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Thermal transport characteristics of AC electrokinetic flow in a micro-annulus

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Abstract

Alternating current electroosmotic flow and associated heat transfer under constant surface heat flux conditions are numerically examined in a micro-annular channel. The channel surfaces are arbitrarily heated and/or cooled, while the resultant heating is normally transferred downstream by the advection mechanism. An important feature of time-periodic electrokinetic flow is that there is not any preferential axial direction. If the excitation frequency is sufficiently small and/or the liquid kinematic viscosity is sufficiently large, momentum diffuses far into the bulk fluid and thus the advection mechanism is intensified. The reverse is true for relatively large frequency and small kinematic viscosity values. Mean Nusselt number fluctuates over a period of time; its time-averaged magnitude is dependent on the electrokinetic diameter and the dimensionless frequency. This quantity approaches a specific value regardless of the thermal scale and the wall heat flux ratios. The system may attain optimal effectiveness for particular magnitudes of the frequency and electrokinetic diameter. An interesting case may exist in the cooling mode where the axial variation of the mean fluid temperature vanishes temporarily while the state of constant surface temperature is instantly satisfied; at the particular points in time, the advection mechanism does not contribute to the development of the liquid temperature field.

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Abbreviations

\(A_{\text{c}}\) :

Dimensionless cross-sectional area

\(c_{\text{p}}\) :

Specific heat (J kg−1 K−1)

\(D_{\text{h}}\) :

Hydraulic diameter

\(e\) :

Fundamental charge of an electron (C)

\(E\) :

Time-periodic axial electric field strength (V m−1)

\(E_{\text{th}}\) :

Thermal scale ratio

\(f\) :

Fanning friction factor

\(F\) :

Time-periodic function of unit magnitude

\(h\) :

Mean convective heat transfer coefficient (W m−2 K−1)

\(k_{\text{B}}\) :

Boltzmann constant (J K−1)

\(k_{{{\text{th}} .}}\) :

Thermal conductivity of the fluid (W m−1 K−1)

\(n_{\infty }\) :

Bulk ionic concentration (m−3)

\(P\) :

Peripheral ratio

\(P_{\text{ad}}\) :

Advection coefficient

\({\text{Po}}\) :

Poiseuille number

Pr:

Prandtl number

\(q^{\prime\prime}\) :

Surface heat flux (W m−2)

Q :

Dimensionless volumetric flow rate

\(r\) :

Radial coordinate (m)

\(R\) :

Dimensionless radial coordinate

\(\Re\) :

Radius of the outer cylinder (m)

\(\text{Re}\) :

Reynolds number

\(t\) :

Time (s)

T :

Temperature (K)

\({\text{TF}}_{\text{ix}}\) :

Thermal/frictional index

\(U_{\text{HS}}\) :

Helmholtz–Smoluchowski reference velocity (m s−1)

\(V_{\text{z}}\) :

Axial velocity in the annulus (m s−1)

\(V\) :

Dimensionless axial velocity

\(z\) :

Axial coordinate (m)

\({\mathbb{Z}}\) :

Absolute value of the ionic valence

\(Z\) :

Dimensionless potential

\(\chi\) :

Electrokinetic diameter

\(\delta\) :

Wall heat flux ratio

\(\varepsilon\) :

Electric permittivity of solution (F m−1)

\(\varPhi\) :

Dimensionless temperature

\(\gamma\) :

Radius ratio

\(\kappa\) :

Debye–Hückel parameter (m−1)

\(\mu\) :

Dynamic viscosity of the fluid (Ns m−2)

\(\theta\) :

Dimensionless time

\(\rho\) :

Fluid density (kg m−3)

\(\rho_{\text{e}}\) :

Net volume charge density (C m−3)

\(\sigma\) :

Electrical conductivity of the liquid (S m−1)

\(\tau\) :

Shear stress (Pa)

\(\omega\) :

Frequency (s−1)

\(\varOmega\) :

Dimensionless frequency

\(\psi\) :

Electrical potential (V)

\(\varPsi\) :

Dimensionless electrical potential

\(\zeta\) :

Zeta potential (V)

i:

Inner wall

m:

Mean value

o:

Outer wall

w:

Wall

References

  1. Hardt S, Schonfeld F. Microfluidic technologies for miniaturized analysis systems. New York: Springer; 2007.

    Book  Google Scholar 

  2. Bruus H. Theoretical microfluidics. New York: Oxford University Press Inc.; 2008.

    Google Scholar 

  3. Tabeling P. Introduction to microfluidics. New York: Oxford University Press; 2005.

    Google Scholar 

  4. Li D. Electrokinetics in microfluidics. London: Elsevier Academic Press; 2004.

    Google Scholar 

  5. Kandlikar S, Garimella S, Li D, Colin S, King MR. Heat transfer and fluid flow in minichannels and microchannels. Oxford: Elsevier; 2004.

    Google Scholar 

  6. Arulanandam S, Li D. Liquid transport in rectangular microchannels by electro-osmotic pumping. Colloids Surf A. 2000;161:89–102.

    Article  CAS  Google Scholar 

  7. Erickson D, Li D. Analysis of AC electroosmotic flows in a rectangular microchannel. Langmuir. 2003;19:5421–30.

    Article  CAS  Google Scholar 

  8. Xuan XC, Li D. Electroosmotic flow in microchannels with arbitrary geometry and arbitrary distribution of wall charge. J Colloid Interface Sci. 2005;289:291–303.

    Article  CAS  Google Scholar 

  9. Moghadam AJ. An exact solution of AC electro-kinetic-driven flow in a circular micro-channel. Eur J Mech B Fluids. 2012;34:91–6. https://doi.org/10.1016/j.euromechflu.2012.03.006.

    Article  Google Scholar 

  10. Dutta P, Beskok A. Analytical solution of time periodic electroosmotic flows: analogies to stokes second problem. Anal Chem. 2001;73:5097–102.

    Article  CAS  Google Scholar 

  11. Green NG, Ramos A, Gonzalez A, Morgan H, Castellanos A. Fluid flow induced by non-uniform AC electric fields in electrolytes on microelectrodes I: experimental measurements. Phys Rev E. 2000;61:4011–8.

    Article  CAS  Google Scholar 

  12. Gonzalez A, Ramos A, Green NG, Castellanos A, Morgan H. Fluid flow induced by non-uniform AC electric fields in electrolytes on microelectrodes II: a linear double layer analysis. Phys Rev E. 2000;61:4019–28.

    Article  CAS  Google Scholar 

  13. Brown ABD, Smith CG, Rennie AR. Pumping of water with an AC electric field applied to asymmetric pairs of microelectrodes. Phys Rev E. 2002;63:016305.

    Article  Google Scholar 

  14. Moghadam AJ. Exact solution of AC electro-osmotic flow in a microannulus. ASME J Fluids Eng. 2013;135:091201. https://doi.org/10.1115/1.4024205.

    Article  Google Scholar 

  15. Moghadam AJ. Effect of periodic excitation on alternating current electroosmotic flow in a microannular channel. Eur J Mech B Fluids. 2014;48:1–12. https://doi.org/10.1016/j.euromechflu.2014.03.015.

    Article  Google Scholar 

  16. Moghadam AJ. Unsteady electrokinetic flow in a microcapillary: effects of periodic excitation and geometry. ASME J Fluids Eng. 2019;141(11):111104. https://doi.org/10.1115/1.4043337.

    Article  CAS  Google Scholar 

  17. Moghadam AJ. AC EOF in a rectangular microannulus. SN Appl Sci. 2019;1(12):1707. https://doi.org/10.1007/s42452-019-1795-3.

    Article  Google Scholar 

  18. Moghadam AJ. Two-fluid electrokinetic flow in a circular microchannel. Int J Eng (IJE) Trans A Basics. 2016;29(10):1469–77. https://doi.org/10.5829/idosi.ije.2016.29.10a.18.

    Article  CAS  Google Scholar 

  19. Moghadam AJ, Akbarzadeh P. AC two-immiscible-fluid EOF in a microcapillary. J Braz Soc Mech Sci Eng. 2019;41:194.

    Article  Google Scholar 

  20. Moghadam AJ, Akbarzadeh P. Time-periodic electroosmotic flow of non-Newtonian fluids in microchannels. IJE Trans B Appl. 2016;29:736–44. https://doi.org/10.5829/idosi.ije.2016.29.05b.15.

    Article  Google Scholar 

  21. Moghadam AJ, Akbarzadeh P. Non-Newtonian fluid flow induced by pressure gradient and time-periodic electroosmosis in a microtube. J Braz Soc Mech Sci Eng. 2017;39:5015–25. https://doi.org/10.1007/s40430-017-0876-8.

    Article  CAS  Google Scholar 

  22. Soong CY, Wang SH. Theoretical analysis of electrokinetic flow and heat transfer in a microchannel under asymmetric boundary conditions. J Colloid Interface Sci. 2003;265(1):202–13.

    Article  CAS  Google Scholar 

  23. Yang C, Li D, Masliah JH. Modeling forced liquid convection in rectangular microchannels with electrokinetic effects. Int J Heat Mass Transf. 1998;41:4229–49.

    Article  CAS  Google Scholar 

  24. Maynes D, Webb BW. Fully developed electro-osmotic heat transfer in microchannels. Int J Heat Mass Transf. 2003;46:1359–69.

    Article  Google Scholar 

  25. Chen C-H. Thermal transport characteristics of mixed pressure and electro-osmotically driven flow in micro- and nonochannels with Joule heating. ASME J Heat Transf. 2009;131:022401.

    Article  Google Scholar 

  26. Sadeghi A, Saidi MH. Viscous dissipation effects on thermal transport characteristics of combined pressure and electroosmotically driven flow in microchannels. Int J Heat Mass Transf. 2010;53:3782–91.

    Article  CAS  Google Scholar 

  27. Derakhshan S, Adibi I, Sarrafha H. Numerical study of electroosmotic micropump using lattice Boltzmann method. Comp Fluids. 2015;114:232–41.

    Article  Google Scholar 

  28. Maynes D, Webb BW. The effect of viscous dissipation in thermally fully-developed electro-osmotic heat transfer in microchannels. Int J Heat Mass Transf. 2004;47:987–99.

    Article  Google Scholar 

  29. Moghadam AJ. Electrokinetic-driven flow and heat transfer of a non-Newtonian fluid in a circular microchannel. ASME J Heat Transf. 2013;135:021705. https://doi.org/10.1115/1.4007542.

    Article  Google Scholar 

  30. Moghadam AJ. Exact solution of electroviscous flow and heat transfer in a semi-annular microcapillary. ASME J Heat Transf. 2016;138(1):011702. https://doi.org/10.1115/1.4031084.

    Article  CAS  Google Scholar 

  31. Karabi M, Moghadam AJ. Non-Newtonian fluid flow and heat transfer in a semicircular microtube induced by electroosmosis and pressure gradient. ASME J Heat Transf. 2018;140(12):122403. https://doi.org/10.1115/1.4041189.

    Article  Google Scholar 

  32. Shokouhmand H, Jafari A. Investigation of mixed convection in a vertical microchannel affected by EDL. In: Proceedings of the world congress on engineering. London; 2010.

  33. Kwak HS, Kim H, Hyun JM, Song TH. Thermal control of electroosmotic flow in a microchannel through temperature-dependent properties. J Colloid Interface Sci. 2009;335:123–9.

    Article  CAS  Google Scholar 

  34. Dutta P, Horiuchi K. Thermal characteristics of mixed electroosmotic and pressure-driven microflows. Comput Math. 2006;52:651–70.

    Google Scholar 

  35. Prabhakaran RA, Zhou Y, Patel S, Kale A, Song Y, Hu G, Xuan X. Joule heating effects on electroosmotic entry flow. Electrophoresis. 2017;38:572–9.

    Article  Google Scholar 

  36. Liu ZP, Speetjens MFM, Frijns AJH, Van-Steenhoven AA. Heat-transfer enhancement in AC electroosmotic microflows. In: 6th European thermal sciences conference. Journal of physics: conference series. 2012. vol. 395, p. 012094. https://doi.org/10.1088/1742-6596/395/1/012094.

  37. Babaie A, Sadeghi A, Saidi MH. Thermal transport characteristics of non-Newtonian electroosmotic flow in a slit microchannel. In: ASME 9th international conference on nanochannels, microchannels and minichannels. 2011. Vol. 1.

  38. Moghadam AJ. Thermal characteristics of time-periodic electroosmotic flow in a circular microchannel. Heat Mass Transf. 2015;51:1461–73. https://doi.org/10.1007/s00231-015-1513-7.

    Article  CAS  Google Scholar 

  39. Nguyen NT, Wereley ST. Fundamentals and applications of microfluidics. Boston: Artech House; 2006.

    Google Scholar 

  40. White FM. Viscous fluid flow. Singapore: Mc.Graw-Hill; 1991.

    Google Scholar 

  41. Kays WM, Crawford ME. Convective heat and mass transfer. New York: Mc.Graw-Hill; 1993.

    Google Scholar 

  42. Tannehill JC, Anderson DA, Pletcher RH. Computational fluid mechanics and heat transfer. Washington: Taylor & Francis; 1997.

    Google Scholar 

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  1. Faculty of Mechanical Engineering, Shahrood University of Technology, P.O. Box 316, Shahrood, Iran

    Ali Jabari Moghadam

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Moghadam, A.J. Thermal transport characteristics of AC electrokinetic flow in a micro-annulus. J Therm Anal Calorim 145, 2727–2740 (2021). https://doi.org/10.1007/s10973-020-09793-7

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