Magnetohydrodynamic and Ferrohydrodynamic Interactions on the Biomagnetic Flow and Heat Transfer Containing Magnetic Particles Along a Stretched Cylinder
Keywords:BFD, Blood, magnetic particles, stretched cylinder, magnetic dipole, finite difference method.
In this paper, the laminar, incompressible and viscous flow of a biomagnetic fluid containing Fe33O44 magnetic particles, through a two dimensional stretched cylinder is numerically studied in the presence of a magnetic dipole. The extended formulation of Biomagnetic Fluid Dynamics (BFD) which involves the principles of MagnetoHydroDynamic (MHD) and FerroHydroDynamic (FHD) is adopted. The pressure terms are also taken consideration. The physical problem which is described by a coupled system of partial differential equations along with corresponding boundary conditions is converted to a coupled system of nonlinear ordinary differential equations subject to analogous boundary conditions utilizing similarity approach. The numerical solution is obtained by using an efficient technique which is based on a common finite difference method with central differencing, a tridigonal matrix manipulation and an iterative procedure. For verification proposes a comparison with previously published results is also made. The numerous results concerning the axial velocity, temperature, pressure, skin friction coefficient, rate of heat transfer and wall pressure parameter are presented for various values of the parameters. The axial velocity is decreased as the ferromagnetic number increases, temperature is enhanced with increasing values of the magnetic parameter.
Stark, D.D., Weissleder, R., Elizondo, G., Hahn, P.F., Saini, S., Todd, L.E., Wittenberg, J. and Ferucci, J.T. (1988). Superparamagnetic iron oxide: clinical application as a contrast for MR imaging of the liver, Radiology, 168: 297–301.
Lu, J., Ma, S., Sun, J., Xia, C., Liu, C., Wang, Z. (2009). Magnetese ferrite nanoparticle micellarnanocomposites as MRI contrast agent for liver imaging, Biomaterials, 30:2919–2928.
Suzuki, M., Honda, H., Kobayashi, T., Wakabayashi, T., Yoshida, J., and Takahashi, M. (1997). Development of a target directed magnetic resonance contrast agent using monoclonal antibody-conjugated magnetic particles, Brain Tumor Pathol, 13: 127–132.
Durr, S., Janko, C., Lyer, S., Tripal, p., Schwarz, M., Zaloga, J., Toetze, R. and Alexiou, C. (2013). Magnetic nanoparticles for cancer therapy. Nanotechnol Rev. 2(4): 395–409.
Jordan, A., Scholz, R., Wust, P., Fahling, H. and Felix, R. (1999). Magnetic fluid hyperthermia(MCFH): Cancer treatment with AC magnetic field induced excitation of biocompatible superparamagnetic nanoparticles, J. Magn. Magn. Mater., 201: 413–9.
Mah, C., Zolotukhin, I., Fraites, T.J., Dobson, J., Batich, C. and Byrne, B.J. (2000). Micro-sphere mediated delivery of recombinant: AAV vectors in vitro and in vivo. Mol Therapy, 1:S239.
Panatarotto, D., Prtidos, C.D., Hoebeke, J., Brown, F., Karmer, E., Briand, J.P., Muller, S., Prato, M. and Bianco, A. (2003). Immunization with peptide-functionalized carbon nanotubes enhances virus-specific neutralizing antibody responses. Chemistry & Biology, 10: 961–966.
Joubert, J.C. and Quim, A.N. (1997). Magnetic microcomposites as vectors for bioactive agents, The state of Art. Intd. Ed.: 93S70.
Goodwin, S. (2000). Magnetic targeted carries offer site-specific drug delivery. Oncol News Int, 9:22
Dubertret, B., Skourides, P., Norris, D.J., Noireaux, V., Brivanlou, A.H. (2002). In vivo imaging of quantum dots encapsulated in phospholipids micelles, Science, 298(5599): 1759–1762.
Gao, X.H., Cui, Y.Y., Levenson, R.M., Chung, L.W.K. and Nie, S.M. (2004). In vivo cancer targeting and imaging with semiconductor quantum dots. Nat Biotechnol, 22(8): 969–976.
Haik,Y., Chen, J.C., Pai, V.M. (1996). Development of bio-magnetic fluid dynamics, in: S.H. Winoto, Y.T. Chew, N.E. Wijeysundera (Eds.),Proceedings of the IX International Symposium on Transport Properties in Thermal Fluids Engineering, Singapore, Pacific Center of Thermal Fluid Engineering, Hawaii, USA, 121–126.
Tzirtzilakis, E.E. (2005). A mathematical model for blood flow in magnetic field, Phys. Fluids,17(7): 077103-1–14.
Murtaza, M.G., Tzirtzilakis, E.E. and Ferdows, M. (2017). Effect of electrical conductivity and magnetization on the biomagnetic fluid flow over a stretching sheet, Zeitschrift fur angewandteMathematik und Physik, 68: 93.
Misra, J.C. and Shit G.C. (2009). Biomagnetic viscoelastic fluid flow over a stretching sheet, Appl. Math. Comput., 210: 350.
Murtaza, M.G., Ferdows, M., Tzirtzilakis, E.E. (2020). Stability and convergence analysis of a biomagnetic fluid flow over a stretching sheet in the presence of a magnetic field, Symmetry, 12:253.
Murtaza, M.G., Ferdows, M., Tzirtzilakis, E.E., Misra, J.C. (2019). Three dimensional biomagnetic Maxwell fluid flow over a stretching surface in presence of heat source/sink, Internation Journal of Biomathematics, 12(3):12.
Misra, J.C. and Shit G.C. (2009). Flow of a biomagnetic viscoelastic fluid in a channel with stretching walls, Journal of Applied Mechanics Trans. ASME, 76, 06106: 1–9.
Tzirtzilakis, E.E. and Kafoussias, N. G. (2003). Biomagnetic fluid flow over a stretching sheet with nonlinear temperature dependent magnetization, Z. Angew. Math. Phys (ZAMP), 8:54–65.
Tzirtzilakis, E.E., Xenos, M., Loukopoulos., V.C., Kafoussias, N.G. (2006). Turbulent biomagnetic fluid flow in a rectangular channel under the action of a localized magnetic field, International Journal of Engineering Science, 44(18–19), 1205–1224.
Choi, SUS. (1995). Enhancing thermal conductivity of fluids with nanoparticles, in Proceedings of the ASME International Mechanical Engineering Congress and Exposition, San Francisco, CA, USA, 99–105.
Misra, S. and Kamatam G. (2020). Effect of magnetic field, heat generation and absorption on nanofluid flow over a nonlinear stretching sheet, Journal of Nanotechnology, 11: 976–990.
Neuringer, J.L. (1996). Some viscous flows of a saturated ferrofluid under the combined the influence of thermal and magnetic field gradients, Int. J. of Non-linear Mech., 1(2): 123–137.
Elsayed, M. and Abd-Elaziz Mohamed, I.A. (2019). Effect of Thomson and thermal loading to laser pulse in a magneto-thermo elastic porous medium with energy dissipation, Z. Angew Math Mech (ZAMM), 99, e201900079.
Sheikholeslami, M. and Ellahi, R. (2015). Electrohydrodynamicnanofluid hydrothermal treatment in an enclosure with sinusoidal upper wall, Appl. Sci., 5: 294–306.
Rashidi, M.M. and Abelman, S. and FreidooniMehr, N. (2013). Entropy generation in steady MHD flow due to rotating porous disk in a nanofluid, Int. J. Heat and mass Transfer, 62: 515–525.
Ishak, A. and Nazar, R. (2009). Laminar boundary flow along a stretching cylinder, Eur. J. Sci. Res., 36(1):22–29.
Bachok, N. and Ishak, A. (2010). Flow and heat transfer over a stretching cylinder with prescribed heat flux, Malyasian Journal of Mathematical Sciences, 4: 159–169.
Mukhopadhyay, S. (2013). MHD boundary layer slip flow along a stretching cylinder, Ain Shams Eng. J., 4: 317–324.
Qasim, M., Khan, Z.H., Khan, W.A. and Ali shah I. (2014). MHD boundary layer slip flow and heat transfer of ferrofluid along a stretching cylinder with prescribed heat flux, PLos One, 9(1):e83930.
Nadeem, S., Ullah, N., Khan, A.U. and Akbar, T. (2017). Effect of homogeneous-heterogeneous reactions on ferrofluid in the presence of magnetic dipole along a stretching cylinder, Results in Physics, 7: 3574–3582.
Tahir, H., Khan, U., Din, A., Chu, Y.U. and Muhammad, N. (2020). Heat transfer in a ferromagnetic chemically reactive species, Journal of Thermophysics and Heat Transfer, doi: 10.2514/1.T6143.
Tzirtzilakis, E.E. (2015). Biomagnetic fluid flow in an aneurysm using ferrohydrodynamics principles, Physics Fluids, 27:061902.
Reddy, S.R.R., Reddy, P.B.A. (2018). Biomathematical analysis for the stagnation point flow over a nonlinear stretching surface with the second order velocity slip and Titanium alloy nanoparticle, Front. Heat Mass Transfer, 12.
Tzirtzilakis, E.E. and Xenos, M.A. (2013). Biomagnetic fluid flow in a driven cavity, Meccanica, 48:187.
Aziz, A., Jamshed, W., Ali, Y. and Shams, M. (2020). Heat transfer and entropy analysis of Maxwell Hybrid nanofluid including effects of inclined magnetic field joule heating and thermal radiation, Discrete and Continous Dynamical Systems series S, 13(10): 2667–2690.
Liqat, A., Xiaomin, L., Bagh, A., Saima, M. and Sohaib, A. (2019). Finite element simulation of multi-slip effects on unsteady MHD bioconvectivemicropolarnanofluid flow over a sheet with solutal and thermal convective boundary conditions, Coatings, 9:842.
Tzirtzilakis, E.E. and Tanoudis, G.B. (2003). Numerical study of biomagnetic fluid flow over a stretching sheet with heat transfer, Int. J. of Numerical Methods for Heat and Fluid Flow, 13: 830.
Kuttan, B.A., Manjunathan, B., Jayanthi, B. and Gireesha, B.J. (2020). Performance of four different nanoparticles in boundary layer flow over a stretching sheet in porous medium driven by buoyancy force, Int. J. of Applied Mechanics and Engineering, 25(2): 1–10.
Kafoussias, N.G. and Williams, E.W. (1993). An improved approximation technique to obtain numerical solution of a class of two point boundary value similarity problems in fluid mechanics, International Journal for Numerical Methods in Fluids, 17: 145–162.
Tzirtzilakis, E.E., Loukopoulos., V.C. (2005). Biofluid flow in a channel under the action of a uniform localized magnetic field, Comput Mech., 36:360–374.