Abstract.
The flow of micropolar fluids through a microparallel channel with corrugated walls is performed in this paper. The corrugations of the two walls are described as periodic sinusoidal waves with small amplitude and phase difference \( \theta\). The flow generated by the constant pressure gradient is assumed to be steady and unidirectional. Approximate analytical solutions of velocity, vorticity of micro-rotation and volume flow rate are obtained by perturbation techniques. The effects of the corrugation on the flow are graphically analyzed by using numerical computation. The dependences of velocity, vorticity of micro-rotation and leading-order perturbations to the mean velocity of micropolar fluids on the Reynolds number Re, the phase difference \( \theta\) of the two corrugated walls and couple stress parameter s0 are explained graphically.
Similar content being viewed by others
References
A.C. Eringen, Int. J. Eng. Sci. 2, 205 (1964)
H.A. Stone, A.D. Stroock, A. Ajdari, Annu. Rev. Fluid Mech. 36, 381 (2004)
D.J. Laster, J.G. Santiago, J. Micromech. Microeng. 14, R35 (2004)
G. Karniadakis, A. Beskok, N. Aluru, Micorflows and Nanoflows: Fundamentals and Simulation (Springer, New York, 2005)
A.C. Eringen, J. Math. Mech. 16, 1 (1966)
T. Ariman, M.A. Turk, N.D. Sylvester, Int. J. Eng. Sci. 11, 905 (1973)
T. Ariman, M.A. Turk, N.D. Sylvester, Int. J. Eng. Sci. 12, 273 (1974)
V.K. Stokes, Theories of Fluids with Microstructures (Springer, New York, 1984)
G. Lukaszewicz, Micropolar Fluids: Theory and Application (Birkhäuser, Basel, 1999)
A.C. Eringen, Microcontinnum Field Theories: II. Fluent Media (Springer, New York, 2001)
A.G. Willson, Proc. Camb. Philos. Soc. 67, 469 (1970)
J.R.J. Peddieson, R.P. McNitt, Recent Adv. Eng. Sci. 5, 405 (1970)
G. Nath, Rheol. Acta 14, 850 (1975)
J. Delhommelle, D.J. Evans, Mol. Phys. 100, 2857 (2002)
A.J. Chamkha, T. Grosan, I. Pop, Int. Commun. Heat Transf. 29, 1021 (2002)
A. Ishak, R. Nazar, I. Pop, Phys. Lett. A 372, 559 (2008)
J.P. Kumar, J.C. Umavathi, A.J. Chamkha et al., Appl. Math. Model. 34, 1175 (2010)
K. Bhattacharyya, S. Mukhopadhyay, G.C. Layek et al., Int. J. Heat Mass Transf. 55, 2945 (2012)
J.V.R. Murthy, J. Srinivas, Int. J. Heat Mass Transf. 65, 254 (2013)
M. Devakar, T.K.V. Iyengar, Eur. Phys. J. Plus 128, 41 (2013)
A. Borrelli, G. Giantesio, M.C. Patria, Int. J. Heat Mass Transf. 80, 614 (2015)
C.Y. Wang, J. Appl. Mech. 46, 462 (1979)
Z.K.H. Chu, Mech. Res. Commun. 26, 457 (1999)
B. Tashtoush, M. Al-Odat, J. Magn. & Magn. Mater. 268, 357 (2004)
N.M. Bujurke, R.B. Kudenatti, Fluid Dyn. Res. 39, 334 (2007)
N.M. Bujurke, N.B. Naduvinamani, D.P. Basti, Tribol. Int. 44, 916 (2011)
N.B. Naduvinamani, B.N. Hanumagowda, S.T. Fathima, Tribol. Int. 56, 19 (2012)
M. Buren, Y.J. Jian, L. Chang, J. Phys. D: Appl. Phys. 47, 425501 (2014)
D.Q. Si, Y.J. Jian, J. Phys. D: Appl. Phys. 48, 085501 (2015)
M. Buren, Y.J. Jian, Electrophoresis 36, 1539 (2015)
H.C. Weng, C.K. Chen, M.H. Chang, J. Fluid Mech. 631, 343 (2009)
K.H. Hoffmann, D. Marx, N.D. Botkin, J. Fluid Mech. 590, 319 (2007)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, L., Jian, Y. & Li, F. The flow of micropolar fluids through a microparallel corrugated channel. Eur. Phys. J. Plus 131, 338 (2016). https://doi.org/10.1140/epjp/i2016-16338-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/i2016-16338-5