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Research Papers: Multiphase Flows

Fully-Developed Flow in Semicircular and Isosceles Triangular Ducts With Nonuniform Slip

[+] Author and Article Information
C. Y. Wang

Departments of Mathematics and
Mechanical Engineering,
Michigan State University,
East Lansing, MI 48824
e-mail: cywang@mth.msu.edu

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received August 3, 2017; final manuscript received May 18, 2018; published online June 26, 2018. Assoc. Editor: Praveen Ramaprabhu.

J. Fluids Eng 140(12), 121302 (Jun 26, 2018) (5 pages) Paper No: FE-17-1478; doi: 10.1115/1.4040362 History: Received August 03, 2017; Revised May 18, 2018

A modified Ritz method for solving nonuniform slip flow in a duct is applied to the semicircular duct and the isosceles triangular duct. These ducts are important in microfluidics. Detailed flow fields and Poiseuille numbers show the large effects of nonuniform slip. A rare exact solution for the semicircular duct with nonzero slip is also found.

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References

Nguyen, N. T. , and Wereley, S. T. , 2006, Fundamentals and Applications of Microfluidics, 2nd ed., Artech House, Boston, MA.
Seo, C. T. , Bae, C. H. , Eun, D. S. , Shin, J. K. , and Lee, J. H. , 2004, “ Fabrication of Circular Type Microchannel Using Photoresist Reflow and Isotropic Etching for Microfluidic Devices,” Jap. J. Appl. Phys., 43(11A), pp. 7773–7776. [CrossRef]
Yu, H. B. , and Zhou, G. Y. , 2013, “ Deformable Mold Based on-Demand Microchannel Fabrication Technology,” Sens. Actuators B: Chem., 183, pp. 40–45. [CrossRef]
Pekas, N. , Zhang, Q. , Nannini, M. , and Juncker, D. , 2010, “ Wet Etching of Structures With Straight Facets and Adjustable Taper Into Glass Substrates,” Lab Chip, 10(4), pp. 494–498. [CrossRef] [PubMed]
Sharipov, F. , and Seleznev, V. , 1988, “ Data on Internal Rarefied Gas Flows,” J. Phys. Chem. Ref. Data, 27(3), pp. 657–706. [CrossRef]
Choi, C. H. , and Kim, C. J. , 2006, “ Large Slip of Aqueous Liquid Flow Over a Nanoengineered Superhydrophobic Surface,” Phys. Rev. Lett., 96(6), p. 066001. [CrossRef] [PubMed]
Varoutis, S. , Naris, S. , Hauer, V. , Day, C. , and Valougeorgis, D. , 2009, “ Experimental and Computational Investigation of Gas Flows Through Long Channels of Various Cross Sections in the Whole Range of the Knudsen Number,” J. Vac. Sci. Tech. A, 27(1), pp. 89–100. [CrossRef]
Struchtrup, H. , and Taheri, P. , 2011, “ Macroscopic Transport Models for Rarefied Gas Flow- a Brief Review,” IMA J. Appl. Math., 76(5), pp. 672–697. [CrossRef]
Ng, C. O. , and Wang, C. Y. , 2010, “ Apparent Slip Arising From Stokes Shear Flow Over a Bidirectional Patterned Surface,” Microfluid. Nanofluid., 8(3), pp. 361–371. [CrossRef]
Duan, Z. , and Muzychka, Y. S. , 2007, “ Sip Flow in Non-Circular Microchannels,” Microfluid. Nanofluid., 3(4), pp. 473–484. [CrossRef]
Hooman, K. , 2008, “ A Superposition Approach to Study Slip Flow Forced Convection in Straight Microchannels of Uniform but Arbitrary Cross Section,” Int. J. Heat Mas Trans., 51(15–16), pp. 3753–3762. [CrossRef]
Bahrami, M. , Tamayol, A. , and Taheri, P. , 2009, “ Slip- Flow Pressure Drop in Microchannels of General Cross Section,” ASME J. Fluids Eng., 131(3), p. 031201. [CrossRef]
Wang, C. Y. , 2012, “ Brief Review of Exact Solutions in Ducts and Channels,” ASME J. Fluids Eng., 134(9), p. 094501. [CrossRef]
Jang, J. , and Kim, Y. H. , 2010, “ Gaseous Slip Flow of a Rectangular Microchannel With Nonuniform Slip Boundary Conditions,” Microfluid. Nanofluid., 9(2–3), pp. 513–522. [CrossRef]
Sparrow, E. M. , and Siegel, R. , 1959, “ A Variational Method for Fully Developed Laminar Heat Transfer in Ducts,” ASME J. Heat Transfer, 81, pp. 157–167.
Banerjee, S. , and Hadaller, G. I. , 1973, “ Longitudinal Laminar Flow Between Cylinders Arranged in a Rectangular Array by a Variational Technique,” ASME J. Appl. Mech., 40(4), pp. 1136–1138. [CrossRef]
Wang, C. Y. , 2014, “ Ritz Method for Slip Flow in Super-Elliptic Ducts,” Eur. J. Mech./B Fluids, 43, pp. 85–89. [CrossRef]
Rektorys, K. , 1972, Variational Methods in Mathematics, Science and Engineering, Academic Press, New York.
Lei, Q. M. , and Trupp, A. C. , 1989, “ Maximum Velocity Location and Pressure Drop of Fully Developed Laminar Flow in Circular Sector Ducts,” ASME J. Heat Transfer, 111(4), pp. 1085–1087. [CrossRef]
Wang, C. Y. , 2003, “ Slip Flow in a Triangular Duct- an Exact Solution,” Z. Angew. Math. Mech., 83(9), pp. 629–631. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

(a) The semicircular duct and (b) the isosceles triangular duct

Grahic Jump Location
Fig. 2

Constant velocity lines for the semi-circular duct: (a) λ1=λ2=0.0001 (almost no-slip) from inside: w = 0.09, 0.08, 0.07, 0.06, 0.05, 0.04, 0.03, 0.02, 0.01, 0. Maximum is w = 0.0969, (b) λ1=1,  λ2=0.0001 from inside: w = 0.22, 0.2, 0.175, 0.15, 0.125, 0.1, 0.075, 0.05, 0.025, 0. Maximum is w = 0.222, (c) λ1=0.0001,  λ2=1 from inside: w = 0.175, 0.15, 0.125, 0.1, 0.075, 0.05, 0.025, 0. Maximum is w = 0.178, and (d) λ1=λ2=1 from inside: w = 0.424, 0.4, 0.375, 0.35, 0.325, 0.3, 0.275, 0.25 Maximum is w = 0.426, minimum is w=0.228 at the corners.

Grahic Jump Location
Fig. 3

Constant velocity lines for the isosceles triangular duct b = 0.3 (aspect ratio 0.15): (a) λ1=λ2=0.0001 (almost no-slip) from inside: w = 0.0075, 0.006, 0.0045, 0.003, 0.0015, 0, (b) λ1=1,  λ2=0.0001 from inside: w = 0.024, 0.021, 0.018, 0.015, 0.012, 0.009, 0.006, 0.003, 0, (c) λ1=0.0001,  λ2=1 from inside: w = 0.024, 0.021, 0.018, 0.015, 0.012, 0.009, 0.006, 0.003, 0, and (d) λ1=λ2=1 from inside: w = 0.1095, 0.1, 0.09, 0.08, 0.07, 0.06, 0.05, 0.04

Grahic Jump Location
Fig. 4

Constant velocity lines for the isosceles triangular duct b = 3 (aspect ratio 1.5): (a)λ1=λ2=0.0001 (almost no-slip) from inside: w = 0.175, 0.15, 0.125, 0.1, 0.075, 0.05, 0.025, 0, (b) λ1=1,  λ2=0.0001 from inside: w = 0.24, 0.21, 0.18, 0.15, 0.12, 0.09, 0.06, 0.03, 0, (c) λ1=0.0001,  λ2=1 from inside: w = 0.45, 0.4, 0.35, 0.3, 0.25, 0.2, 0.15, 0.1, 0.05, 0, and (d) λ1=λ2=1 from inside: w = 0.6, 0.55, 0.5, 0.45, 0.4, 0.35, 0.3

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