Theoretical investigation of micropolar fluid flow between two porous disks

Abstract

The steady, laminar, incompressible and two dimensional micropolar flow between two porous disks was investigated using optimal homotopy asymptotic method (OHAM) and fourth order Runge-Kutta numerical method. Comparison between OHAM and numerical method shows that OHAM is an exact and high efficient method for solving these kinds of problems. The results are presented to study the velocity and rotation profiles for different physical parameters such as Reynolds number, vortex viscosity parameter, spin gradient viscosity and microinertia density parameter. As an important outcome, the magnitude of the microrotation increases with an increase in the values of injection velocity while it decreases by increasing the values of suction velocity.

Keywords

theoretical investigation / porous disks / micropolar fluid flow / optimal homotopy asymptotic method (OHAM) / microrotation

References

[1] KarmanT VÜber laminare und turbulente reibung [J]. ZAMM-Journal of Applied Mathematics and Mechanics, 1921, 1: 233-252

[2] AshrafM, AnwarK M, SyedK S. Numerical investigations of asymmetric flow of a micropolar fluid between two porous disks [J]. Acta Mechanica Sinica, 2009, 25: 787-794

[3] NazirA, MahmoodT. Analysis of flow and heat transfer of viscous fluid between contracting rotating disks [J]. Applied Mathematical Modelling, 2011, 35: 3154-3165

[4] SiX H, ZhengL C, ZhangX X, SiX Y. Homotopy analysis method for the asymmetric laminar flow and heat transfer of viscous fluid between contracting rotating disks [J]. Applied Mathematical Modelling, 2012, 36: 1806-1820

[5] IbrahimF. Unsteady flow between two rotating discs with heat transfer [J]. Journal of Physics D: Applied Physics, 1991, 24: 1293-1299

[6] ErsoyV H. An approximate solution for flow between two disks rotating about distinct axes at different speeds [J]. Mathematical Problems in Engineering, 2007

[7] HatamiM, SheikholeslamiM, GanjiD D. Nanofluid flow and heat transfer in an asymmetric porous channel with expanding or contracting wall [J]. Journal of Molecular Liquids, 2014, 195: 230-239

[8] HatamiM, GanjiD D. Heat transfer and nanofluid flow in suction and blowing process between parallel disks in presence of variable magnetic field [J]. Journal of Molecular Liquids, 2014, 190: 159-168

[9] EringenA C. Theory of micropolar fluids [M]. DTIC Document, 196522-48

[10] AnwarK M, AshrafM, SyedK S. Numerical solution of steady viscous flow of a micropolar fluid driven by injection between two porous disks [J]. Applied Mathematics and Computation, 2006, 179: 1-10

[11] AshrafM, WehgalA. MHD flow and heat transfer of micropolar fluid between two porous disks [J]. Applied Mathematics and Mechanics, 2012, 33: 51-64

[12] DarvishiM T, KhaniF, AwadF G, KhidirA A, SibandaP. Numerical investigation of the flow of a micropolar fluid through a porous channel with expanding or contracting walls [J]. Propulsion and Power Research, 2014, 3: 133-142

[13] GhasemiS E, Jalili PalandiS, HatamiM, GanjiD D. Efficient analytical approaches for motion of a spherical solid particle in plane couette fluid flow using nonlinear methods [J]. The Journal of Mathematics and Computer Science, 2012, 5(2): 97-104

[14] GhasemiS E, ZolfagharianA, GanjiD D. Study on motion of rigid rod on a circular surface using MHPM [J]. Propulsion and Power Research, 2014, 3(3): 159-164

[15] GhasemiS E, HatamiM, MehdizadehA G R, GanjiD D. Electrohydrodynamic flow analysis in a circular cylindrical conduit using least square method [J]. Journal of Electrostatics, 2014, 72: 47-52

[16] GhasemiS E, HatamiM, GanjiD D. Thermal analysis of convective fin with temperature-dependent thermal conductivity and heat generation [J]. Case Studies in Thermal Engineering, 2014, 4: 1-8

[17] GhasemiS E, ValipourP, HatamiM, GanjiD D. Heat transfer study on solid and porous convective fins with temperature-dependent heat generation using efficient analytical method [J]. Journal of Central South University, 2014, 21: 4592-4598

[18] MarincaV, HerisanuN. Application of optimal homotopy asymptotic method for solving nonlinear equations arising in heat transfer [J]. International Communications in Heat and Mass Transfer, 2008, 35: 710-715

[19] MarincaV, HerisanuN, BotaC, MarincaB. An optimal homotopy asymptotic method applied to the steady flow of a fourth-grade fluid past a porous plate [J]. Applied Mathematics Letters, 2009, 22: 245-251

[20] GhasemiS E, HatamiM, GanjiD D. Analytical thermal analysis of air-heating solar collectors [J]. Journal of Mechanical Science and Technology, 2013, 27(11): 3525-3530

[21] JoneidiA, GanjiD D, BabaelahiM. Micropolar flow in a porous channel with high mass transfer [J]. International Communications in Heat and Mass Transfer, 2009, 36: 1082-1088

[22] EsmaeilpourM, GanjiD D. Solution of the Jeffery-Hamel flow problem by optimal homotopy asymptotic method [J]. Computers & Mathematics with Applications, 2010, 59: 3405-3411