Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-28T02:42:59.437Z Has data issue: false hasContentIssue false
  • English
  • Français

Electromagnetohydrodynamic Flow of Powell-Eyring Fluids in a Narrow Confinement

Published online by Cambridge University Press:  09 September 2016

F.-Q. Li ,
Y.-J. Jian ,
Z.-Y. Xie  and
L. Wang
F.-Q. Li
Affiliation:
School of Mathematical ScienceInner Mongolia UniversityHohhot, China
Y.-J. Jian*
Affiliation:
School of Mathematical ScienceInner Mongolia UniversityHohhot, China
Z.-Y. Xie
Affiliation:
School of Mathematical ScienceInner Mongolia UniversityHohhot, China
L. Wang
Affiliation:
School of Mathematical ScienceInner Mongolia UniversityHohhot, China
*
*Corresponding author ([email protected])
Get access

Abstract

In this work, we investigate electromagnetohydrodynamic (EMHD) flow of Powell-Eyring fluid through a slit confinement. The approximate analytical solution and numerical result of EMHD velocity are obtained by using homotopy perturbation method and Chebyshev spectral method, respectively. The analytical solutions are found to be in good agreement with numerical results under the same conditions. The influences of Hartmann number Ha, electrical field strength parameter S, the Powell-Eyring fluid parameters γ and β on velocity are discussed in detail. It is found that the volume flow rate of Newtonian fluid is always larger than that of Powell-Eyring fluid. The results reveal the intricate interaction between EMHD effect and fluid rheology involving non-Newtonian fluid. Therefore, the results are useful in dealing with some non-Newtonian biomicrofluidic systems.

Keywords

EMHD micropumpPowell-Eyring fluidHartmann numberHomotopy perturbation method
Type
Research Article
Information
Journal of Mechanics , Volume 33 , Issue 2 , April 2017 , pp. 225 - 233
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Stone, H. A., Stroock, A. D. and Ajdari, A., “Engineering flows in small devices: Microfluidics toward a lab-on-a-chip,” Annual Review of Fluid Mechanics, 36, pp. 381–411 (2004).CrossRefGoogle Scholar
2. Das, S. and Chakraborty, S., “Analytical solutions for velocity, temperature and concentration distribution in electroosmotic microchannel flows of a non-Newtonian bio-fluid,” Analytica Chimica Acta, 559, pp. 15–24 (2006).CrossRefGoogle Scholar
3. Ghosal, S., “Lubrication theory for electro-osmotic flow in a microfluidic channel of slowly varying cross-section and wall charge.” Journal of Fluid Mechanics, 459, pp. 103–128 (2002).CrossRefGoogle Scholar
4. Wang, C. Y., Liu, Y. H. and Chang, C. C., “Analytical solution of electro-osmotic flow in a semicircular microchannel,” Physics of Fluids, 20, 063105 (2008).CrossRefGoogle Scholar
5. Li, S. X., Jian, Y. J., Xie, Z. Y., Liu, Q. S. and Li, F. Q., “Rotating electro-osmotic flow of third grade fluids between two microparallel plates,” Colloids and Surfaces A: Physicochemical and Engineering Aspects, 470, pp. 240–247 (2015).CrossRefGoogle Scholar
6. Jian, Y. J., Su, J., Chang, L., Liu, Q. S. and He, G. W., “Transient electroosmotic flow of general Maxwell fluids through a slit microchannel,” Zeitschrift für Angewandte Mathematik und Physik (ZAMP), 65, pp. 435–447 (2014).CrossRefGoogle Scholar
7. Lemoff, A. V. and Lee, A. P., “An AC magnetohydrodynamic micropump,” Sensors and Actuators B: Chemical, 63, pp. 178–185 (2000).CrossRefGoogle Scholar
8. Bau, H. H., Zhu, J., Qian, S. and Xiang, Y., “A magneto-hydrodynamically controlled fluidic network,” Sensors Actuators B, 88, pp. 205–216 (2003).CrossRefGoogle Scholar
9. Qian, S. Z. and Bau, H. H., “Magneto-hydrodynamics based microfluidics,” Mechanics Research Communications, 36, pp. 10–21 (2009).CrossRefGoogle ScholarPubMed
10. Gelb, A., Gleeson, J. P., West, J. and Roche, O. M., “Modeling annular micromixers,” SIAM Journal on Applied Mathematics, 64, pp. 1294–1310 (2004).CrossRefGoogle Scholar
11. Pamme, N., “Magnetism and microfluidics,” Lab on a Chip, 6, pp. 24–38 (2006).CrossRefGoogle ScholarPubMed
12. Peter, L. O. and Sedat, B., “Direct numerical simulations of low Reynolds number turbulent channel flow with EMHD control,” Physics of Fluids, 10, pp. 1169–1181 (1998).Google Scholar
13. Abdullah, M. and Duwairi, H. M., “Thermal and flow analysis of two-dimensional fully developed flow in an AC magneto-hydrodynamic micropump,” Microsystem technologies, 14, pp. 1117–1123 (2008).CrossRefGoogle Scholar
14. Buren, M., Jian, Y. J. and Chang, L., “Electromagnetohydrodynamic flow through a microparallel channel with corrugated walls,” Journal of Physics D: Applied Physics, 47, 425501 (2014).CrossRefGoogle Scholar
15. Reddy, P. D. S., Bandyopadhyay, D., Joo, S. W., Sharma, A. and Qian, S., “Parametric study on instabilities in a two-layer electromagnetohydrodynamic channel flow confined between two parallel electrodes,” Physical Review E, 83, 036313 (2011).CrossRefGoogle Scholar
16. Shojaeian, M. and Shojaeian, M., “Analytical solution of mixed electromagnetic/pressure driven gaseous flows in microchannel,” Microfluidics and nanofluidics, 12, pp. 553–564 (2012).CrossRefGoogle Scholar
17. Si, D. Q. and Jian, Y. J., “Electromagnetohydrodynamic (EMHD) micropump of Jeffrey fluids through two parallel microchannels with corrugated walls,” Journal of Physics D: Applied Physics, 48, 085501 (2015).CrossRefGoogle Scholar
18. Duwairi, H. M. and Abdullah, M., “Numerical computation of fluid flow in a magnetohydrodynamic micropump,” Turkish Journal of Engineering and Environmental Sciences, 32, pp. 1–5 (2008).Google Scholar
19. Jang, J. and Lee, S. S., “Theoretical and experimental study of MHD magnetohydrodynamic micropump,” Sensors and Actuators A: Physical, 80, pp. 84–89 (2000).CrossRefGoogle Scholar
20. Chakraborty, S. and Paul, D., “Microchannel flow control through a combined electromagnetohydrodynamic transport,” Journal of Physics D: Applied Physics, 39, pp. 5364–5371 (2006).CrossRefGoogle Scholar
21. Jian, Y. J. and Chang, L., “Electromagnetohydrodynamic (EMHD) micropumps under a spatially nonuniform magnetic field,” AIP Advances, 5, 057121 (2015).CrossRefGoogle Scholar
22. Tso, C. P. and Sundaravadivelu, K., “Capillary flow between parallel plates in the presence of an electromagnetic field,” Journal of Physics D: Applied Physics, 34, pp. 3522–3527 (2001).CrossRefGoogle Scholar
23. Sun, Y. J., Jian, Y. J., Chang, L. and Liu, Q. S., “Thermally fully developed electroosmotic flow of power-law fluids in a circular microchannel,” Journal of Mechanics, 29, pp. 609–616 (2013).CrossRefGoogle Scholar
24. Jian, Y. J., Liu, Q. S. and Yang, L. G., “AC electroosmotic flow of generalized Maxwell fluids in a rectangular microchannel,” Journal of Non-Newtonian Fluid Mechanics, 166, pp. 1304–1314 (2011).CrossRefGoogle Scholar
25. Liu, Q. S., Jian, Y. J. and Yang, L. G., “Alternating current electroosmotic flow of the Jeffreys fluids through a slit microchannel,” Physics of Fluids, 23, 102001 (2011).CrossRefGoogle Scholar
26. Sun, L. X., Jian, Y. J., Chang, L., Zhang, H. Y. and Liu, Q. S., “Alternating current electro-osmotic flow of the Maxwell fluids through a circular micro-pipe,” Journal of Mechanics, 29, pp. 233–240 (2013).CrossRefGoogle Scholar
27. Powell, R. E. and Eyring, H., “Mechanism for the relaxation theory of viscosity,” Nature, 154, pp. 427–428 (1944).CrossRefGoogle Scholar
28. Islam, S., Shah, A., Zhou, C. Y. and Ali, I., “Homotopy perturbation analysis of slider bearing with Powell-Eyring fluid,” Zeitschrift für Angewandte Mathematik und Physik (ZAMP), 60, pp. 1178–1193 (2009).CrossRefGoogle Scholar
29. Patel, M. and Timol, M. G., “Numerical treatment of Powell–Eyring fluid flow using Method of Satisfaction of Asymptotic Boundary Conditions (MSABC),” Applied Numerical Mathematics, 59, pp. 2584–2592 (2009)CrossRefGoogle Scholar
30. Hayat, T., Iqbal, Z., Qasim, M. and Obaidat, S., “Steady flow of an Eyring Powell fluid over a moving surface with convective boundary conditions,” International Journal of Heat and Mass Transfer, 55, pp. 1817–1822 (2012).CrossRefGoogle Scholar
31. Hayat, T., Shah, S. I., Ahmad, B. and Mustafa, M., “Effect of slip on peristaltic flow of Powell-Eyring fluid in a symmetric channel,” Applied Bionics and Biomechanics, 11, pp. 69–79 (2014).CrossRefGoogle Scholar
32. Goswami, P., Mondal, P. K., Dutta, S. and Chakraborty, S., “Electroosmosis of Powell–Eyring fluids under interfacial slip,” Electrophoresis, 36, pp. 703–711 (2015).CrossRefGoogle ScholarPubMed
33. He, J. H., “A review on some new recently developed nonlinear analytical techniques,” International Journal of Nonlinear Sciences and Numerical Simulation, 1, pp. 51–70 (2000).CrossRefGoogle Scholar
34. He, J. H., “Homotopy perturbation method, a new analytical technique,” Applied Mathematics and computation, 135, pp. 73–79 (2003).CrossRefGoogle Scholar
35. Peyret, R., Spectral methods for incompressible viscous flow, Springer, New York, pp. 46–70 (2001).Google Scholar
36. Trefethen, L. N., Spectral methods in MATLAB, SIAM, Philadelphia, pp. 71–78 (2000).CrossRefGoogle Scholar