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Studies on Fluid Flow Through an Elliptical Microchannel of Different Aspect Ratios

  • Sudip SimlandiEmail author
  • Soumyanil Nayek
  • Raunak Joshi
Conference paper
Part of the Lecture Notes on Multidisciplinary Industrial Engineering book series (LNMUINEN)

Abstract

The present work considers fluid flow analysis within a straight microchannel of elliptical cross section. Variational method with slip boundary conditions is adopted to determine velocity distribution. One can use no-slip boundary conditions with incorporating an average slip velocity with little modifications. The proposed result is validated with existing literature and agrees well. The velocity distribution thus obtained is also used to determine Poiseuille number and slip coefficient. Finally, the velocity profile, Poiseuille number, and slip coefficient are presented graphically as the function of aspect ratio and Knudsen number. It is predicted that the velocity profile and Poiseuille number greatly depend on the Knudsen number and aspect ratio, whereas slip coefficient has negligible dependency on the Knudsen number. The present work is further extended to determine velocity profile, Poiseuille number, and slip coefficient for a rectangular microchannel and thus the results obtained have been compared with the elliptical microchannel. The present analytical solutions offer a suitable and power technique for studying fluid flow analysis in a variety of fundamental and engineering applications such as in microfluidics.

Keywords

Slip flow Elliptical microchannel Variational method Knudsen number Poiseuille number 

Nomenclature

A

Aspect ratio (=b/a)

\(B\)

Coefficient defined in Eq. (27.12)

a

Major semi-axis of ellipse (m)

b

Minor semi-axis of ellipse (m)

Dh

Hydraulic diameter (m)

dA

Differential area (m2)

F

Tangential momentum accommodation coefficient (=1)

I[U]

Functional defined in Eq. (27.15)

Kn

Knudsen number (=λ/Dh)

Po

Poiseuille number

\(\frac{{{\text{d}}p}}{{{\text{d}}z}}\)

Pressure gradient in the flow direction (N/m3)

U

Dimensionless velocity considering no-slip condition

\(\overline{U}\)

Normalized dimensionless velocity considering slip

u

Velocity along the axis of the channel (m/s)

um

Mean velocity along the axis of the channel (m/s)

us

Slip velocity at the walls (m/s)

x

X-axis coordinate

X

Dimensionless coordinate (=x/a)

y

Y-axis coordinate

Y

Dimensionless coordinate (=y/b)

Greek symbols

\(\mu\)

Dynamic viscosity (Pa s)

\(\beta\)

Slip coefficient

Subscripts

m

Mean

ns

No-slip

s

Slip

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringJadavpur UniversityKolkataIndia

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