Non-Similar Analysis of Mixed Convection Biomagnetic Boundary Layer Flow Over a Vertical Plate with Magnetization and Localized Heating/Cooling

Authors

  • Rayhan Prodhan 1) Research group of Fluid Flow Modeling and Simulation, Department of Applied Mathematics University of Dhaka, Dhaka-1000, Bangladesh 5) Department of Mathematics, Jashore University of Science and Technology, Jashore-7408, Bangladesh
  • Mohammad Ferdows Research group of Fluid Flow Modeling and Simulation, Department of Applied Mathematics University of Dhaka, Dhaka-1000, Bangladesh
  • J. C. Misra Centre for Theoretical Studies, Indian Institute of Technology, Kharagpur-721302, India
  • Efstratios Tzirtzilakis Fluid Mechanics & Turbomachinery Laboratory, Department of Mechanical Engineering, University of the Peloponnese, Patras, Greece
  • M. G. Murtaza Department of Mathematics, Comilla University, Cumilla 3506, Bangladesh

DOI:

https://doi.org/10.13052/ejcm2642-2085.3321

Keywords:

Magnetization, dipole, convective flow, variability, numerical model

Abstract

Theoretical and numerical investigation of an applied magnetic field on mixed convection flow of a biofluid through a vertical plate using contained heating or cooling is observed in this study. The mathematical formulation is that of the full Biomagnetic Fluid Dynamics (BFD) model which deals with on the ferrohydrodynamics (FHD) and magnetohydrodynamics (MHD) principle. In this work, the study is performed on a specific biofluid, viz. human blood. Assume that the magnetization very linearly with magnetic field strength, temperature dependency of dynamic viscosity and thermal conductivity is noticed. A system of non-linear equations with appropriate boundary condition is obtained by familiarizing suitable non-dimensional variables in the physical problem. For the numerical solution, we used finite difference method which is based on an efficient technique is applied in the problem. Computations for flow profiles, local skin friction coefficient and local heat transfer coefficient are performed with the magnetic parameter Mn, the viscosity/temperature parameter θr and the thermal/conductivity parameter S∗. The effect of the localized heating or cooling is examined. The computational results presented graphically and have been validated in an appropriate manner. The study reveals that the impact of a magnetic field for blood flow in arteries is found significantly. The results presented bear the promise of valuable applications in physiology, medicine and bioengineering.

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Author Biographies

Rayhan Prodhan, 1) Research group of Fluid Flow Modeling and Simulation, Department of Applied Mathematics University of Dhaka, Dhaka-1000, Bangladesh 5) Department of Mathematics, Jashore University of Science and Technology, Jashore-7408, Bangladesh

Rayhan Prodhan got the bachelor’s degree in Mathematics from University of Dhaka in 2016 and the Master’s degree in Applied Mathematics from University of Dhaka in 2017. Since 2021, he has been working as a Lecturer at the Department of Mathematics, Faculty of Science, Jashore University of Science and Technology, Jashore-7408. His research focuses on the modeling, analysis and implementation of numerical simulation of fluid flow problems, and analysis their appropriate applications.

Mohammad Ferdows, Research group of Fluid Flow Modeling and Simulation, Department of Applied Mathematics University of Dhaka, Dhaka-1000, Bangladesh

Mohammad Ferdows received his Ph.D. degrees from the Department of Mechanical Engineering, Tokyo Metropolitan University, Japan. He worked as a Postdoctoral Research Associate at several Institute/University and also worked as Professor and Visiting Professor in Louisiana Tech University, King Abdulaziz University, King Abdullah University of Science and Technology. Currently he is working as Professor at the Department of Applied Mathematics, University of Dhaka, Bangladesh. His research interests are in fluid mechanics, transport phenomena and biomedical flow phenomena.

J. C. Misra, Centre for Theoretical Studies, Indian Institute of Technology, Kharagpur-721302, India

J. C. Misra received his D.Sc. in Mathematics from Calcutta University, India. He mainly focuses on Mechanics, Pressure gradient, Flow, Magnetohydrodynamics and Thermodynamics. His Mechanics research incorporates elements of Numerical analysis and Peristalsis. The various areas that he examines in his Peristalsis study include Wave propagation, Non-Newtonian fluid and Transport phenomena. His biological study spans a wide range of topics, including Critical ionization velocity, Porosity and Darcy number. J. C. Misra interconnects Volumetric flow rate and Shear stress in the investigation of issues within Flow. His Newtonian fluid research incorporates themes from Theoretical physics and Blood flow.

Efstratios Tzirtzilakis, Fluid Mechanics & Turbomachinery Laboratory, Department of Mechanical Engineering, University of the Peloponnese, Patras, Greece

Efstratios Tzirtzilakis is professor at the Department of Mechanical Engineering, University of the Peloponnese, Greece. He has a degree in Mathematics, an MSc in Applied Mathematics, and a PhD in Biomagnetic Fluid Dynamics (BFD). His research field lies in Computational Fluid Mechanics.

M. G. Murtaza, Department of Mathematics, Comilla University, Cumilla 3506, Bangladesh

M. G. Murtaza received the bachelor’s degree in Mathematics from University of Dhaka in 2006, the master’s degree in Applied Mathematics from University of Dhaka in 2008, and the philosophy of doctorate degree (Ph.D.) in Applied Mathematics from University of Dhaka in 2020. Since 2020, he has been working as an Associate professor at the Department of Mathematics, Faculty of Science, Comilla University, Cumilla-3506, Bangladesh. His research focuses on the modeling, analysis and implementation of numerical simulation of fluid flow problems with Blood flow, and analysis their appropriate applications.

References

Alimohamadi, H., and Sadeghy, K. (2015). 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.

Misra, J. C., Sinha, A., and Shit, G. C. (2010). Flow of a biomagnetic viscoelastic fluid; application to estimate of blood flow in arteries during electromagnetic hyperthermia, a therapeutic procedure for cancer treatment. Applied Mathematics in Mechanical Engineering, 31(11), 1405–1420.

Haik, Y., Pai, V., and Chen, C. J. (1999). Development of magnetic device for cell separation. Journal of Magnetism and Magnetic Materials, 194(1–3), 254–261.

Higashi, T., Yamagishi, A., Takeuchi, T., Kawaguchi, N., Sagawa, S., Onishi, S., et al. (1993). Orientation of erythrocytes in a strong static magnetic field. Blood, 82(4), 1328–1334.

Gasparovic, C., and Matweiyoff, N. A. (1992). The magnetic properties and water dynamics of the red blood cell. Magnetic Resonance in Medicine, 26(2), 274–299.

Higashi, T., Ashida, N., and Takeuchi, T. (1997). Orientation of blood cells in static magnetic field. Physica B: Condensed Matter, 237, 616–620.

Pauling, L., and Coryell, C. D. (1936). The magnetic properties and structure of hemoglobin, oxyhemoglobin and carbonmonoxy hemoglobin. Proceedings of the National Academy of Science of the United States of America, 22(4), 210–216.

Motta, M., Haik, Y., Gandhari, A., and Chen, C. J. (1998). High magnetic field effects on human deoxygenated hemoglobin light absorption. Bioelectrochemistry and Bioenergetics, 47(2), 297–300.

Alam, J., Murtaza, M. G., Tzirtzilakis, E. E., and Ferdows, M. (2022). Mixed convection flow and heat transfer of Biomagnetic fluid with magnetic/non-magnetic particles due to a stretched cylinder in the presence of a magnetic dipole. Proceedings of International Exchange and Innovation Conference on Engineering & Sciences (IEICES), 8, 76–83.

Ruuge, E. K., and Rusetski, A. N. (1993). Magnetic fluids as drug carriers: targeted transport of drugs by a magnetic field. Journal of Magnetism and Magnetic Materials, 122(1–3), 335–339.

Lauva, M., and Plavins, J. (1993). Study of colloidal magnetic binding erythrocytes: prospects for cell separation. Journal of Magnetism and Magnetic Materials, 122, 349–353.

Haik, Y., Pai, V., and Chen, C. J. (1999). Biomagnetic fluid dynamics. Cambridge University Press, 439–452.

Haik, Y., Chen, J. C., and Pai, V. M. (1996, June 25–28). 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, pp. 121–126.

Rosensweig, R. E. (1987). Magnetic fluids. Annual Review of Fluid Mechanics, 19, 437–461.

Tzirtzilakis, E. E. (2006, July 10–14). A mathematical model for blood flow in magnetic field. International Symposium on Trends in Applications of Mathematics to Mechanics (STAMM 2006), Vienna, Austria.

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. Journal of Applied Mathematics and Physics, 68, 93.

Ferdows, M., Alam, J., Murtaza, G., Tzirtzilakis, E. E., and Sun, S. (2022). Biomagnetic flow with CoFe2

O4

magnetic particles through an unsteady stretching/shrinking cylinder. Magnetochemistry, 8, 27.

Kafoussias, N. G., and Williams, E. W. (1999). 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 Fluid, 17(2), 145–162.

Tzirtzilakis, E. E., and Kafoussias, N. G. (2003). Biomagnetic fluid flow over a stretching sheet with nonlinear temperature dependent magnetization. Zeitschriftfur Angewandte Mathematik and Physik, 54(4), 551–565.

Tzirtzilakis, E. E., Xenos, M., Loukopoulos, V. C., and 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.

Fukada, E., and Kaibara, M. (1980). Viscoelastic study of aggregation of red blood cells. Biorheology, 17(1–2), 177–182.

Kafoussias, N. G., Raptis, A., and Tzirtzilakis, E. E. (2008). Free-forced convective boundary layer flow of a biomagnetic fluid under the action of a localized magnetic field. Canadian J. of Physics, 86, 447–457.

Stoltz, J. F., and Lucius, M. (1981). Viscoelasticity and thixotropy of human blood. Biorheology, 18(3–6), 453–473.

Thurston, G. B. (1972). Viscoelasticity of human blood. Biophysical Journal, 12(9), 1205–1217.

Tzirtzilakis, E. E., Kafoussias, N. G., and Raptis, A. (2010). Numerical study of forced and free convective boundary layer flow of a magnetic fluid over a flat plate under the action of alocalized magnetic field. ZAMP, 929–947.

Murtaza, M. G., Tzirtzilakis, E. E., and Ferdows, M. (2018). Numerical solution of three dimensional unsteady biomagnetic flow and heat transfer through stretching/shrinking sheet using temperature dependent magnetization. Archives of Mechanics, 70(2), 161–185.

Merkin, J. H., and Mahmood, T. (1989). Mixed convection boundary layer similarity solution. Prescribed wall heat flux. ZAMP, 40, 61–68.

Chamkha, A. J., Takhar, H. S., and Nath, G. (2004). Mixed convection flow over a vertical plate with localized heating (cooling), magnetic field and suction (injection). Heat and Mass Transfer, 40, 835–841.

Loukopoulos, V. C., and Tzirtzilakis, E. E. (2004). Biomagnetic channel flow in spatially varying magnetic field. International Journal of Engineering Science, 42, 571–590.

Alam, J., Murtaza, M. G., Tzirtzilakis, E. E., and Ferdows, M. (2022). Application of Biomagnetic fluid dynamics modelling for simulation of flow with magnetic particles and variable fluid property over a stretching cylinder. Mathematics and Computers in Simulation, 199, 438–462.

Gnaneswara, R., Ahmed, M., and Abbas, W. (2021). Modeling of MHD fluid flow over an unsteady stretching sheet with thermal radiation, variable fluid properties and heat flux. Math. Comput. Simulat., 185, 583–593.

Ashraf, M., Abbas, A., Zia, S., Chu, Y., and Khan, I. (2020). Computational analysis of the effect of nanoparticle material motion on mixed convection flow in the presence of heat generation and absorption. Computers, Materials & Continua, 65, 1809–1823.

Reddy, Y. D., and Goud, B. S. (2022). Comprehensive analysis of thermal radiation impact on an unsteady MHD nanofluid flow across an infinite vertical flat plate with ramped temperature with heat consumption. Results in Engineering, 17, 100796.

Annord Mwapinga. (2012). Computational modeling of arterial blood flow in the presence of body exercise. University of Dar es Salaam.

Harjeet Kumar, Chandel, R. S., Sanjeev Kumar, and Sanjeet Kumar. (2013). A mathematical model for blood flow through a narrow catheterized artery. International Journal of Theoretical & Applied Sciences, 5(2), 101–108.

Voltairas, P. A., Fotiadis, D. I., and Michalis, L. K. (2002). Hydrodynamics of magnetic drug targeting. Journal of Biomechanics, 35(6), 813–821.

Anderson, H. I., and Valnes, O. A. (1998). Flow of a heated ferrofluid over a stretching sheet in the presence of a magnetic dipole. Acta Mechanica, 128(1–2), 39–47.

Misra, J. C., Shit, G. C., and Rath, H. J. (2008). Flow and heat transfer of an MHD viscoelastic fluid in a channel with stretching walls: some applications to hemodynamics. Computers and fluids, 37, 1–11.

Tzirtzilakis, E. E. (2008). Biomagnetic fluid flow in a channel with stenosis. Physica D: Nonlinear Phenomenna, 237(1), 66–81.

Tzirtzilakis, E. E. (2015). Biomagnetic fluid flow in an aneurysm using ferrohydrodynamics principles. Physics of Fluids, 27, 061902.

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Published

2024-07-06

How to Cite

Prodhan, R., Ferdows, M., Misra, J. C., Tzirtzilakis, E., & Murtaza, M. G. (2024). Non-Similar Analysis of Mixed Convection Biomagnetic Boundary Layer Flow Over a Vertical Plate with Magnetization and Localized Heating/Cooling. European Journal of Computational Mechanics, 33(02), 91–120. https://doi.org/10.13052/ejcm2642-2085.3321

Issue

2024: Vol 33 Iss 2

Section

Original Article