Abstract
The biomagnetic fluid flow (blood) over a stretching sheet in the presence of magnetic field is studied. For the mathematical formulation of the problem both magnetization and electrical conductivity of blood are taken into account and consequently both principles of magnetohydrodynamics (MHD) and ferrohydrodynamics (FHD) are adopted. The physical problem is described by a coupled, nonlinear system of ordinary differential equations subject to appropriate boundary conditions. This solution is obtained numerically by applying an efficient numerical technique based on finite differences method. The obtained results are presented graphically for different values of the parameters entering into the problem under consideration. Emphasis is given to the study of the effect of the MHD and FHD interaction parameters on the flow field. It is apparent that both parameters effect significantly on various characteristics of the flow and consequently neither electrical conductivity nor magnetization of blood could be neglected.
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Alimohamadi, H., Sadeghy, K.: On the use of magnetic fields for controlling the temperature of hot spots on porous plaques in stenosis arteries. Nihon Reoroji Gakkaishi 43(5), 135–144 (2015)
Misra, J.C., Sinha, A., Shit, G.C.: Flow of a biomagnetic viscoelastic fluid: application to estimate of blood flow in arteries during electromagnetic hyperthermia, a therapeutic procedure for cancer treatment. Appl. Math. Mech. Engl. Ed. 31(11), 1405–1420 (2010). doi:10.1007/s10483-010-1371-6
Haik, Y., Pai, V., Chen, C.J.: Development of magnetic device for cell separation. J. Magn. Magn. Mater. 194(1), 254–261 (1999)
Haik, Y., Chen, J.C., Pai, V.M.: Development of biomagnetic fluid dynamics. In: Proceedings of the IX International Symposium on Transport Properties in Thermal Fluid Engineering, Singapore, Pacific Center of Thermal Fluid Engineering, 25–28 June, pp. 121–126 (1996)
Rosensweig, R.E.: Magnetic fluids. Ann. Rev. Fluid Mech. 19, 437–461 (1987)
Tzirtzilakis, E.E.: A mathematical model for blood flow in magnetic field. Phys. Fluids 17(7), 077103 (2005)
Crane, L.J.: Flow past a stretching plate. J. Appl. Math. Phys. (ZAMP) 21, 645–647 (1970)
Anderson, H.I.: An exact solution of the Navier–Stokes equations for magnetohydrodynamics flow. Acta Mech. 113, 241–244 (1995)
Jat, R.N., Chaudhary, S.: Radiation effects on the MHD flow near the stagnation point of a stretching sheet. Z. Angew. Math. Phys. 61, 1151–1154 (2010). doi:10.1007/s00033-010-0072-5
Pop, I., Ishak, A., Aman, F.: Radiation effects on the MHD flow near the stagnation point of a stretching sheet: revisited. Z. Angew. Math. Phys. 62, 953–956 (2011). doi:10.1007/s00033-011-0131-6
Das, S., Chakraborty, S., Jana, R.N., Makinde, O.D.: Entropy analysis of unsteady magneto-nanofluid flow past accelerating stretching sheet with convective boundary condition. Appl. Math. Mech. (Engl. Ed.) 36(12), 1593–1610 (2015). doi:10.1007/s10483-015-2003-6
Dandapat, B.S., Santra, B., Singh, S.K.: Thin film flow over a non-linear stretching sheet in presence of uniform transverse magnetic field. Z. Angew. Math. Phys. 61, 685–695 (2010). doi:10.1007/s00033-010-0074-3
Misra, J.C., Shit, G.C., Rath, H.J.: Flow and heat transfer of a MHD viscoelastic fluid in a channel with stretching walls: some applications to haemodynamics. Comput. Fluids 37(1), 1–11 (2008)
Andersson, H.I., Valnes, O.A.: Flow of a heated ferrofluid over a stretching sheet in the presence of a magnetic dipole. Acta Mech. 128(1), 39–47 (1998)
Zeeshan, A., Majeed, A., Ellahi, R.: Effect of magnetic dipole on viscous ferro-fluid past a stretching surface with thermal radiation. J. Mol. Liq. 215, 549–554 (2016)
Tzirtzilakis, E.E., Kafoussias, N.G.: Three dimensional magnetic fluid boundary layer flow over a linearly stretching sheet. J. Heat Transf. 132(1), 1–8 (2010)
Tzirtzilakis, E.E., Kafoussias, N.G.: Biomagnetic fluid flow over a stretching sheet with nonlinear temperature dependent magnetization. Z. Angew. Math. Phys. (ZAMP) 54(4), 551–565 (2003)
Tzirtzilakis, E.E., Tanoudis, G.B.: Numerical study of biomagnetic fluid flow over a stretching sheet with heat transfer. Int. J. Numer. Methods Heat Fluid flow 13(7), 830–848 (2003)
Misra, J.C., Shit, G.C.: Biomagnetic viscoelastic fluid flow over a stretching sheet. Appl. Math. Comput. 210(2), 350–361 (2009)
Kafoussias, N.G., Williams, E.W.: An improved approximation technique to obtain numerical solution of a class of two-point boundary value similarity problems in fluid mechanics. Int. J. Numer. Methods Fluids 17(2), 145–162 (1993)
Tzirtzilakis, E.E., Xenos, M.A.: Biomagnetic fluid flow in a driven cavity. Meccanica 48(1), 187–200 (2013)
Matsuki, H., Yamasawa, K., Murakami, K.: Experimental considerations on a new automatic cooling device using temperature sensitive magnetic fluid. IEEE Trans. Magn. 13(5), 1143–1145 (1977)
Tzirtzilakis, E.E.: A simple numerical methodology for BFD problems using stream function vorticity formulation. Commun. Numer. Methods Eng. 24(8), 683–700 (2008)
Tzirtzilakis, E.E.: Biomagnetic fluid flow in an aneurysm using ferrohydynamics principles. Phys. Fluids 27(6), 061902 (2015)
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Murtaza, M.G., Tzirtzilakis, E.E. & Ferdows, M. Effect of electrical conductivity and magnetization on the biomagnetic fluid flow over a stretching sheet. Z. Angew. Math. Phys. 68, 93 (2017). https://doi.org/10.1007/s00033-017-0839-z
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DOI: https://doi.org/10.1007/s00033-017-0839-z