculated by integrating the velocity distribution over the width as Equation (2).…”
Section: 𝑱 (đ‘„ 𝑩mentioning
confidence: 99%
“…The physics of the problem and governing equations have been thoroughly explained in our previous manuscript [34]. In that work, we limited our approach to no-slip BCs and solve the equations based on that assumption.…”
Section: Formulations and Governing Equationsmentioning
confidence: 99%
“…Previously, we obtained the momentum equation as follows [34]: where and ⁄ is the velocity and pressure gradient in the streamwise direction (i.e., z)…”
Section: =0mentioning
confidence: 99%