Research Papers: Forced Convection

Entropy Generation Minimization in an Electroosmotic Flow of Non-Newtonian Fluid: Effect of Conjugate Heat Transfer

[+] Author and Article Information
Prakash Goswami

Department of Mechanical Engineering,
Indian Institute of Technology Kharagpur,
Kharagpur, West Bengal 721302, India

Pranab Kumar Mondal

Department of Mechanical Engineering,
Indian Institute of Technology Kharagpur,
Kharagpur, West Bengal 721302, India;
Advanced Technology Development Center,
Indian Institute of Technology Kharagpur,
Kharagpur, West Bengal 721302, India

Anubhab Datta

Department of Mechanical Engineering,
Jadavpur University,
Kolkata, West Bengal 700032, India

Suman Chakraborty

Department of Mechanical Engineering,
Indian Institute of Technology Kharagpur,
Kharagpur, West Bengal 721302, India;
Advanced Technology Development Center,
Indian Institute of Technology Kharagpur,
Kharagpur, West Bengal 721302, India
e-mail: suman@mech.iitkgp.ernet.in

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received January 13, 2015; final manuscript received December 22, 2015; published online February 3, 2016. Assoc. Editor: Oronzio Manca.

J. Heat Transfer 138(5), 051704 (Feb 03, 2016) (9 pages) Paper No: HT-15-1030; doi: 10.1115/1.4032431 History: Received January 13, 2015; Revised December 22, 2015

We investigate the entropy generation characteristics of a non-Newtonian fluid in a narrow fluidic channel under electrokinetic forcing, taking the effect of conjugate heat transfer into the analysis. We use power-law model to describe the non-Newtonian fluid rheology, in an effort to capture the essential thermohydrodynamics. We solve the conjugate heat transfer problem in an analytical formalism using the thermal boundary conditions of third kind at the outer surface of the walls. We bring out the alteration in the entropy generation behavior as attributable to the rheology-driven alteration in heat transfer, coupled with nonlinear interactions between viscous dissipation and Joule heating originating from electroosmotic effects. We unveil optimum values of different parameters, including both the geometric as well as thermophysical parameters, which lead to the minimization of the entropy generation rate in the system. We believe that the inferences obtained from the present study may bear far ranging consequences in the design of various cooling and heat removal devices/systems, for potential use in microscale thermal management.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.


Anderson, J. L. , 1985, “ Effect of Nonuniform Zeta Potential on Particle Movement in Electric Fields,” J. Colloid Interface Sci., 105(1), pp. 45–54. [CrossRef]
Anderson, J. L. , and Keith Idol, W. , 1985, “ Electroosmosis Through Pores With Nonuniformly Charged Walls,” Chem. Eng. Commun., 38(3–6), pp. 93–106. [CrossRef]
Ajdari, A. , 2000, “ Pumping Liquids Using Asymmetric Electrode Arrays,” Phys. Rev. E, 61(1), pp. R45–R48. [CrossRef]
Ajdari, A. , 1996, “ Generation of Transverse Fluid Currents and Forces by an Electric Field: Electro-Osmosis on Charge-Modulated and Undulated Surfaces,” Phys. Rev. E, 53(5), pp. 4996–5005. [CrossRef]
Squires, T. M. , and Bazant, M. Z. , 2004, “ Induced-Charge Electro-Osmosis,” J. Fluid Mech., 509, pp. 217–252. [CrossRef]
Culbertson, C. T. , Ramsey, R. S. , and Ramsey, J. M. , 2000, “ Electroosmotically Induced Hydraulic Pumping on Microchips: Differential Ion Transport,” Anal. Chem., 72(10), pp. 2285–2291. [CrossRef] [PubMed]
Das, S. , and Chakraborty, S. , 2006, “ Analytical Solutions for Velocity, Temperature and Concentration Distribution in Electroosmotic Microchannel Flows of a Non-Newtonian Bio-Fluid,” Anal. Chim. Acta, 559(1), pp. 15–24. [CrossRef]
Zhao, C. , Zholkovskij, E. , Masliyah, J. H. , and Yang, C. , 2008, “ Analysis of Electroosmotic Flow of Power-Law Fluids in a Slit Microchannel.,” J. Colloid Interface Sci., 326(2), pp. 503–510. [CrossRef] [PubMed]
Gravesen, P. , Branebjerg, J. , and Jensen, O. S. , 1993, “ Microfluidics—A Review,” J. Micromech. Microeng., 3(4), pp. 168–182. [CrossRef]
Nguyen, T. , Xie, Y. , de Vreede, L. J. , van den Berg, A. , and Eijkel, J. C. T. , 2013, “ Highly Enhanced Energy Conversion From the Streaming Current by Polymer Addition,” Lab Chip, 13(16), pp. 3210–3216. [CrossRef] [PubMed]
Chen, C.-K. , and Cho, C.-C. , 2007, “ Electrokinetically-Driven Flow Mixing in Microchannels With Wavy Surface,” J. Colloid Interface Sci., 312(2), pp. 470–480. [CrossRef] [PubMed]
Jain, A. , and Jensen, M. K. , 2007, “ Analytical Modeling of Electrokinetic Effects on Flow and Heat Transfer in Microchannels,” Int. J. Heat Mass Transfer, 50(25–26), pp. 5161–5167. [CrossRef]
Becker, H. , and Gärtner, C. , 2000, “ Polymer Microfabrication Methods for Microfluidic Analytical Applications,” Electrophoresis, 21(1), pp. 12–26. [CrossRef] [PubMed]
Chen, X. Y. , Toh, K. C. , Chai, J. C. , and Yang, C. , 2004, “ Developing Pressure-Driven Liquid Flow in Microchannels Under the Electrokinetic Effect,” Int. J. Eng. Sci., 42(5–6), pp. 609–622. [CrossRef]
Escandón, J. , Bautista, O. , and Méndez, F. , 2013, “ Entropy Generation in Purely Electroosmotic Flows of Non-Newtonian Fluids in a Microchannel,” Energy, 55, pp. 486–496. [CrossRef]
Sánchez, S. , Arcos, J. , Bautista, O. , and Méndez, F. , 2013, “ Joule Heating Effect on a Purely Electroosmotic Flow of Non-Newtonian Fluids in a Slit Microchannel,” J. Non-Newtonian Fluid Mech., 192, pp. 1–9. [CrossRef]
Maynes, D. , and Webb, B. W. , 2004, “ The Effect of Viscous Dissipation in Thermally Fully-Developed Electro-Osmotic Heat Transfer in Microchannels,” Int. J. Heat Mass Transfer, 47(5), pp. 987–999. [CrossRef]
Liechty, B. C. , Webb, B. W. , and Maynes, R. D. , 2005, “ Convective Heat Transfer Characteristics of Electro-Osmotically Generated Flow in Microtubes at High Wall Potential,” Int. J. Heat Mass Transfer, 48(12), pp. 2360–2371. [CrossRef]
Dutta, P. , Horiuchi, K. , and Yin, H.-M. , 2006, “ Thermal Characteristics of Mixed Electroosmotic and Pressure-Driven Microflows,” Comput. Math. Appl., 52(5), pp. 651–670. [CrossRef]
Akgül, M. B. B. , and Pakdemirli, M. , 2008, “ Analytical and Numerical Solutions of Electro-Osmotically Driven Flow of a Third Grade Fluid Between Micro-Parallel Plates,” Int. J. Non-Linear Mech., 43(9), pp. 985–992. [CrossRef]
Matin, M. H. , and Khan, W. A. , 2013, “ Entropy Generation Analysis of Heat and Mass Transfer in Mixed Electrokinetically and Pressure Driven Flow Through a Slit Microchannel,” Energy, 56, pp. 207–217. [CrossRef]
Tang, G. , Yan, D. , Yang, C. , Gong, H. , Chai, C. , and Lam, Y. , 2007, “ Joule Heating and Its Effects on Electrokinetic Transport of Solutes in Rectangular Microchannels,” Sens. Actuators, A, 139(1–2), pp. 221–232. [CrossRef]
Tang, G. Y. , Yang, C. , Chai, J. C. , and Gong, H. Q. , 2004, “ Joule Heating Effect on Electroosmotic Flow and Mass Species Transport in a Microcapillary,” Int. J. Heat Mass Transfer, 47(2), pp. 215–227. [CrossRef]
Horiuchi, K. , and Dutta, P. , 2004, “ Joule Heating Effects in Electroosmotically Driven Microchannel Flows,” Int. J. Heat Mass Transfer, 47(14–16), pp. 3085–3095. [CrossRef]
Mondal, M. , Misra, R. P. , and De, S. , 2014, “ Combined Electroosmotic and Pressure Driven Flow in a Microchannel at High Zeta Potential and Overlapping Electrical Double Layer,” Int. J. Therm. Sci., 86, pp. 48–59. [CrossRef]
Dey, R. , Ghonge, T. , and Chakraborty, S. , 2013, “ Steric-Effect-Induced Alteration of Thermal Transport Phenomenon for Mixed Electroosmotic and Pressure Driven Flows Through Narrow Confinements,” Int. J. Heat Mass Transfer, 56(1–2), pp. 251–262. [CrossRef]
Sadeghi, A. , Veisi, H. , Hassan Saidi, M. , and Asghar Mozafari, A. , 2013, “ Electroosmotic Flow of Viscoelastic Fluids Through a Slit Microchannel With a Step Change in Wall Temperature,” ASME J. Heat Transfer, 135(2), p. 021706. [CrossRef]
Yavari, H. , Sadeghi, A. , Hassan Saidi, M. , and Chakraborty, S. , 2013, “ Temperature Rise in Electroosmotic Flow of Typical Non-Newtonian Biofluids Through Rectangular Microchannels,” ASME J. Heat Transfer, 136(3), p. 031702. [CrossRef]
Moghadam, A. J. , 2013, “ Electrokinetic-Driven Flow and Heat Transfer of a Non-Newtonian Fluid in a Circular Microchannel,” ASME J. Heat Transfer, 135(2), p. 021705. [CrossRef]
Babaie, A. , Sadeghi, A. , and Saidi, M. H. , 2011, “ Combined Electroosmotically and Pressure Driven Flow of Power-Law Fluids in a Slit Microchannel,” J. Non-Newtonian Fluid Mech., 166(14–15), pp. 792–798. [CrossRef]
Bejan, A. , 1979, “ A Study of Entropy Generation in Fundamental Convective Heat Transfer,” ASME J. Heat Transfer, 101(4), pp. 718–725. [CrossRef]
Bejan, A. , 1980, “ Second Law Analysis in Heat Transfer,” Energy, 5(8–9), pp. 720–732. [CrossRef]
Bejan, A. , 1996, Entropy-Generation Minimization, CRC Press, Boca Raton, FL.
Abbassi, H. , 2007, “ Entropy Generation Analysis in a Uniformly Heated Microchannel Heat Sink,” Energy, 32(10), pp. 1932–1947. [CrossRef]
Makinde, O. D. , 2008, “ Entropy-Generation Analysis for Variable-Viscosity Channel Flow With Non-Uniform Wall Temperature,” Appl. Energy, 85(5), pp. 384–393. [CrossRef]
Bejan, A. , 1994, Entropy Generation Through Heat and Fluid Flow, Wiley, Hoboken, NJ.
Ibáñez, G. , and Cuevas, S. , 2008, “ Optimum Wall Conductance Ratio in Magnetoconvective Flow in a Long Vertical Rectangular Duct,” Int. J. Therm. Sci., 47(8), pp. 1012–1019. [CrossRef]
Ibáñez, G. , Cuevas, S. , and López de Haro, M. , 2003, “ Minimization of Entropy Generation by Asymmetric Convective Cooling,” Int. J. Heat Mass Transfer, 46(8), pp. 1321–1328. [CrossRef]
Cuevas, S. , and Río, J. , 2001, “ Dynamic Permeability of Electrically Conducting Fluids Under Magnetic Fields in Annular Ducts,” Phys. Rev. E, 64(1), p. 016313. [CrossRef]
Ibáñez, G. , and Cuevas, S. , 2010, “ Entropy Generation Minimization of a MHD (Magnetohydrodynamic) Flow in a Microchannel,” Energy, 35(10), pp. 4149–4155. [CrossRef]
Aydin, O. , Avci, M. , Bali, T. , and Arıcı, M. E. , 2014, “ Conjugate Heat Transfer in a Duct With an Axially Varying Heat Flux,” Int. J. Heat Mass Transfer, 76, pp. 385–392. [CrossRef]
Avcı, M. , Aydın, O. , and Emin Arıcı, M. , 2012, “ Conjugate Heat Transfer With Viscous Dissipation in a Microtube,” Int. J. Heat Mass Transfer, 55(19–20), pp. 5302–5308. [CrossRef]
Ibáñez, G. , López, A. , Pantoja, J. , Moreira, J. , and Reyes, J. A. , 2013, “ Optimum Slip Flow Based on the Minimization of Entropy Generation in Parallel Plate Microchannels,” Energy, 50, pp. 143–149. [CrossRef]
Hettiarachchi, H. D. M. , Golubovic, M. , Worek, W. M. , and Minkowycz, W. J. , 2008, “ Slip-Flow and Conjugate Heat Transfer in Rectangular Microchannels,” ASME Paper No. HT2008-56233.
Hunter, R. J. , 1981, Zeta Potential in Colloid Science: Principles and Applications, Academic, London.
Masliyah, J. H. , and Bhattacharjee, S. , 2006, Electrokinetic and Colloid Transport Phenomena, Wiley, Hoboken, NJ.
Sheu, T. W. H. , Kuo, S. H. , and Lin, R. K. , 2012, “ Prediction of a Temperature-Dependent Electroosmotically Driven Microchannel Flow With the Joule Heating Effect,” Int. J. Numer. Methods Heat Fluid Flow, 22(5), pp. 554–575. [CrossRef]
Keramati, H. , Sadeghi, A. , Saidi, M. H. , and Chakraborty, S. , 2016, “ Analytical Solutions for Thermo-Fluidic Transport in Electroosmotic Flow Through Rough Microtubes,” Int. J. Heat Mass Transfer, 92, pp. 244–251. [CrossRef]
Escandón, J. P. , Bautista, O. , Méndez, F. , and Bautista, E. , 2011, “ Theoretical Conjugate Heat Transfer Analysis in a Parallel Flat Plate Microchannel Under Electro-Osmotic and Pressure Forces With a Phan-Thien-Tanner Fluid,” Int. J. Therm. Sci., 50(6), pp. 1022–1030. [CrossRef]
Sugioka, H. , 2014, “ Nonlinear Thermokinetic Phenomena Due to the Seebeck Effect,” Langmuir, 30(28), pp. 8621–8630. [CrossRef] [PubMed]
Ghosal, S. , 2006, “ Electrokinetic Flow and Dispersion in Capillary Electrophoresis,” Annu. Rev. Fluid Mech., 38(1), pp. 309–338. [CrossRef]
Snyder, W. T. , 1964, “ The Influence of Wall Conductance on Magnetohydrodynamic Channel-Flow Heat Transfer,” ASME J. Heat Transfer, 86(4), pp. 552–556. [CrossRef]
De Groot, S. R. , and Mazur, P. , 1984, Non-Equilibrium Thermodynamics, Dover, New York.
Ibáñez, G. , López, A. , and Cuevas, S. , 2012, “ Optimum Wall Thickness Ratio Based on the Minimization of Entropy Generation in a Viscous Flow Between Parallel Plates,” Int. Commun. Heat Mass Transfer, 39(5), pp. 587–592. [CrossRef]
Holman, J. P. , 1990, Heat Transfer, McGraw-Hill, New York. [PubMed] [PubMed]
Dey, R. , Chakraborty, D. , and Chakraborty, S. , 2011, “ Analytical Solution for Thermally Fully Developed Combined Electroosmotic and Pressure-Driven Flows in Narrow Confinements With Thick Electrical Double Layers,” ASME J. Heat Transfer, 133(2), p. 024503. [CrossRef]
Chakraborty, R. , Dey, R. , and Chakraborty, S. , 2013, “ Thermal Characteristics of Electromagnetohydrodynamic Flows in Narrow Channels With Viscous Dissipation and Joule Heating Under Constant Wall Heat Flux,” Int. J. Heat Mass Transfer, 67, pp. 1151–1162. [CrossRef]


Grahic Jump Location
Fig. 1

Schematic depicting the physical dimensions of the problem. The external applied electric field Ex actuates the flow in the positive x -direction. The walls of the channel are kept at unequal temperatures.

Grahic Jump Location
Fig. 2

Comparison between the approximate analytical and numerical solutions for the normalized velocity distribution obtained for different values of power-law index: n=0.8, 1.0, and  1.2. We take κ¯=10 for this plot. The analytical solutions show a good agreement with the numerical results for all the values of n considered.

Grahic Jump Location
Fig. 3

Plot of normalized global entropy generation versus δU, for three different values of n=0.8,1.0, and 1.2, respectively, while κ¯=10 and J=1. The parameter δU used as a x -axis variable is the upper wall thickness (dimensionless). The other parameters considered are: Pe=0.01, B=1, δL=0.1, BiL=2, BiU=20, and λL=λU=0.5. The global entropy generation rate in the system initially decreases, attains a minimum value, and finally shows an increasing trend for all the cases of power-law fluids considered.

Grahic Jump Location
Fig. 4

Plot of normalized global entropy generation as a function of λU, for three different values of n=0.8, 1.0, and 1.2, while κ¯=10 and J=1. The x -axis variable λU is the ratio of wall to fluid thermal conductivity at the upper wall. We have taken the following values of the other parameters: Pe=0.01, B=1, δL=δU=0.1, BiL=BiU=2, and λL=10. The variations predict an optimum value of λU,opt, leading to a minimum entropy generation rate in the system. A careful observation of the figure reveals that a change in fluid rheology alters the λU,opt value.

Grahic Jump Location
Fig. 5

Normalized entropy generation rate (normalized by its value when BiU=0) as a function of BiU is plotted, for three different values of n=0.8, 1.0, and 1.2. Note that the x -axis variable BiU is the Biot number at the upper wall of the channel. We have consider κ¯=10 and J=1. The other parameters are as follows: Pe=0.01, B=1, δL=δU=0.1, λL=λU=2, and BiL=4. We observe an optimum value of BiU,opt from the figure, leading to a minimum entropy generation rate in the system, which changes with a change in rheological behavior of the fluid.

Grahic Jump Location
Fig. 6

Variation of global entropy generation with B, while three different values of n=0.8, 1.0, and 1.2 have been considered. The x -axis variable B represents the axial temperature gradient. We have taken κ¯=10 and J=1. The other parameters considered have the following values: Pe=0.01, δL=δU=0.1, BiL=2, BiU=20, and λL=λU=10. The optimum value of axial temperature gradient Bopt exists that minimizes the irreversibility associated to the present system, for all the values of n considered.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In