Biomagnetic Fluid Flow on a Nonlinearly Stretching Sheet with Variable Thickness in a Magnetic Environment
PDF

Keywords

Ferrofluid
Magnetization
Stretching sheet
Biomagnetic fluid
Variable thickness

How to Cite

Murtaza, M. G., Misra, J. C., Tzirtzilakis, E. E., & Ferdows, M. (2023). Biomagnetic Fluid Flow on a Nonlinearly Stretching Sheet with Variable Thickness in a Magnetic Environment. Journal of Advances in Applied & Computational Mathematics, 10, 163–177. https://doi.org/10.15377/2409-5761.2023.10.14

Abstract

The main contribution of the current work is a numerical and mathematical investigation of the effects of magnetic dipole and electrical conductivity on the heat and flow transfer of biomagnetic fluid over a non-linear stretched sheet with variable thickness. Static magnetic fields are produced by magnetic dipoles, which are used in medical a pplications such as MRI, drug administration, and cancer therapy. Additionally, the impact of non-linear heat source/sink features was examined in the study, leading to an interesting phenomenon. The PDEs are attenuated to nonlinear ODEs with dealing appropriate similarity variables. These resultant ODEs are computed by developing an effective method emerged on the application of the finite differences technique. In the end, this section offers a summary of the implications resulting from different physical limitations on blood flow, including variable thickness and power index effects. It was discovered that the rise in Kelvin and Lorentz forces in the boundary layer significantly affected blood flow. The current findings for the biomagnetic fluid model are novel and inventive since they effectively expand upon the issues previously addressed by previously published scientific documentation.

https://doi.org/10.15377/2409-5761.2023.10.14
PDF

References

Haik Y, Pai V, Chen CJ. Development of magnetic device for cell separation. J Magn Magn Mater. 1999; 194: 254-61. https://doi.org/10.1016/S0304-8853(98)00559-9

Voltaira PA, Fotiadis DI, Michalis LK. Hydrodynamics of magnetic drug targeting. J Biomech. 2002; 35: 813-21. https://doi.org/10.1016/S0021-9290(02)00034-9

Ruuge EK, Rusetski AN. Magnetic fluid as drug carries: targeted transport of drugs by a magnetic field. J Magn Magn Mater. 1993; 122: 335-9. https://doi.org/10.1016/0304-8853(93)91104-F

Misra JC, Shit GC. Flow of a biomagnetic viscoelastic fluid in a channel with stretching walls. J Appl Mech. 2009; 76: 1-9. https://doi.org/10.1115/1.3130448

Misra JC, Shit GC. Biomagnetic viscoelastic fluid flow over a stretching sheet. Appl Math Comput. 2009; 210: 350-61. https://doi.org/10.1016/j.amc.2008.12.088

Misra JC, Sinha A, Shit GC. Flow of a biomagnetic viscoelastic fluid: application to estimation of blood flow in arteries during electromagnetic hyperthermia, a therapeutic procedure for cancer treatment. Appl Math Mech. 2011; 13: 1405-20. https://doi.org/10.1007/s10483-010-1371-6

Andersson HI, Valnes OA. Flow of a heated ferrofluid over a stretching sheet in the presence of a magnetic dipole. Acta Mechanica. 1998; 128: 39-47. https://doi.org/10.1007/BF01463158

Tzirtzilakis EE, Kafoussias NG. Biomagnetic fluid flow over a stretching sheet with nonlinear temperature dependent magnetization. Z Angew Math Phys. 2003; 54: 551-65. https://doi.org/10.1007/s00033-003-1100-5

Tzirtzilakis EE, Tanoudis GB. Numerical study of biomagnetic fluid flow over a stretching sheet with heat transfer. Int J Num Methods Heat Fluid Flow. 2003; 13: 830-48. https://doi.org/10.1108/09615530310502055

Higashi T, Yamagishi A, Takeuchi T, Kawaguchi N, Sagawa S, Onishi S, et al. Orientation of erythrocytes in a strong static magnetic field. J Blood. 1993; 82: 1328. https://doi.org/10.1182/blood.V82.4.1328.1328

Haik Y, Pai V, Chen CJ. Biomagnetic fluid dynamics, In: Shyy W, Narayanan R, Eds., Fluid dynamics at interfaces. Cambridge University Press; 1999, pp. 439-52.

Rosensweig RE. Magnetic fluids. Ann Rev Fluid Mech. 1987; 19: 437-61. https://doi.org/10.1146/annurev.fl.19.010187.002253

Rosensweig RE. Ferrohydrodynamics. Cambridge University Press; 1985.

Bashtovoy VG, Berkovsky BM, Vislovich AN. Introduction to Thermomechanics of magnetic fluids. Heidelberg: Spinger-Verlag, Berlin; 1988.

Tzirtzilakis EE. A Mathematical model for blood flow in magnetic field. Phys Fluids. 2005; 17: 077103-1-14. https://doi.org/10.1063/1.1978807

Ramamurthy G, Shanker B. Magnetohydrodynamic effects on blood flow through porous channel. Med Biol Eng Comput. 1994; 32: 655-9. https://doi.org/10.1007/BF02524242

Rusli N, Beng Hong A, Kasima EH, Yassin AYM, Amin N. Numerical computation of a two-dimensional biomagnetic channel flow. Int J Mod Phys. 2012; 9: 178-92. https://doi.org/10.1142/S2010194512005247

Tzirtzilakis EE, Xenos M, Loukopolos VC, Kafoussias NG. Turbulent biomagnetic fluid flow in a rectangular channel under the action of localized magnetic field. Int J Eng Sci. 2006; 44: 1205-24. https://doi.org/10.1016/j.ijengsci.2006.07.005

Misra JC, Sinha A. Effect of thermal radiation on MHD flow of blood and heat transfer in a permeable capillary in stretching motion. Heat Mass Transfer. 2013; 9: 617-28. https://doi.org/10.1007/s00231-012-1107-6

Pavlov KB. Magnetohydrodynamic flow of an incompressible viscous fluid caused by deformation of a plane surface. Magnitnaya Gidrodinamika. 1974; 10: 146-8. http://doi.org/10.22364/mhd

Andersson HI. An exact solution of the Navier-Stokes equations for magnetohydrodynamic flow. Acta Mechanica. 1995; 113: 241-4. https://doi.org/10.1007/BF01212646

Andersson HI. Slip flow past a stretching surface. Acta Mechanica. 2002; 158: 121-5. https://doi.org/10.1007/BF01463174

Loke YY, Merkin JH, Pop I. MHD oblique stagnation point flow towards a stretching / shrinking surface. Mechanica. 2015; 50: 2949-61. https://doi.org/10.1007/s11012-015-0188-y

Dulal P, Gopinath M. MHD convective stagnation point flow of nanofluids over a non-isothermal stretching sheet with induced magnetic field. Mechanica. 2015; 50: 2023-35.

Ishak A, Nazar R, Pop I. Mixed convection boundary layers in the stagnation point flow towards a stretching vertical sheet. Meccanica. 2006; 41: 509-18. https://doi.org/10.1007/s11012-006-0009-4

Ishak A, Jafar K, Nazar R, Pop I. MHD stagnation point flow towards a stretching sheet. Physica A. 2009; 388: 3377-83. https://doi.org/10.1016/j.physa.2009.05.026

Ishak A, Bachok N, Nazar R, Pop I. MHD mixed convection flow near the stragnation point on a vertical permeable surface. Physica A. 2010; 389: 40-6. https://doi.org/10.1016/j.physa.2009.09.008

Andersson HI. MDH flow of a viscoelastic fluid past a stretching surface. Acta Mechanica. 1992; 95: 227-30. https://doi.org/10.1007/BF01170814

El-Mistikawy MA. MHD flow due to a linearly stretching sheet with induced magnetic field. Acta Mechanica. 2016; 227: 3049-53. https://doi.org/10.1007/s00707-016-1643-0

Ali FM, Nazar R, Arifin NM, Pop I. MHD boundary layer flow and heat transfer over a stretching sheet with induced magnetic field. Heat Mass Transfer. 2011; 47: 155- 62. https://doi.org/10.1007/s00231-010-0693-4

Ali FM, Nazar R, Arifin NM, Pop I. MHD mixed convective boundary layer flow towards a stagnation point flow on a vertical surface with induced magnetic field. ASME J Heat Transfer. 2011; 133: 022502-1. https://doi.org/10.1115/1.4002602

Pop I, TY Na. A note on MHD flow over a stretching permeable surface. Mech Res Comm. 1998; 25: 263-9. https://doi.org/10.1016/S0093-6413(98)00037-8

Devi SPA, Thiyagarajan M. Steady nonlinear hydromag- netic flow and heat transfer over a stretching surface of variable temperature. Heat Mass Transfer. 2006; 42: 671-7. https://doi.org/10.1007/s00231-005-0640-y

Fang T, Zhang J, Zhong Y. Boundary layer flow over a stretching sheet with variable thickness. Appl Math Comput. 2012; 218: 7241-52. https://doi.org/10.1016/j.amc.2011.12.094

Lee LL. Boundary layer over a thin needle. Phys Fluid. 1967; 10: 822-8. https://doi.org/10.1063/1.1762194

Ishak A, Nazar R, Pop I. Boundary layer flow over a continuously moving thin needle in a parallel free stream. Chinese Phys Lett. 2007; 24: 2895-7. https://doi.org/10.1088/0256-307X/24/10/051

Khader MM, Megahed AM. Approximate solutions for the flow and heat transfer due to a stretching sheet embedded in a porous medium with variable thickness, variable thermal conductivity and thermal radiation using Laguerre collocation method. Appl Appl Math. 2015; 10: 817-34.

Prasad KV, Vajravelu K, Hanumesh V. MHD casson nanofluid flow and heat transfer at a stretching sheet with variable thickness. J Nanofluids. 2016; 5: 1-13. https://doi.org/10.1166/jon.2016.1228

Vajravelu K, Ronald L, Dewasurendra M, Prasad KV. Mixed convective boundary layer MHD flow along a vertical elastic sheet. Int J Appl Comput Math. 2017; 3: 2501-18. https://doi.org/10.1007/s40819-016-0252-x

Rashed AS, Mabrouk SM, Wazwaz AM. Unsteady three-dimensional laminar flow over a submerged plate in electrically conducting fluid with applied magnetic field. Waves Random Complex Media. 2023; 33: 505-24. https://doi.org/10.1080/17455030.2021.1883147

Rashed AS, Mahmoud TA, Kassem MM. Behavior of nanofluid with variable brownian and thermal diffusion coefficients adjacent to a moving vertical plate. J Appl Comput Mech. 2021; 7: 1466-79. https://doi.org/10.22055/JACM.2021.34852.2483

Rashed AS, Mahmoud TA, Kassem MM. Analysis of homogeneous steady state nanofluid surrounding cylindrical solid pipes. Egypt Int J Eng Sci Tchnol. 2020; 31: 71-82. https://doi.org/10.21608/EIJEST.2020.38518.1003

Rashed AS, Nasr EH, Kassem MM. Boundary Layer Analysis Adjacent to Moving Heated Plate Inside Electrically Conducting Fluid with Heat Source/Sink. Int J Heat Technol. 2020; 38: 682-8. https://doi.org/10.18280/ijht.380312

Qi X, Zhang H, Sun X, Wang Z. Numerical investigation on flow-field characteristics towards removal of free-water by a separator with coalescing plates. J Adv App Comput Math. 2023; 10: 1-17. https://doi.org/10.15377/2409-5761.2023.10.1

Wang Z, Qi X, Zhuang Y, Wang Q, Sun X. Effect of flow field and electric field coupling on oil–water emulsion separation. Desalin Water Treat. 2023; 283: 79-6.

Tzirtzilakis EE, Xenos MA. Biomagnetic fluid flow in a driven cavity. Meccanica. 2013; 48: 187-200. https://doi.org/10.1007/s11012-012-9593-7

Abel MS, Mahesha N. Heat transfer in MHD viscoelastic fluid flow over a stretching sheet with variable thermal conductivity, non-uniform heat source and radiation. Appl Math Model. 2008; 32: 1965-83. https://doi.org/10.1016/j.apm.2007.06.038

Raju CSK, Sandeep N, Babu MJ, Sugunamma V. Dual solution for three dimensional MHD flow of a nanofluid over a nonlinearly permeable stretching sheet. Alexandria Eng J. 2016; 55: 151-62. https://doi.org/10.1016/j.aej.2015.12.017

Abel MS, Siddheshwar PG, Nandeppanavar MM. Heat transfer in a viscoelastic boundary layer flow over a stretching sheet with viscous dissipation and non-uniform heat source. Int J Heat Mass Transfer. 2007; 50: 960-6. https://doi.org/10.1016/j.ijheatmasstransfer.2006.08.010

Matsuki H, Yamasawa K, Murakami K. Experimental considerations on a new automatic cooling device using temperature sensitive magnetic fluid. IEEE Trans Magn. 1977; 13: 1143-5. 10.1109/TMAG.1977.1059679

Tzirtzilakis EE. Biomagnetic fluid flow in an aneurysm using ferrohydynamics principles. Phys Fluids. 2015; 27: 061902. https://doi.org/10.1063/1.4922757

Tzirtzilakis EE. Biomagnetic fluid flow in a channel with stenosis. Physica D. 2008; 237: 66-81. https://doi.org/10.1016/j.physd.2007.08.006

Kafoussias NG, Williams EW. 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 Fluid. 1993; 17: 145-62. https://doi.org/10.1002/fld.1650170204

Kafoussias NG, Williams EW. Thermal-diffusion and diffusion-thermo effects on mixed free forced convective and mass transfer boundary layer flow with temperature dependent viscosity. Int J Eng Sci. 1995; 33: 1369-84. https://doi.org/10.1016/0020-7225(94)00132-4

Alam J, Murtaza MG, Tzirtzilakis, EE, Ferdows. Parametric simulation of Biomagnetic fluid with magnetic particles over a swirling stretchable cylinder under magnetic field effet. BioNanoSci. 2023; 13: 929-46. https://doi.org/10.1007/s12668-023-01117-x

Ferdows M, Alam J, Murtaza MG, Tzirtzilakis, EE. Effects of magnetic particles diameter and particles spacing on Biomagnetic flow and heat transfer over a linear/non-linear stretched cylinder in the presence of magnetic dipole. J Mech Med Biol. 2023; 23: 2350036. https://doi.org/10.1142/S0219519423500367

Tzirtzilakis EE. A simple numerical methodology for BFD problems using stream function vorticity formulation. Comput Numer Methods Eng. 2008; 24: 683-700. https://doi.org/10.1002/cnm.981

Murtaza MG, Alam J, Tzirtzilakis EE, Ferdows M. Numerical simulation of slip flow and heat transfer of biomagnetic fluid over a stretching sheet in the presence of a magnetic dipole with temperature dependent viscosity. Contemp Math. 2023; 4: 345-59. https://doi.org/10.37256/cm.4220232685

Alam J, Murtaza MG, Tzirtzilakis, EE, Ferdows M. Magnetohydrodynamic and Ferrohydrodynamic interactions on the biomagnetic flow and heat transfer containing magnetic particles along a stretched cylinder. Eur J Comput Mech. 2022; 31:1-40. 10.13052/ejcm2642-2085.3111

Alam J, Murtaza MG, Tzirtzilakis EE, Ferdows M. A parametric simulation of MHD flow and heat transfer of blood-Fe3O4 over an exponentially stretching cylinder. BioNanoSci. 2023; 13: 891-9. https://doi.org/10.1007/s12668-023-01141-x

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Copyright (c) 2023 Md. Ghulam Murtaza, Jagadis C. Misra, Efstratios E. Tzirtzilakis, Mohammad Ferdows