Analytical solution of magnetohydrodynamic flow of Jeffrey fluid through a circular microchannel

Abstract The magnetohydrodynamic (MHD) flow of Jeffrey fluid in a circular microchannel is presented. Using the method of variable separation, the analytical solutions to both DC-operated MHD and AC-operated MHD micropumps are found. The flow is assumed to be laminar, unidirectional, one dimensional and driven by the Lorentz force. The Lorentz force can be taken as hydrostatic pressure gradient in the momentum equation of the MHD microchannel flow model. The effects of Hartmann number Ha, dimensionless relaxation time λ ¯ 1 and retardation time λ ¯ 2 on the velocity and volumetric flow rate are investigated. The velocity and volumetric flow rate grow and then reduce with Hartmann number Ha. There is a critical value of the Ha for MHD velocity and an optimum Ha for maximum volumetric flow rate. In addition, a comparison with previous works is also provided to confirm the validity of the present results.

[1]  N. Akbar,et al.  Combined effects of magnetic field and partial slip on obliquely striking rheological fluid over a stretching surface , 2015 .

[2]  S. Moghaddam.  MHD micropumping of power-law fluids: A numerical solution , 2013, Korea-Australia Rheology Journal.

[3]  Davood Domiri Ganji,et al.  Nanofluid flow and heat transfer in a rotating system in the presence of a magnetic field , 2014 .

[4]  Davood Domiri Ganji,et al.  Micropolar fluid flow and heat transfer in a permeable channel using analytical method , 2014 .

[5]  Yongjun Jian,et al.  Electromagnetohydrodynamic (EMHD) micropump of Jeffrey fluids through two parallel microchannels with corrugated walls , 2015 .

[6]  Abraham P. Lee,et al.  An AC Magnetohydrodynamic Microfluidic Switch for Micro Total Analysis Systems , 2003 .

[7]  Yean-Der Kuan,et al.  Design and fabrication of a magnetic fluid micropump for applications in direct methanol fuel cells , 2011 .

[8]  Turgut Sarpkaya,et al.  Flow of non‐Newtonian fluids in a magnetic field , 1961 .

[9]  N. Akbar,et al.  Oblique stagnation flow of Jeffery fluid over a stretching convective surface , 2015 .

[10]  Jan C.T. Eijkel,et al.  A circular ac magnetohydrodynamic micropump for chromatographic applications , 2003 .

[11]  Davood Domiri Ganji,et al.  Analytical investigation of MHD nanofluid flow in non-parallel walls , 2014 .

[12]  Xiao-dong Wang,et al.  Optimal and Numerical Solutions for an MHD Micropolar Nanofluid between Rotating Horizontal Parallel Plates , 2015, PloS one.

[13]  Rahmat Ellahi,et al.  Numerical analysis of steady non‐Newtonian flows with heat transfer analysis, MHD and nonlinear slip effects , 2012 .

[14]  Liangui Yang,et al.  Time periodic electro-osmotic flow through a microannulus , 2010 .

[15]  Transient electroosmotic flow of general Maxwell fluids through a slit microchannel , 2014 .

[16]  Guangpu Zhao,et al.  Magnetohydrodynamic flow of generalized Maxwell fluids in a rectangular micropump under an AC electric field , 2015 .

[17]  Sejin Kwon,et al.  Design, fabrication, and testing of a DC MHD micropump fabricated on photosensitive glass , 2014 .

[18]  S Nadeem,et al.  Numerical investigation on MHD oblique flow of Walter's B type nano fluid over a convective surface , 2015 .

[19]  Shizhi Qian,et al.  Modeling RedOx-based magnetohydrodynamics in three-dimensional microfluidic channels , 2007 .

[20]  Zhi-yong Xie,et al.  Rotating electroosmotic flow of power-law fluids at high zeta potentials , 2014 .

[21]  Liangui Yang,et al.  AC electroosmotic flow of generalized Maxwell fluids in a rectangular microchannel , 2011 .

[22]  Hsisheng Teng,et al.  Cyclic Ammonium-Based Ionic Liquids as Potential Electrolytes for Dye-Sensitized Solar Cells , 2012, International Journal of Electrochemical Science.

[23]  Davood Domiri Ganji,et al.  Heat transfer and flow analysis for SA-TiO2 non-Newtonian nanofluid passing through the porous media between two coaxial cylinders , 2013 .

[24]  Albert van den Berg,et al.  A high current density DC magnetohydrodynamic (MHD) micropump. , 2005, Lab on a chip.

[25]  Moonwoo La,et al.  Design and numerical simulation of complex flow generation in a microchannel by magnetohydrodynamic (MHD) actuation , 2014 .

[26]  Amitava Datta,et al.  Characterization of a ferrofluid-based thermomagnetic pump for microfluidic applications , 2011 .

[27]  Champak Das,et al.  Some practical applications of magnetohydrodynamic pumping , 2013 .

[28]  Tasawar Hayat,et al.  Peristalsis of silver-water nanofluid in the presence of Hall and Ohmic heating effects: Applications in drug delivery , 2015 .

[29]  Haim H. Bau,et al.  MAGNETO-HYDRODYNAMIC (MHD) PUMP FABRICATED WITH CERAMIC TAPES , 2002 .

[30]  Jaesung Jang,et al.  Theoretical and experimental study of MHD (magnetohydrodynamic) micropump , 2000 .

[31]  Tasawar Hayat,et al.  On model for three-dimensional flow of nanofluid: An application to solar energy , 2014 .

[32]  Mandula Buren,et al.  Electromagnetohydrodynamic flow through a microparallel channel with corrugated walls , 2014 .

[33]  Y. Jian,et al.  Electromagnetohydrodynamic (EMHD) flow between two transversely wavy microparallel plates , 2015, Electrophoresis.

[34]  A. Lee,et al.  An AC magnetohydrodynamic micropump , 2000 .

[35]  Liangui Yang,et al.  Alternating current electroosmotic flow of the Jeffreys fluids through a slit microchannel , 2011 .