Laminar Viscous Flow of Micropolar Fluid through Non-Darcy Porous Medium Undergoing Uniform Suction or Injection

Document Type : Research Article

Authors

1 DEPT. OF MECH. ENGR., UNIVERSITY OF LAGOS, NIGERIA.

2 DEPT. OF MECH. ENGR., YABA COLLEGE OF TECHNOLOGY, LAGOS

Abstract

In this study, the micropolar fluid flow conveyed through suction or injection in a non-Darcy porous medium with high mass transfer is considered. The micropolar fluid flow is described by coupled systems of higher order, ordinary, nonlinear differential equations. Therefore the variation of parameters method is utilized in generating analytical solutions to the mathematical models arising from flow and rotation of the micropolar fluid. As the variation of parameters method is a relatively easy, yet efficient approach of analyzing both strongly and weakly dependent nonlinear equations with a rapid convergence rate. Pertinent rheological fluid parameter effects such as non-Darcy parameter and Reynolds number on flow and rotation are examined using the obtained analytical solutions. Observations from graphical representation of result illustrate flow increase during injection and slight radial velocity decrease for suction flow. Reynolds parameter effect on fluid particles micro rotation also shows decrease in rotation profile during injection while during suction increased particle rotation is observed as a result of high mass transfer. Results obtained from study compared against existing works in literature prove to be in satisfactory agreement. Therefore this paper can be used to further study of micropolar fluids applications such as blood flow, lubricants and micro channel flows amongst others.

Keywords

Main Subjects

References

[1] A.C.  Eringen,  Theory  of  micropolar  fluids,  Journal  of Mathematics and Mechanics, 16 (1966) 1-18.
[2] R.   Idris,   H.   Othman,   I.   Hashim,   On   the   effect   of non-uniform basic temperature gradient on Benard –Marangoni convection in micropolar fluids, In ternational Communication in Heat and Mass Transfer, 36 (3) (2009) 203-209.
[3]  S.W.  Yuan,  Further  investigation  of  laminar  flow  in channels with porous wall, Journal of Applied Physics, 27 (1956) 267-269.
[4]  N.A. Kelson, A. Desseaux, Effect of surface conditions on flow of a micropolar fluid driven by a stretching sheet, International Journal of Engineering Science, 39 (16) (2001) 1881-1897.
[5]  N.A.  Kelson,  T.W.  Farrell,  Micropolar  flow  over  a porous stretching sheet with strong suction or injection, International Communications in Heat and Mass  Transfer, 28 (4) (2001) 479-488.
[6]  M.B. Zaturska, P.G. Drazin, W.H.H. Banks, On the flow of a viscous fluid driven along a channel by suction at porous walls, Fluid Dynamics Research, 4 (1988) 151-178.
[7]   C. Ching, C. Yang, Natural convection of micropolar fluid from a vertical truncated cone with power –law variation in surface temperature , International Communications in Heat and Mass Tra nsfer, 35(1) (2008) 39-46. 
[8] S.W.  Yuan,  Further  Investigation  of  laminar  flow  in channels with porous walls, Journal of Applied Physics, 27 (1956) 267-269.
[9]  I.H.   Abdel-Halim,   On   solving   some   eigen-   value problems by using a differential transformation, Applied Mathematical Computation, 127 (2002) 1-22.
[10]    E. Magyari, B. Keller, Exact solutions for self-similar boundary layer flows induced by permeable stretching wall, European Journal of Mechanics 19 (2000) 109-122.
[11]    P.VS.V.N. Murthy, P. Singh,  Thermal dispersion effects on non-Darcy natural convection over horizontal plate with surface mass flux, Archive of Applied Mechanics, 67 (1997)487-495.
[12]    M. Sheikholeslami, M., Hatami, D.D. Ganji, Micropolar fluid flow and heat transfer in a permeable channel using analytical methods, Journal of Molecular Liquids, 194 (2014) 30-36.
[13]    N.A.  Kelson,  A.  Desseaux,  Micropolar  flow  over  a porous stretching sheet with strong suction or injection, International Journal of Engineering Science, 39 (2001) 1881-1897.
[14]    R.A.  Mohamed,  S.M.  Abo  Dahab,  The  influence  of chemical reaction and thermal radiation in the heat and mass transfer in MHD micropolar flow over a vertical moving porous plate in a porous medium, International Journal of Thermal Science, 48 (2009) 1800-1813.
[15]    D.A.S.  Rees,  A.P.  Bassom,  Boundary  layer  flow  of a micropolar fluid, Internal Journal of Engineering Science, 34 (1996) 113-124.
[16]    K.  Das,  N.  Acharya,  K.P.  Kundu,  MHD  micropolar fluid flow over a moving plate under slip conditions:An application of lie group analysis, U.P.B. Science Bulletin, 78 (2) (2016) 225-233.
[17]   D.  Srinivasacharya,  M.G.  Rao,  Magnetic  effects  of pulsatile flow of micropolar fluid through a bifurcated artery, World Journal of Modeling and Simulation, 12 (2) (2016) 147-160.
[18]   P.K.   Rout,   S.N.   Sahov,   G.C.   Pash,   S.R.   Mishu, Chemical reaction effect on MHD free convection flow in a micropolar fluid, Alexander Engineering Journal, 55 (2016) 2967-2973.
[19]   W.  Hassan,  H.  Sajjad,  S.  Humaira,  K.  Shanila,  MHD forced convection flow past a moving boundary surface with prescribed heat flux and radiation, British Journal of Mathematics and Computer Science, 21 (1) (2017) 1-14.
[20]   R.N.  Bank,  G.C.  Dash,  Chemical  reaction  effect  on peristaltic motion of micropolar fluid through a porous mediumwith heat absorption the presence of magnetic field, Advances in Applied Science Research, 6 (3) 2015 20-34.
[21]   S.A.   Mekonnen,   T.D.   Negussie,   Hall   effect   and temperature distribution on unsteady micropolar fluid flow in a moving wall, International Journal of Science Basic and Applied Research, 24 (7) (2015) 60-75.
[22]   K.S. Mekheir, S.M. Mohammed, Interaction of pulsatile flow on peristaltic motion of magnetomicropolar fluid through porous medium in a flexible channel:Blood flow model, International Journal Pure and Applied Mathematics, 94 (3)(2014) 323-339.
[23]    K.L. Narayana, K. Gangadhark, Second order slip flow of a MHD micropolar fluid over an unsteady stretching surface, Advances in Applied Science Research, 6 (8) (2015) 224-241.
[24]    P.S.   Ramachandran,   M.N.   Mathur,S.K.   Ohja,   Heat transfer in boundary layer flow of a micropolar fluid past a curved surface with suction and injection, International Journal of Engineering Science, 17 (1979) 625-639.
[25]    A.S. Berman, Laminar flow in a channel with porous wall, Journal of Applied Physics, 27 (1953) 1232-1235.
[26]    G.  Domairry,  M.  Fazeli,  Homotopy  analysis  method to determine the fin efficiency of convective straight   fin with temperature dependent thermal conductivity, Communication in Nonlinear Science and Numerical Simulation, 14 (2009) 489-499.
[27]    S.B.  Cosun,  M.T.  Atay,  Fin  efficiency  analysis  of convective straight fin with temperature dependent thermal conductivity using variational iteration method, Applied Thermal Engineering, 28 (2008) 2345-2352.
[28]    E.M.  Languri,  D.D  Ganji,  N.  Jamshidi,  Variational iteration and homotopy perturbation methods for fin efficiency of convective straight fins with temperature dependent thermal conductivity, 5th WSEAS International Conference on Fluid Mechanics, Acapulco, Mexico, 2008.
[29]    G.  Oguntala,  M.G.  Sobamowo,  Garlerkin  method  of weighted residuals for convective straight fins with temperature dependent conductivity and internal heat generation, International Journal of Engineering and Technology, 6 (2008) 432-442.
[30]    U.  Filobello-Niño,  H.  Vazquez-Leal,  K.  Boubaker,Y. Khan,A. Perez-Sesma, A. Sarmiento Reyes, V.M. Jimenez-Fernandez, A. Diaz-Sanchez, A. Herrera-May, J. Sanchez-Orea, K. Pereyra-Castro, K., Perturbation Method as a Powerful Tool to Solve Highly Nonlinear Problems: The Case of Gelfand’s Equation, Asian Journal of Mathematics and Statistics, (2013) DOI: 10.3923 /ajms.
[31]    C.W.  Lim,B.S.  Wu,  A  modified  Mickens  procedure for certain non-linear oscillators, Journal of Sound and Vibration, 257 (2002) 202-206.
[32]   Y.K.   Cheung,   S.H.   Chen,   S.L.   Lau,   A   modified Lindsteadt-Poincare method for certain strongly non- linear oscillators, International Journal of Non-Linear Mechanics, 26 (1991) 367-378.
[33]   R.W.    Lewis,    P.    Nithiarasu,    K.N.    Seatharamu, Fundamentals of the finite element method for heat and fluid flow, Antony Rowe Ltd, Wiltshire, Great Britain, 2004.
[34]   M.G.   Sobamowo,   L.O.   Jaiyesimi,   M.A.   Waheed, Magneto hydrodynamic squeezing flow analysis of nanofluid under the effect of slip boundary conditions using the variation of parameters method, Karbala International Journal of Modern Science, (2017) https:// doi.org.1016/j.kijoms.2017.12.001,2017.
[35]  G.   Oguntala,   R.   Abd-Alhameed,   Thermal   analysis of convective  radiative  fin  with  temperature dependent thermal conductivity using Chebychev spectral collocation method, Journal of Applied and  Computational Mechanics, (2018) OI.10.22055/ JACM.2017.22435.1130.
[36]    A.A.  Joneidi,  D.D.  Ganji,  M.  Babaelahi,  Micropolar flow in a porous channel with high mass transfer, International Communication in Heat and Mass Transfer, 36 (2009) 1082-1088.
[37]      M.S.  Pour,  S.A.G.  Nassab,  Numerical  investigation of forced laminar convection flow of nanofluid over a backward step under bleeding condition, Journal of Mechanics, 28 (2) (2012) 7-12.
[38]    A.T.   Akinshilo,   Steady   Flow   and   Heat   Transfer Analysis of Third Grade Fluid with Porous Medium and Heat Generation, Journal of Engineering Science and Technology, 20 (2017) 1602-1609.
AUT Journal of Mechanical Engineering
Volume 3, Issue 2
December 2019
Pages 157-164

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