The Effect of Suction and Injection on MHD Flow Between Two Porous Concentric Cylinders Filled with Porous Medium
This Paper deals wit the effects of suction (injection) on magnetohydrodynamic (MHD) steady flow of a viscous and electrically conducting fluid in an annular porous region between two concentric cylinders. The inner cylinder is rotating with uniform angular velocity and the outer one is fixed. The two cylinders are porous with uniform permeability. It is assumed that the suction rate at the inner cylinder is equal to the injection rate at the outer cylinder. A uniform axial magnetic field was applied perpendicular to the flow direction. The flow resistance presented by the porous medium is governed by the Darcy law. By using similarity transformation, the governing partial differential equations have been transformed to a system of nonlinear ordinary differential equations. The solution of the obtained system in its general form has been obtained. Analytical expression for velocity field is obtained in terms of Bessel function of first and second kind. The effects of various parameters such as susction (injection), magnetic and permeability parameters on the flow are discussed and the obtained results are presented graphically. The obtained figures show that, the velocity distribution increased with the increase of permeability parameter of the the porous medium and with suction process. On the other hand, the velocity distribution decreased with the increase of magnetic parameter and with injection parameter.
Pantokratoras, A. and Fang, T. Flow of a weakly conducting ?uid in a channel ?lled with a porous medium. Transport in Porous Media, 83 ( 2010) 667-676.
Zhao, B. Q., Pantokratoras, A., Fang, T. G. and Liao, S.J. Flow of a weakly conducting fluid in a channel filled with a Darcy - Brinkman - Forchheimer porous medium. Transport in Porous Media, 85 (2010) 131–142.
Verma, V. K. and Datta, S. Flow in a channel ?lled by heterogeneous porous media with a linear permeability variation. Special Topics and Reviews in Porous Media An International Journal, 3 (3)(2012a) 201–208.
Verma, V. K. and Datta, S. Flow in an annular channel ?lled with a porous medium of variable permeability. Journal of Porous Media, 15(10) (2012b) 891–899.
Verma, V. K. Analytical solution of magnetohydrodynamic ?ow with varying viscosity in an annular channel. Adv. Theor. Appl. Math., 9 (2014) 105–122.
Verma, V. K. and Singh, S. Flow between coaxial rotating cylinders ?lled by porous medium of variable permeability. Special Topics and Reviews in Porous Media An International Journal, 5(4)(2014) 355–359.
Verma, V. K. and Singh, S. Magnetohydrodynamic ?ow in a circular channel ?lled with aporous medium. Journal of Porous Media, 18(9) (2015) 923–928.
Fukumoto, Y. General unsteady circulatory ?ow outside a porous circular cylinder with suction or injection. J. Phys. Soc. Jpn., 59 (1990) 918–926.
Daskalakis, J. E. Mixed free and forced convection in the incompressible boundary layer along a rotating vertical cylinder with ?uid injection. Int. J. Energy Res., 17 (1993) 689–695.
Casarella, M. J. and Laura, P. A. Drag on an oscillating rod with longitudinal and torsional motion. J. Hydronaut., 3 (1969) 180–183.
Rajagopal, K. R. and Kaloni, P. N. Some remarks on boundary conditions for ?ows of ?uids of the differential type. Continuum Mechanics and Its Applications, Hemisphere, Washington, DC, 1989.
Terrill, R. M. Flow through a porous annulus. Appl. Sci. Res. 17 (1967) 204-222.
Abu-hijleh, B. Natural convection heat transfer from a cylinder with high conductivity permeable fins. ASME J. Heat Transfer, 125 (2002) 282-288.
Abu-hijleh, B. Natural convection heat transfer from a cylinder covered with an orthotropic porous layer. Numer. Heat Transfer, 40 (2001) 767-782.
Hamza, E. A., Rajvanshi S. C. and Sacheti, N. C. Pulsatile flow between two coaxial prous cylinders with slip on inner cylinder. Matematicas, XV (1) (2007) 51-66.
Sharma, B. K., Sharma, P. K. and Chaudhary, R. C. Unsteady flow through porous medium induced by periodically rotating half-filled horizontal concentric cylindrical annulus with heat transfer. International Journal of Physical Sciences, 7(10) (2012) 1530-1539.
Kiwan, S and Al-Zahrani, M. S. Effect of porous inserts on natural convection heat transfer between two concentric vertical cylinders. Numer. Heat Transfer Part A, 53 (2008) 870–889.
Jha B. K. and Apere C. A. Unsteady MHD two-phase Couette flow of fluid-particle suspension in an annulus. AIP Advances, 1 (2011) 042121-042136.
Tan, W. C. and Masuoka, T. Stokes first problem for a second grad fluid in a porous half space with heated boundary. Int. J. Non-Linear Mech., 40 (2005) 515-522.
Fetecau, C. and Fetecau, C. Starting solutions for the motion of a second grade fluid due to longitudinal and torsional oscillations of a circular cylinder. Int. J. Eng. Sci. 44 (2006) 788-796.
Hayat, T., Khan, M. and Ayub, M. Some analytical solutions for second grade fluid flows for cylindrical geometries. Math. Comp. Model., 43 (2006) 16–29.
Erdogan, M. E. and Imrak, C. E. On the comparison of two different solutions in the form of series of the governing equation of an unsteady flow of a second grade fluid. Int. J. Non-Linear Mech. 40 (2005) 545–550.
Sahoo, B. Effects of slip viscous dissipation and Joule heating on the MHD flow and heat transfer of a second grade fluid past a radially stretching sheet. Appl. Math. Mech., 31 (2010) 159–173.
Ariel, P. D. Flow of a third grade fluid through a porous flat channel. Int. J. Eng. Sci. 41 (2003) 1267–1285.
Hayat, T., Naz, R. and Sajid, M. On the homotopy solution for Poiseuille flow of a fourth grade fluid. Commun Nonlinear Sci. Numer. Simul., 15 (2010) 581–589.
Hayat, T., Asghar, S., Khalique, C. M. and Ellahi, R. Influence of partial slip on flows of a second grade fluid in a porous medium. J. Porous Media, 10 (2007) 797–805.
Hayat, T., Abbas, Z. and Asghar, S. Effects of Hall current and heat transfer on rotating flow of a second grade fluid through a porous medium. Commun. Nonlinear Sci. Numer. Simul., 13 (2008) 2177–2192.
Hayat, T., Naz, R. and Abbasbandy, S. Poiseuille flow of a third grade fluid in a porous medium. Transport in Porous Media, 87 (2011) 355-366.
Mahapatra J. R. A note on the unsteady motion of a viscous conducting liquid between two porous concentric circular cylinders acted on by a radial magnetic field. Appl. Sci. Res. 27 (1973), 274-282.
Khan, M., Abbas, Z. and Hayat, T. Analytic solution for flow of Sisko fluid through a porous medium. Transport in Porous Media, 71 ( 2008) 23–37.
Hayat, T., Javed, M. and Ali, N. MHD peristaltic transport of a Je?ery fluid in a channel with compliant walls and porous space. Trans Porous Med, 74(2008) 259–274.
Pantokatoras, A. and Fang, T. Flow of weakly conducting fluid in a channel filled with a porous medium. Transport in Porous Media, 83 (2010) 667-676.
Zhao, B. Q., Pantokratoras, A., Fang, T. G. and Liao, S. J. Flow of a weakly conducting fluid in a channel filled with a Darcy-Brinkman-Forchheimer porous medium. Transport in Porous Media, 85 (2010) 131-142.
Srivastava, B. G. and Satya Deo. E?ect of magnetic ?eld on the viscous ?uid fow in achannel ?lled with porous medium of variable permeability. A pplied Mathematics and Computation, 219 (2013) 8959–8964.
Ghasemi, E., Mirhabibi, A. and Edrissi, M. Synthesis and rheological properties of an iron oxide ferrofluid. J Magn Magn Mater, 320 (2008) 2635–2639.
Hong, R. Y., Ren, Z. Q., Han, Y. P., Zheng, Y. and Ding, J. Rheological properties of water-based Fe3O4 ferrofluids. Chem. Eng. Scie., 62 (2007) 5912–5924.
Sheikhzadeh, G. A., Mollamahdi, M. and Abbaszadeh, M. Analytical study of flow field and heat transfer of a non-Newtonian fluid in an axisymmetric channel with a permeable wall. Journal of Computational and Applied Research in Mechanical Engineering, 7(2) (2018) 161-173
Santhosh, N. and Radhakrishnamacharya, G. Jeffrey fluid flow through a narrow tubes in the presence of a magnetic field. Procedia Engineering, 127 (2015) 185-192.
Santhosh, N., Radhakrishnamacharya, G. and Chamkha, A. J. Flow of a Jeffrey fluid through a porous medium in narrow tubes, J. Por. Media., 18(1) (2015) 71-78.
Fakour, M., Ganji, D. D., Khalili, A. and Bakhshi, A. Heat transfer in nanofluid MHD flow in a channel with permeable walls. Heat Transfer Research, 48(3) (2017) 221-228.
Aberkane, S., Ihdene, M., Moderes, M. and Ghezal, A. Effect of an axial magnetic field on the heat and mass transfer in rotating annulus. Int. J. Phys. Sci. 9 (16) (2014) 368-379.
Aminfar, H., Mohammadpourfard, M. and Maroofiazar, R. Experimental study on the effect of magnetic field on critical heat flux of ferrofluid flow boiling in a vertical annulus. Experimental Thermal and fluid Science 58 (2014) 156-169.
Seth, G. S. and Singh, J. K. Effects of Hall current of unsteady MHD Couette flow of class-II in a rotating system. J. Appl. Fluid Mech. 6(4) (2013) 473-484.
Verma, V. K. and Dixit, P. K. MHD Couette flow in annular porous region between two coaxial cylinders. International Journal of Pure and Applied Mathematics, 114 (3) (2017) 571-582.
Beg, O. A., Makinde, O. D., Zueco, J. and Ghosh, S. K. Hydromagnetic viscous flow in a rotating annular high porosity medium with nonlinear forchheimer drag effects: numerical study. World Journal of Modelling and Simulation, 8 (2) (2012) 83-95.
Dizaji, A. F., Salimpour, M. R. and Jam, F. Flow field of a third-grade non-Newtonian fluid in the annulus of rotating concentric cylinders in the presence of magnetic field. J. Math. Anal. Appl., 337 (2008) 632-645.
Copyright (c) 2019 S.E. E. Hamza
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors retain the copyright of their manuscripts, and all Open Access articles are distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided that the original work is properly cited.