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Research Papers: Micro/Nanoscale Heat Transfer

On the Enhancement of Heat Transfer and Reduction of Entropy Generation by Asymmetric Slip in Pressure-Driven Non-Newtonian Microflows

[+] Author and Article Information
Vishal Anand

School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47907

Ivan C. Christov

School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47907
e-mail: christov@purdue.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 13, 2018; final manuscript received November 7, 2018; published online December 17, 2018. Assoc. Editor: Danesh K. Tafti.

J. Heat Transfer 141(2), 022403 (Dec 17, 2018) (12 pages) Paper No: HT-18-1392; doi: 10.1115/1.4042157 History: Received June 13, 2018; Revised November 07, 2018

We study hydrodynamics, heat transfer, and entropy generation in pressure-driven microchannel flow of a power-law fluid. Specifically, we address the effect of asymmetry in the slip boundary condition at the channel walls. Constant, uniform but unequal heat fluxes are imposed at the walls in this thermally developed flow. The effect of asymmetric slip on the velocity profile, on the wall shear stress, on the temperature distribution, on the Bejan number profiles, and on the average entropy generation and the Nusselt number are established through the numerical evaluation of exact analytical expressions derived. Specifically, due to asymmetric slip, the fluid momentum flux and thermal energy flux are enhanced along the wall with larger slip, which, in turn, shifts the location of the velocity's maximum to an off-center location closer to the said wall. Asymmetric slip is also shown to redistribute the peaks and plateaus of the Bejan number profile across the microchannel, showing a sharp transition between entropy generation due to heat transfer and due to fluid flow at an off-center-line location. In the presence of asymmetric slip, the difference in the imposed heat fluxes leads to starkly different Bejan number profiles depending on which wall is hotter, and whether the fluid is shear-thinning or shear-thickening. Overall, slip is shown to promote uniformity in both the velocity field and the temperature field, thereby reducing irreversibility in this flow.

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References

Lauga, E. , Brenner, M. P. , and Stone, H. A. , 2007, “ Microfluidics: The No-Slip Boundary Condition,” Springer Handbook of Experimental Fluid Mechanics, C. Tropea, A. L. Yarin, and J. F. Foss, eds., Springer, Berlin, Chap. 19.
Denn, M. M. , 1990, “ Issues in Viscoelastic Fluid Mechanics,” Annu. Rev. Fluid Mech., 22(1), pp. 13–32. [CrossRef]
Gad-el Hak, M. , 1999, “ The Fluid Mechanics of Microdevices—The Freeman Scholar Lecture,” ASME J. Fluids Eng., 121, pp. 5–33. [CrossRef]
Nguyen, N.-T. , and Wereley, S. T. , 2006, Fundamentals and Applications of Microfluidics (Integrated Microsystems Series), 2nd ed., Artech House, Norwood, MA.
Shu, J.-J. , Teo, J. B. M. , and Chan, W. K. , 2017, “ Fluid Velocity Slip and Temperature Jump at a Solid Surface,” ASME Appl. Mech. Rev., 69(2), p. 020801. [CrossRef]
Denn, M. M. , 2001, “ Extrusion Instabilities and Wall Slip,” Annu. Rev. Fluid Mech., 33(1), pp. 265–287. [CrossRef]
Kalyon, D. M. , 2005, “ Apparent Slip and Viscoplasticity of Concentrated Suspensions,” J. Rheol., 49(3), pp. 621–640. [CrossRef]
Thompson, P. A. , and Troian, S. M. , 1997, “ A General Boundary Condition for Liquid Flow at Solid Surfaces,” Nature, 389(6649), pp. 360–362. [CrossRef]
Navier, C. L. M. H. , 1823, “ Mémoire sur les lois du Mouvement des Fluides,” Mémoire de l'Académie Royale des Sci. de l'Institut de France, 6, pp. 389–440.
Cloitre, M. , and Bonnecaze, R. T. , 2017, “ A Review on Wall Slip in High Solid Dispersions,” Rheol. Acta, 56(3), pp. 283–305. [CrossRef]
Matthews, M. T. , and Hill, J. M. , 2007, “ Newtonian Flow With Nonlinear Navier Boundary Condition,” Acta Mech., 191(3–4), pp. 195–217. [CrossRef]
Bird, R. B. , 1959, “ Unsteady Pseudoplastic Flow Near a Moving Wall,” AIChE J., 5(4), pp. 565–566. [CrossRef]
Acrivos, A. , Shah, M. J. , and Petersen, E. E. , 1960, “ Momentum and Heat Transfer in Laminar Boundary-Layer Flows of Non-Newtonian Fluids Past External Surfaces,” AIChE J., 6(2), pp. 312–317. [CrossRef]
Yan, Y. , and Koplik, J. , 2008, “ Flow of Power-Law Fluids in Self-Affine Fracture Channels,” Phys. Rev. E, 77(3), p. 036315. [CrossRef]
Bird, R. B. , 1976, “ Useful Non-Newtonian Models,” Annu. Rev. Fluid Mech., 8(1), pp. 13–34. [CrossRef]
Ferrás, L. L. , Nóbrega, J. M. , and Pinho, F. T. , 2012, “ Analytical Solutions for Newtonian and Inelastic Non-Newtonian Flows With Wall Slip,” J. Non-Newtonian Fluid Mech., 175–176, pp. 76–88. [CrossRef]
Pritchard, D. , McArdle, C. R. , and Wilson, S. K. , 2011, “ The Stokes Boundary Layer for a Power-Law Fluid,” J. Non-Newtonian Fluid Mech., 166(12–13), pp. 745–753. [CrossRef]
Wei, D. , and Jordan, P. M. , 2013, “ A Note on Acoustic Propagation in Power-Law Fluids: Compact Kinks, mild Discontinuities, and a Connection to Finite-Scale Theory,” Int. J. Non-Linear Mech., 48, pp. 72–77. [CrossRef]
Garimella, S. V. , and Sobhan, C. B. , 2003, “ Transport in Microchannels—A Critical Review,” Annu. Rev. Heat Transfer, 13(13), pp. 1–50. [CrossRef]
Yovanovich, M. M. , and Khan, W. A. , 2015, “ Friction and Heat Transfer in Liquid and Gas Flows in Micro- and Nanochannels,” Advances in Heat Transfer, Vol. 47, E. M. Sparrow , J. P. Abraham , and J. M. Gorman , eds., Elsevier, Waltham, MA, pp. 203–307.
Barbati, A. C. , Desroches, J. , Robisson, A. , and McKinley, G. H. , 2016, “ Complex Fluids and Hydraulic Fracturing,” Annu. Rev. Chem. Biomol. Eng., 7, pp. 415–453. [CrossRef] [PubMed]
Barletta, A. , 1996, “ Fully Developed Laminar Forced Convection in Circular Ducts for Power Law Fluids With Viscous Dissipation,” Int. J. Heat Mass Transfer, 40(1), pp. 15–26. [CrossRef]
Cruz, D. A. , Coelho, P. M. , and Alves, M. A. , 2012, “ A Simplified Method for Calculating Heat Transfer Coefficients and Friction Factors in Laminar Pipe Flow of Non-Newtonian Fluids,” ASME J. Heat Transfer, 134(9), p. 091703. [CrossRef]
Jambal, O. , Shigechi, T. , Davaa, G. , and Momoki, S. , 2005, “ Effects of Viscous Dissipation and Fluid Axial Heat Conduction on Heat Transfer for Non-Newtonian Fluids in Ducts With Uniform Wall Temperature—Part II: Annular Ducts,” Int. Commun. Heat Mass Transfer, 32(9), pp. 1174–1183. [CrossRef]
Tso, C. P. , Sheela-Francisca, J. , and Hung, Y.-M. , 2010, “ Viscous Dissipation Effects of Power-Law Fluid Flow Within Parallel Plates With Constant Heat Fluxes,” J. Non-Newtonian Fluid Mech., 165(11–12), pp. 625–630. [CrossRef]
Sheela-Francisca, J. , Tso, C. P. , Hung, Y. M. , and Rilling, D. , 2012, “ Heat Transfer on Asymmetric Thermal Viscous Dissipative Couette–Poiseuille Flow of Pseudo-Plastic Fluids,” J. Non-Newtonian Fluid Mech., 169–170(2), pp. 42–53. [CrossRef]
Straughan, B. , 2015, Convection With Local Thermal Non-Equilibrium and Microfluidic Effects (Advances in Mechanics and Mathematics), Vol. 32, Springer International Publishing, Cham, Switzerland.
Kaushik, P. , Mondal, P. K. , Pati, S. , and Chakraborty, S. , 2017, “ Heat Transfer and Entropy Generation Characteristics of a Non-Newtonian Fluid Squeezed and Extruded Between Two Parallel Plates,” ASME J. Heat Transfer, 139(2), p. 022004. [CrossRef]
Sefid, M. , and Izadpanah, E. , 2013, “ Developing and Fully Developed Non-Newtonian Fluid Flow and Heat Transfer Through Concentric Annuli,” ASME J. Heat Transfer, 135(7), p. 071702. [CrossRef]
Bejan, A. , 1999, “ The Method of Entropy Generation Minimization,” Energy and the Environment (Environmental Science and Technology Library), Vol. 15, A. Bejan , P. Vadász , and D. G. Kröger , eds., Springer, Dordrecht, The Netherlands, pp. 11–22.
Mahmud, S. , and Fraser, R. A. , 2002, “ Thermodynamic Analysis of Flow and Heat Transfer Inside Channel With Two Parallel Plates,” Exergy, 2(3), pp. 140–146. [CrossRef]
Mahmud, S. , and Fraser, R. A. , 2006, “ Second Law Analysis of Forced Convection in a Circular Duct for Non-Newtonian Fluids,” Energy, 31(12), pp. 2226–2244. [CrossRef]
Hung, Y. M. , 2008, “ Viscous Dissipation Effect on Entropy Generation for Non-Newtonian Fluids in Microchannels,” Int. Commun. Heat Mass Transfer, 35(9), pp. 1125–1129. [CrossRef]
Shojaeian, M. , and Koşar, A. , 2014, “ Convective Heat Transfer and Entropy Generation Analysis on Newtonian and Non-Newtonian Fluid Flows Between Parallel-Plates Under Slip Boundary Conditions,” Int. J. Heat Mass Transfer, 70(3), pp. 664–673. [CrossRef]
Anand, V. , 2014, “ Slip Law Effects on Heat Transfer and Entropy Generation of Pressure Driven Flow of a Power Law Fluid in a Microchannel Under Uniform Heat Flux Boundary Condition,” Energy, 76, pp. 716–732. [CrossRef]
Goswami, P. , Mondal, P. , Datta, A. , and Chakraborty, S. , 2016, “ Entropy Generation Minimization in an Electroosmotic Flow of Non-Newtonian Fluid: Effect of Conjugate Heat Transfer,” ASME J. Heat Transfer, 138(5), p. 051704. [CrossRef]
Mondal, P. K. , 2014, “ Entropy Analysis for the Couette Flow of Non-Newtonian Fluids Between Asymmetrically Heated Parallel Plates: Effect of Applied Pressure Gradient,” Phys. Scr., 89(12), p. 125003.
Vayssade, A.-L. , Lee, C. , Terriac, E. , Monti, F. , Cloitre, M. , and Tabeling, P. , 2014, “ Dynamical Role of Slip Heterogeneities in Confined Flows,” Phys. Rev. E, 89(5), p. 052309. [CrossRef]
Panaseti, P. , Vayssade, A.-L. , Georgiou, G. C. , and Cloitre, M. , 2017, “ Confined Viscoplastic Flows With Heterogeneous Wall Slip,” Rheol. Acta, 56(6), pp. 539–553. [CrossRef]
Stone, H. A. , 2017, “ Fundamentals of Fluid Dynamics With an Introduction to the Importance of Interfaces,” Soft Interfaces (Lecture Notes of the Les Houches Summer School), Vol. 98, L. Bocquet , D. Quéré , T. A. Witten , and L. F. Cugliandolo , eds., Oxford University Press, New York, pp. 3–76.
Leal, L. G. , 2007, Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes, Cambridge University Press, Cambridge, UK.
Chhabra, R. P. , 2010, “ Non-Newtonian Fluids: An Introduction,” Rheology of Complex Fluids, J. Murali Krishnan , A. P. Deshpande , and P. B. Sunil Kumar , eds., Springer Science+Business Media, New York, pp. 3–34.
Bird, R. B. , Armstrong, R. C. , and Hassager, O. , 1987, Dynamics of Polymeric Liquids, 2nd ed., Vol. 1, Wiley, New York.
Koo, J. , and Kleinstreuer, C. , 2004, “ Viscous Dissipation Effects in Microtubes and Microchannels,” Int. J. Heat Mass Transfer, 47(14–16), pp. 3159–3169. [CrossRef]
Bergman, T. L. , Lavine, A. S. , Incropera, F. P. , and DeWitt, D. P. , 2011, Fundamentals of Heat and Mass Transfer, 7th ed., Wiley, New York.
Paoletti, S. , Rispoli, F. , and Sciubba, E. , 1989, “ Calculation of Exergetic Losses in Compact Heat Exchanger Passages,” Analysis and Design of Energy Systems: Fundamentals and Mathematical Techniques, R. A. Bajura , H. N. Shapiro , and J. R. Zaworksi , eds., American Society of Mechanical Engineers, New York, pp. 21–29.
Petrescu, S. , 1994, “ Comments on ‘The Optimal Spacing of Parallel Plates Cooled by Forced Convection,’” Int. J. Heat Mass Transfer, 37(8), p. 1283. [CrossRef]
Jones, E. , Oliphant, T. , and Peterson, P. , 2001, “ SciPy: Open Source Scientific Tools for Python,” SciPY, accessed Dec. 12, 2018, http://www.scipy.org
Panton, R. L. , 2013, Incompressible Flow, 4th ed., Wiley, Hoboken, NJ.
Blasius, H. , 1908, “ Grenzschichten in Flüssigkeiten mit kleiner Reibung,” Z. Math. Phys., 56, pp. 1–37.
Pohlhausen, E. , 1921, “ Der Wärmeaustausch zwischen festen Körpern und Flüssigkeiten mit kleiner Reibung und kleiner Wärmeleitung,” Z. Angew. Math. Mech., 1(2), pp. 115–121. [CrossRef]
Jessee, R. , 2015, “ An Analytic Solution of the Thermal Boundary Layer at the Leading Edge of a Heated Semi-Infinite Flat Plate Under Forced Uniform Flow,” M.S. thesis, Louisiana State University, Baton Rouge, LA. https://digitalcommons.lsu.edu/gradschool_theses/2013/
Bejan, A. , 2013, Convection Heat Transfer, 4th ed., Wiley, Hoboken, NJ.
Illingworth, J. B. , Hills, N. J. , and Barnes, C. J. , 2005, “ 3D Fluid–Solid Heat Transfer Coupling of an Aero Engine Pre-Swirl System,” ASME Paper No. GT2005-68939.
Asako, Y. , and Hong, C. , 2017, “ On Temperature Jump Condition for Slip Flow in a Microchannel With Constant Wall Temperature,” ASME J. Heat Transfer, 139(7), p. 072402. [CrossRef]
Hong, C. , and Asako, Y. , 2010, “ Some Considerations on Thermal Boundary Condition of Slip Flow,” Int. J. Heat Mass Transfer, 53(15–16), pp. 3075–3079. [CrossRef]
Sparrow, E. M. , and Lin, S. H. , 1962, “ Laminar Heat Transfer in Tubes Under Slip-Flow Conditions,” ASME J. Heat Transfer, 84(4), pp. 363–369. [CrossRef]
Smoluchowski von Smolan, M. , 1898, “ Ueber Wärmeleitung in verdünnten Gasen,” Ann. Phys., 300(1), pp. 101–130. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Schematic of the physical model, coordinates and notation. We work the problem per unit width out of the page (i.e., the +z-direction).

Grahic Jump Location
Fig. 2

Dimensionless velocity profiles u¯(y¯) across the channel for different values of the dimensionless slip coefficient K¯1. Dashed curves correspond to n =0.5 (shear-thinning fluid), while solid curves correspond to n =1.5 (shear-thickening fluid). The gray curve on the left corresponds to a Newtonian fluid subject to no slip boundary conditions. Filled circles denote the vertical location of the velocity maximum.

Grahic Jump Location
Fig. 3

Dimensionless shear stress at the channel walls τ¯w versus the power-law index n for different values of the slip coefficient K¯1. The dashed lines show the shear stress on the upper wall, τ¯w2, while the solid curves show the shear stress on the lower wall, τ¯w1.

Grahic Jump Location
Fig. 6

The Nusselt number along the lower wall (y¯=0) for different values of the power-law exponent n and the slip coefficient K¯1. The ratio of imposed heat fluxes is q2/q1 = 0.5.

Grahic Jump Location
Fig. 7

The Nusselt number along the lower wall (y¯=0) for different values of the power-law exponent n and the slip coefficient K¯1. The ratio of imposed heat fluxes is q2/q1 = 2.0.

Grahic Jump Location
Fig. 4

Dimensionless temperature distribution θ across the height y¯ of the channel with a larger imposed heat flux at the lower wall (q2/q1=0.5<1), for different values of the slip coefficient K¯1. The dashed curves show the profiles of a shear-thinning fluid with power-law exponent n =0.5, while the solid curves show the profiles of a shear-thickening fluid with n =1.5.

Grahic Jump Location
Fig. 5

Dimensionless temperature distribution θ across the height y¯ of the channel with a larger imposed heat flux at the upper wall (q2/q1=2.0>1), for different values of the slip coefficient K¯1. The dashed curves show the profiles of a shear-thinning fluid with power-law exponent n =0.5, while the solid curves show the profiles of a shear-thickening fluid with n =1.5.

Grahic Jump Location
Fig. 10

Distribution of Bejan number Be(y¯) across the channel width for different values of the slip coefficient K¯1 and q2/q1 = 0.5. The dashed curves correspond to a shear-thinning fluid with n =0.5, while the solid curves correspond to a shear-thickening fluid with n =1.5. The black vertical denotes Be = 1/2.

Grahic Jump Location
Fig. 11

Distribution of Bejan number Be(y¯) across the channel width for different values of the slip coefficient K¯1 and q2/q1 = 2.0. The dashed curves correspond to a shear-thinning fluid with n =0.5, while the solid curves correspond to a shear-thickening fluid with n =1.5. The black vertical denotes Be = 1/2.

Grahic Jump Location
Fig. 8

Average entropy generation rate 〈Ns〉 as a function of the power-law index n for different values of the slip coefficient K¯1. The ratio of imposed heat fluxes is q2/q1 = 0.5.

Grahic Jump Location
Fig. 9

Average entropy generation rate 〈Ns〉 as a function of the power-law index n for different values of the slip coefficient K¯1. The ratio of imposed heat fluxes is q2/q1 = 2.0.

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