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Nonlinear instability analysis of a vertical cylindrical magnetic sheet | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 12، شماره 2، بهمن 2021، صفحه 583-601 اصل مقاله (621.15 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2020.19429.2078 | ||
| نویسندگان | ||
| Marwa H Zekry* 1؛ Galal M. Moatimid2؛ Yusry El-Dib2 | ||
| 1Department of Mathematics and Computer Science, Faculty of Science, Beni-Suef University, Egypt | ||
| 2Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt | ||
| تاریخ دریافت: 11 دی 1398، تاریخ پذیرش: 25 فروردین 1399 | ||
| چکیده | ||
| This paper concerns with the nonlinear instability analysis of double interfaces separated three perfect, incompressible cylindrical magnetic fluids. The cylindrical sheet is acted upon by an axial uniform magnetic field. The current nonlinear approach depends mainly on solving the linear governing equations of motion and subjected to the appropriate nonlinear boundary conditions. This procedure resulted in two nonlinear characteristic equations governed the behavior of the interfaces deflection. By means of the Taylor expansion, together with the multiple time scales, technique, the stability analysis of linear as well as the nonlinear is achieved. The linear stability analysis reveals a quadratic dispersion equation in the square of growth rate frequency of the surface wave. On the other hand, the nonlinear analysis is accomplished by a coupled nonlinear Schrödinger equation of the evolution amplitudes of the surface waves. The stability criteria resulted in a polynomial of the eleventh degree in the square of the magnetic field strength, together with resonance transition curves. Several special cases are reported upon appropriate data choices. The stability criteria are numerically discussed, at which regions of stability and instability are identified. In the stability profile, the magnetic field intensity is plotted versus the wave number. The influences of the parameters on the stability are addressed. The nonlinear stability approach divides the phase plane into several parts of stability/instability. The nonlinear stability shows an in contrast mechanism of the role of the sheet thickness. | ||
| کلیدواژهها | ||
| Nonlinear Stability Analysis؛ Magnetic Fluids؛ Multiple Time Scales؛ Coupled Nonlinear Schrödinger Equations | ||
| مراجع | ||
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[1] B. Berkovski and V. Bashtovoy, Magnetic Fluids and Applications Hndbook, Begel House, New York, 1996. [2] T. Rheinl¨ander, R. K¨otitz, W. Weitschies and W. Semmler, Magnetic fluids: biomedical applications and magnetic fractionation, Magnetic and Electrical Separation, 10(2000) 179-199. [3] R.N. Chaniyilparampu, P. Kopˇcansk´y and R.V. Mehta, Applications of magnetic fluids in medicine and biotechnology, Indian J. Pure Ap. Phy., 39 (2001) 683-686. [4] S. Mornet, S. Vasseur, F. Grasset and E. Duguet, Magnetic nanoparticle design for medical diagnosis and therapy, J. Mater. Chemistry, 14 (2004) 2161-2175. [5] R. Ganguly, A.P. Gaind, S. Sen and I.K. Puri, Analyzing ferrofluid transport for magnetic drug targeting, J. Magn. Magn. Mater., 289 (2005) 331-334. [6] C. Scherer and A.M.F. Neto, Ferrofluids: Properties and Applications, Braz. J. Phys., 35 (2005) 718-727. [7] S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Clarendon Press, Oxford, 1961. [8] S.F. El Shehawey, Y.O. El-Dib and A.A. Mohamed, Electrohydrodynamic stability of a fluid layer: Effect of a tangential field, IL Nuovo Cimento D, 6 (1985) 291-308. [9] A.A. Mohamed, E.F. El Shehawey and Y.O. El Dib, Electrohydrodynamic stability of a fluid layer: Effect of a tangential periodic field, IL Nuovo Cimento, 8 (1986) 177-192. [10] A.A. Mohamed, E.F. El Shehawey and Y.O. El Dib, Electrohydrodynamic stability of a fluid layer:II. Effect of a normal field, J. Chem. Phys., 85 (1986) 445-455. [11] N.T. El-Dabe, E.F. El Shehawey, G.M. Moatimid and A.A. Mohamed, Electrohydrodynamic stability of two cylindrical interfaces under influence of a tangential periodic field, J. Math. Phys., 26 (1985) 2072-2081.[12] Y.O. El-Dib and R.T. Matoog, Stability of streaming in an electrified Maxwell fluid sheet influenced by a vertical periodic field in the absence of surface charges, J. Colloid Interface Sci., 229 (2000) 29-52. [13] G.M. Moatimid, Y.O. El-Dib and M.H. Zekry, Stability analysis using multiple scales homotopy approach of coupled cylindrical interfaces under the influence of periodic electrostatic fields, Chinese J. Phys., 56 (2018) 2507- 2522. [14] G.M. Moatimid, Y.O. El-Dib and M.H. Zekry, Instability analysis of a streaming electrified cylindrical sheet through porous media, Pramana J. Phys., 92:22 (2019). [15] A. Arnold, Numerically absorbing boundary conditions for quantum evolution equations, VLSI Design, 6 (1998)313-319. [16] M. Levy, Parabolic Equation Methods for Electromagnetic Wave Propagations, IEEE, (2000). [17] G. Arora, V. Joshi, and R.C. Mittal, Numerical simulation of nonlinear Schr¨odinger equation in one and two dimensions, Math. Models Comp. Simulations, 11 (2019) 634-648. [18] A.H. Nayfeh, Nonlinear propagation of wave packets on fluid interfaces, J. Appl. Math., ASME 98E (1976) 584-588. [19] A.F. Elhefnawy, The nonlinear stability of mass and heat transfer in magnetic fields, ZAMM, 77 (1997) 19-31. [20] D.S. Lee, Nonlinear stability in magnetic fluids of cylindrical interface with mass and heat transfer, Eur. Phys. J. B, 28 (2002) 495-503. [21] K. Zakaria, Nonlinear dynamics of magnetic fuids with a relative motion in the presence of an oblique magnetic field, Physica A, 327 (2003) 221-248. [22] Y.O. El-Dib, Nonlinear wave-wave interaction and stability criterion for parametrically coupled nonlinear schr¨odinger equations, Nonlinear Dynam., 24 (2001) 399-418. [23] G.M. Moatimid, Non-linear electrorheological instability of two streaming cylindrical fluids, J. phys. A Math. Gen., 36 (2003) 11343-11365. [24] A.F. Elhefnawy, G.M. Moatimid and A.K. Elcoot, Nonlinear electrohydrodynamic instability of a finitely conducting cylinder: Effect of interfacial surface charges, ZAMP, 55 (2004) 63-91. [25] G.M. Moatimid, Y.O. El-Dib and M.H. Zekry, The nonlinear instability of a cylindrical interface between two hydromagnetic Darcian flow, Arab J. Sci. Eng., 45 (2020) 391–409. [26] J.H. Dumbleton and J.J. Hermans, Capillary stability of a hollow inviscid cylinder, Phys. Fluids, 13 (1970) 12-17. [27] J.R. Melcher, Field Coupled Surface Waves, MIT Press, Cambridge 1963. [28] R.E. Rosensweig, Ferrohydrodynamic, Cambridge University Press, Cambridge, 1985. [29] G.M. Moatimid, Nonlinear waves on the surface of a magnetic fluid jet in porous media, Physica A, 328 (2003) 525-544. [30] M. D. Cowley and R. E. Rosensweig, The interfacial stability of a ferromagnetic fluid, J. Fluid Mech., 30 (1968) 671-688. [31] G.M. Moatimid, Stability conditions of an electrified miscible viscous fluid sheet, J. Colloid Interface Sci., 259 (2003) 186-199. [32] M.F. El-Sayed, G.M. Moatimid and T.M.N. Metwaly, Nonlinear electrohydrodynamic stability of two superposed streaming finite dielectric fluids in porous medium with interfacial surface charges, Transport in Porous Med., 86 (2011) 559-578. [33] Y. Li-Jun Y., D. Ming-Long, F. Qing-Fei and Z. Wei, Linear stability analysis of a power-law liquid jet, Atomization Sprays, 22 (2012) 123-141. [34] M.K. Awasthi and R. Asthana, Viscous potential flow analysis of capillary instability with heat and mass transfer through porous media, Int. Commun. Heat Mass Tran., 40 (2013) 7-11. | ||
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